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The beetle tree of life reveals that Coleoptera survived end‐Permian mass extinction to diversify during the Cretaceous terrestrial revolution

Here we present a phylogeny of beetles (Insecta: Coleoptera) based on DNA sequence data from eight nuclear genes, including six single‐copy nuclear protein‐coding genes, for 367 species representing 172 of 183 extant families. Our results refine existing knowledge of relationships among major groups of beetles. Strepsiptera was confirmed as sister to Coleoptera and each of the suborders of Coleoptera was recovered as monophyletic. Interrelationships among the suborders, namely Polyphaga (Adephaga (Archostemata, Myxophaga)), in our study differ from previous studies. Adephaga comprised two clades corresponding to Hydradephaga and Geadephaga. The series and superfamilies of Polyphaga were mostly monophyletic. The traditional Cucujoidea were recovered in three distantly related clades. Lymexyloidea was recovered within Tenebrionoidea. Several of the series and superfamilies of Polyphaga received moderate to maximal clade support in most analyses, for example Buprestoidea, Chrysomeloidea, Coccinelloidea, Cucujiformia, Curculionoidea, Dascilloidea, Elateroidea, Histeroidea and Hydrophiloidea. However, many of the relationships within Polyphaga lacked compatible resolution under maximum‐likelihood and Bayesian inference, and/or lacked consistently strong nodal support. Overall, we recovered slightly younger estimated divergence times than previous studies for most groups of beetles. The ordinal split between Coleoptera and Strepsiptera was estimated to have occurred in the Early Permian. Crown Coleoptera appeared in the Late Permian, and only one or two lineages survived the end‐Permian mass extinction, with stem group representatives of all four suborders appearing by the end of the Triassic. The basal split in Polyphaga was estimated to have occurred in the Triassic, with the stem groups of most series and superfamilies originating during the Triassic or Jurassic. Most extant families of beetles were estimated to have Cretaceous origins. Overall, Coleoptera experienced an increase in diversification rate compared to the rest of Neuropteroidea. Furthermore, 10 family‐level clades, all in suborder Polyphaga, were identified as having experienced significant increases in diversification rate. These include most beetle species with phytophagous habits, but also several groups not typically or primarily associated with plants. Most of these groups originated in the Cretaceous, which is also when a majority of the most species‐rich beetle families first appeared. An additional 12 clades showed evidence for significant decreases in diversification rate. These clades are species‐poor in the Modern fauna, but collectively exhibit diverse trophic habits. The apparent success of beetles, as measured by species numbers, may result from their associations with widespread and diverse substrates – especially plants, but also including fungi, wood and leaf litter – but what facilitated these associations in the first place or has allowed these associations to flourish likely varies within and between lineages. Our results provide a uniquely well‐resolved temporal and phylogenetic framework for studying patterns of innovation and diversification in Coleoptera, and a foundation for further sampling and resolution of the beetle tree of life.


Fig. 1. An adult weevil -Cholus cinctus Schoenherr in the family
Curculionidae -taking flight in lowland tropical rain forest (Heredia Province, Costa Rica). Note the forewings hardened to form elytra, a feature characteristic of the order Coleoptera (beetles). Curculionidae is the second most diverse family of metazoans (surpassed only by the rove beetle family Staphylinidae, which is older) with more than 51 000 named extant species in more than 4600 genera. Conservatively, it is estimated that there are more than 200 000 additional undescribed species of Curculionidae alone (Oberprieler et al., 2007). Photo ©Piotr Naskrecki, used with permission.
Factors responsible for the apparent success of beetles are widely debated. The most trivial factor is the age of beetles; they have had more time to diversify than younger clades. Other factors that could explain the diversity of beetles are high speciation rates and/or low extinction rates, perhaps through mechanisms such as ecological opportunity (Crowson, 1981;Farrell, 1998;Grimaldi & Engel, 2005;Hunt et al., 2007;. Ecological opportunity is proposed to operate by way of entry into new 'adaptive zones', whether through the evolution of 'key innovations' -for example, hardened forewings forming elytra that confer the ability to occupy concealed tight spaces by protecting the folded hindwings (Crowson, 1981;Lawrence & Newton, 1982;Beutel, 1997;Grimaldi & Engel, 2005) or facilitate the invasion of arid or aquatic habitats through elytral covering of the spiracles (Lawrence & Newton, 1982;Beutel, 1996) -or via existing 'pre-adaptations' such as feeding strategies that facilitate exploitation of newly available niches (Leschen, 1993;McKenna & Farrell, 2006;Leschen & Buckley, 2007). Examples include the diversification and rise to dominance of angiosperms (flowering plants) facilitating diversification of angiosperm-associated beetles (e.g. Farrell, 1998;Bernhardt, 2000;). High diversification rates, whether arising from high origination rates, low extinction rates or both, are expected to produce more species over a given period than lineages with lower diversification rates.
Two broadly taxon-sampled molecular timetrees have been produced for beetles: Hunt et al. (2007) is based on data from three genes for 340 species, and  is based on 18S rDNA sequences for 955 species. Both studies recovered relatively little resolution and nodal support at deep nodes; however, their estimates for the timing of the subordinal splits in beetles are very similar, falling in the middle to Late Permian Period. That their age estimates are similar is not surprising because they are based on largely overlapping 18S rRNA datasets. Molecular timetrees focused on individual series or superfamilies of beetles have now been estimated for the superfamilies Chrysomeloidea (Farrell, 1998;Gómez-Zurita et al., 2007), Curculionoidea (Farrell, 1998;, Hydrophiloidea (Bloom et al., 2014), Scarabaeoidea  and Tenebrionoidea (Kergoat et al., 2014a).
Existing large-scale molecular phylogenetic studies of beetles are based on DNA sequence data from nuclear ribosomal genes (28S, 18S) and/or mitochondrial genes (COI, COII, 16S, mitochondrial genomes) (Shull et al., 2001;Vogler, 2005;Hunt et al., 2007;Hunt & Vogler, 2008;Sheffield et al., 2008Sheffield et al., , 2009Song et al., 2010;Bocak et al., 2014). These studies are based on data from four or fewer genes (except for those based on mitochondrial genomes, which are based upon only one linkage group) and typically contain much missing data, resulting in matrices where some combinations of taxa lack overlapping data and phylogenetic signal. Nodal support in the resulting phylogenies is characteristically weak, molecular data sampling in some subgroups of beetles, such as the suborder Archostemata, is typically very limited, and rooting and outgroups are often problematic or little-explored. Nonetheless, these datasets collectively sample a large fraction of extant beetle subfamilies, and some of these studies, perhaps most notably Hunt et al. (2007),  and Bocak et al. (2014), report some of the most densely taxon-sampled phylogenies available for any ordinal-level group of insects (e.g. Bocak et al., 2014, sampled >8000 beetle terminals).
Mitochondrial genomes have been widely used to reconstruct the phylogeny of beetles or suprafamilial groups of beetles (Sheffield et al., 2008(Sheffield et al., , 2009Cameron et al., 2009;Kim et al., 2009;Pons et al., 2010;Song et al., 2010;Timmermans & Vogler, 2012;Haran et al., 2013;Gillett et al., 2014). Although such data have contributed to resolving the internal phylogeny of some subfamilies, families and (to a lesser degree) superfamilies, they usually do not provide definitive results and can be problematic at higher taxonomic levels, for example between suborders, series and superfamilies, due to base-compositional heterogeneity and among-site rate variation (e.g. Song et al., 2010).
To date, no near-comprehensive molecular phylogenetic studies of beetles have included data from nuclear protein-coding (NPC) genes, even though they have been shown to help resolve many problematic relationships in beetles (e.g. Wild & Maddison, 2008;McKenna, 2011aMcKenna, ,2011b. A lack of primers and protocols for amplifying and sequencing these genes across beetles contributed to their relatively infrequent use at higher taxonomic levels prior to the publications of Wild & Maddison (2008) and  which made public many of the primers and protocols established for NPC and other genes as part of the Beetle Tree of Life (BToL) Project. Even so, many NPC genes remain difficult to amplify and/or sequence in certain groups of beetles because of the deep evolutionary divergences in beetles and widely varying evolutionary rates among taxa.
Morphological data have been widely used to reconstruct the phylogeny of beetles (reviewed in the Handbook of Zoology volumes on beetles: e.g. Beutel & Leschen, 2005a;Leschen et al., 2010;Leschen & Beutel, 2014), including the most comprehensive family-group study to date, by Lawrence et al. (2011), which sampled 516 adult and larval characters for 359 beetle taxa plus seven outgroups (OG), including most of the same beetle families and genera as in the present study. Topologies recovered to date from phylogenetic analyses of morphological data differ, often substantially, from those recovered through analyses of molecular data. As for molecular phylogenetic trees of beetles to date, phylogenetic trees of beetles based on morphological data generally lack resolution and nodal support at higher taxonomic levels.
Most higher-level relationships in beetles therefore remain contentious, unresolved or inadequately tested (reviewed in McKenna, 2014). Here we present a study of beetle molecular phylogeny and evolution based on analyses of nuclear DNA sequence data (eight genes, six of which are NPC) with nearly comprehensive family-level sampling. We incorporate exemplars of most (172 of 183) extant families of beetles, including 20 families not included in other such studies to date, and Strepsiptera (twisted-wing parasites), the recently confirmed sister group of beetles (Niehuis et al., 2012;McKenna, 2014;Misof et al., 2014;Peters et al., 2014). Through analyses of these data, we establish working hypotheses for the composition and relationships of the major taxonomic groups of beetles (including comprehensive family-level samples of most supra-ordinal groups of beetles), and present a reconstruction of timing and patterns of beetle macroevolution. Our results provide a foundation for further sampling of beetle taxa and molecular phylogenetic data towards a comprehensive and maximally resolved reconstruction of beetle phylogeny and evolution, and provide much-needed evolutionary context for interpreting observations emerging from comparative studies involving beetles.
Our OG taxon sample included one species from each of the three neuropterid orders [Megaloptera (Sialis Latreille), Neuroptera (Plega Navás) and Raphidioptera (Agulla Handlirsch)], and one species of Strepsiptera (Mengenilla Hofeneder) (Table S1). Neuropterida and Strepsiptera are known near OGs of beetles based on analyses of genomic and transcriptomic data (Niehuis et al., 2012;McKenna, 2014;Misof et al., 2014;Peters et al., 2014). Two relatively more distant OGs were sampled from the order Hymenoptera [Apis Linnaeus (Apidae) and Cephus Latreille (Cephidae)] for a total sample of 373 species. Voucher specimens from which DNA was extracted are deposited at the Harvard University Museum of Comparative Zoology (MCZ) in Cambridge, MA, U.S.A. (most species; subset of OGs and most Polyphaga), or at the Oregon State University Arthropod Collection (OSAC) in Corvallis, OR, U.S.A.

DNA extraction, amplification and sequencing
Specimens for DNA were mostly collected as adults and preserved in 90-100% EtOH. Total genomic DNA was extracted from the thorax, one or more legs, or the entire specimen, by soaking or grinding, using the QIAquick DNeasy Tissue Kit (Qiagen Inc., Alameda, CA, U.S.A.), and otherwise following the kit manufacturer's protocol. Amplification via PCR was typically carried out using one of two protocols. Some samples were amplified in 25-μL reactions containing 11.6 μL HPLC water, 5 μL 5× buffer, 0.2 μL 10 mm dNTPs, 1.5 μL MgCl 2 , 0.2 μL Taq DNA Polymerase (all from Qiagen) and 1 μL of each primer (10 mm); additionally, 5 μL of Q solution (Qiagen) was added to each reaction for 18S and 28S. The remainder were amplified in 25-30-μL reactions using TaKaRa Ex Taq (Clontech) and the basic protocols recommended by the manufacturer. We targeted approximately 9000 bp of double-stranded DNA sequence data for each specimen, exclusive of introns. These data included ∼1350 bp of 28S rDNA, ∼1850 bp of 18S rDNA and parts of six NPC genes: ∼1000 bp of elongation factor-1 (EF1-), ∼475 bp of wingless (WG), ∼2000 bp of carbamoyl-phosphate synthase domain (CAD), ∼725 bp of arginine kinase (AK), ∼900 bp of alpha-spectrin (AS) and ∼650 bp of phosphoenolpyruvate carboxykinase (PEPCK).
28S was amplified using the paired primers ZX1 ( Van der Auwera et al., 1994) and OP2 (Mallat & Sullivan, 1998), yielding a c. 2900-bp product. The first c. 1300 bp comprising the 5 ′ end of this amplification product was sequenced with the primers ZX1 and rd5b (Whiting, 2002). We used the primers ZX1 and rd5b for amplification when the initial primers (ZX1 and OP2) failed. The primers ZR1 (Mallat & Sullivan, 1998), rd4.2b (Whiting, 2002) and rd7b1 (Whiting, 2002) were used for amplification and/or sequencing when the aforementioned primers failed. Typical amplification conditions for 28S included a single incubation at 94 ∘ C for 1 h 30 min, followed by six cycles (each starting with 30 s at 94 ∘ C) at each of the following six annealing temperatures and times (a touchdown profile): 65 ∘ C/63.5 ∘ C/62 ∘ C/60.5 ∘ C/59 ∘ C/57.5 ∘ C for 1 min, 72 ∘ C for 2 h 30 min, with a single extension step of 7 min at 72 ∘ C. 18S and EF1-were amplified using the primers and protocols in . We gel-extracted 28S, 18S and EF1amplification products using the QIAquick Gel Purification Kit (Qiagen). The nuclear protein-coding genes WG, CAD, AK, AS and PEPCK were amplified using the primers and protocols in Wild & Maddison (2008).
Amplification products were purified using shrimp alkaline phosphatase and exonuclease I (GE Healthcare), were gel purified using the QIAquick Gel Purification Kit, or were purified using EdgeBioSystems ExcelaPure PCR purification blocks (by University of Arizona's UAGC facility). We used the ABI PRISM BigDye Terminator Cycle Sequencing Kit, v3.1 (Life Technologies Corp.), and cycle sequencing reactions were sequenced on an ABI PRISM 3730 automated sequencer (Life Technologies) at Harvard University, the University of Arizona UAGC facility, or the University of Tennessee Health Science Center. Nucleotide sequences were assembled and edited using Sequencher v4.7 (Gene Codes), Geneious v5.5 (Biomatters) (Drummond et al., 2012b) or Phred (Green & Ewing, 2002) and Phrap (Green, 1999) as orchestrated by Mesquite's Chromaseq package ) with subsequent modifications by manual inspection. Sequences newly produced for this study are deposited in GenBank (see Table S1).

Nucleotide sequence alignment and masking
18S and 28S were separately aligned using the E-INS-i algorithm in MAFFT v6.8 (default parameters; keeping existing gaps) (Katoh et al., 2002;Katoh & Toh, 2008). The resulting alignments were then manually refined in Mesquite v2.75+ (Maddison & Maddison, 2011) in cases where the alignment algorithm clearly did not find the optimal solution. The program Gblocks v0.91b (Castresana, 2000;Talavera & Castresana, 2007) was used to separately mask the aligned 18S and 28S DNA sequence matrices, thereby reducing the amount of white space in the matrix and improving the signal-to-noise ratio in the 28S and 18S alignments. Analyses were executed separately on 18S and 28S in the command line version of Gblocks using the 'less stringent parameters' (implemented by the Gblocks webserver; minimum number of sequences for a conserved position = 1/2 the number of sequences, minimum number of sequences for a flank position = 1/2 the number of sequences, maximum number of contiguous nonconserved positions = 8, min. length of a block = 5, allowed gap positions = 'with half'). The 18S and 28S characters identified by Gblocks for exclusion were then removed from the matrices.
Nucleotide sequences for the NPC genes AK, AS, CAD, EF1-, PEPCK and WG were first viewed and manually aligned as nucleotides. The alignment of exons was then refined manually by viewing as translated amino acids (AA) in Mesquite. After alignment, incomplete codons were trimmed from the ends of the sequences. In the case of incomplete codons within the sequence, 'N's were added to those containing at least one actual base, leaving only complete codons in the sequence. In the case of incomplete codons composed entirely of 'N's and adjacent to a gap containing 'N's, we converted the 'N's that did not complete a codon to gaps because the number of 'N's that belonged there was sometimes unclear. All missing data was then converted to gaps. The DNA sequence matrices for each of the NPC genes were then translated into AAs in Mesquite and each matrix was aligned using the program Opal v2.0.1 (Wheeler & Kececioglu, 2007) implemented via Mesquite, with the default alignment parameters (gap costs: 60/16/38/36, Blo-sum62 matrix, fast alignment, with polish). Obviously suboptimal alignment regions were manually refined using the matrix editor in Mesquite. The nucleotide sequence matrix was then aligned to the Opal-aligned AAs using Mesquite. Gblocks was used to improve the signal-to-noise ratio and reduce the amount of white space in the matrix (using the same 'less stringent parameters' as were applied to 18S and 28S; see above). The regions identified by Gblocks for exclusion (masking) were removed, leaving only the aligned, final nucleotides. The regions identified for exclusion (masking) by Gblocks in the AA alignments were also removed, leaving only the aligned, final AAs. Uncertainties and polymorphisms in the AA matrices were converted to missing. The files output by Gblocks after processing each matrix are available as supporting information (File S1).

Data partitions and model selection
The masked nucleotide sequence alignments for the eight nuclear genes were concatenated in Mesquite to produce a supermatrix containing 8377 aligned nucleotide positions for 373 species (File S2). The greedy algorithm in the program Par-titionFinder v1.0.1 (Lanfear et al., 2012) was used for selection of both a data-partitioning scheme and best-fitting models of nucleotide substitution for each partition. The supermatrix was analysed with 20 partitions (18S, 28S and each NPC gene partitioned by codon position) and the best-fit substitution model for each partition was selected using the Bayesian Information Criterion (Sullivan & Joyce, 2005). A scheme with three unlinked partitions: (i) 28S and 18S, (ii) NPC gene first and second positions, and (iii) NPC gene third positions, employing the GTR+I+G model of nucleotide substitution for all partitions, was identified as optimal.
The protein sequence alignments for all six NPC genes were concatenated in Mesquite to produce a supermatrix containing 1973 aligned AA positions for 373 species. All taxa that were missing data from more than 50% of the aligned AA positions (see Table S1) were removed from the supermatrix. The resulting matrix contained 1747 aligned AA positions for 319 species (File S3). The greedy algorithm in PartitionFinder v1.0.1 (Lanfear et al., 2012) was used for selection of both a data-partitioning scheme and best-fitting substitution models for each partition. The supermatrix was analysed with six partitions, one for each gene, and the best-fit substitution model for each partition was selected using the Bayesian Information Criterion (Sullivan & Joyce, 2005). A scheme with one partition employing the LG+I+G model was identified as optimal for this AA matrix. A scheme with one partition employing the GTR+I+G model of nucleotide substitution for all partitions, was identified as optimal for the corresponding matrix of nucleotide sequences (see below).

Phylogenetic analyses
Unconstrained partitioned searches under maximumlikelihood inference (ML; 500 replicates) were executed in the program Garli v2.0 (Zwickl, 2006) on the concatenated DNA sequence matrix (all genes) using fast ML stepwise addition starting trees, the abovementioned partitioning scheme and the GTR+I+G substitution model. Additional ML analyses were executed using starting trees with suprafamilial relationships constrained to be consistent with Beutel & Haas (2000;morphological data), Hunt et al. (2007;molecular data), McKenna & Farrell (2009;molecular data) and Lawrence et al. (2011;morphological data), and using the 25 best ML trees obtained from all analyses as starting trees for additional ML searches. A separate starting tree was used for each study. Partitioned ML rapid bootstrapping (MLB; 1000 replicates) was executed on the concatenated DNA sequence matrix in the program RAxML GUI v1.2 (RAxML v7.3.2) (Stamatakis, 2006;Stamatakis et al., 2008;Silvestro & Michalak, 2011). In unconstrained analyses, Strepsiptera was sometimes drawn to various nonpolyphagan ingroup taxa (see Results). However, recent phylogenomic studies, such as Niehuis et al. (2012), McKenna (2014, Misof et al. (2014) and Peters et al. (2014), show that Strepsiptera is the sister group of beetles. Strepsiptera was also recovered as the sister group of beetles in the morphological cladogram of Lawrence et al. (2011). With this in mind, we performed an additional partitioned MLB analysis (1000 replicates) on the DNA sequence matrix with Strepsiptera constrained to the OG, to explore how such an analytical constraint affected the results. We also executed unconstrained MLB analyses on matrices containing: (i) the AA sequences alone (one partition; LG+I+G substitution model), (ii) the concatenated nucleotide sequences from the six NPC genes alone (same partitioning scheme for these genes as in the above ML analysis of all eight genes; GTR+I+G), and (iii) on a matrix containing the nuclear rDNA sequences (18S and 28S) plus the aforementioned AA sequences (two partitions; GTR+I+G for rDNA; LG+I+G for AAs). We used the greedy algorithm in PartitionFinder v1.0.1 (Lanfear et al., 2012) for selection of data partitioning schemes and best-fitting models of nucleotide substitution for each partition. MLB support for all analyses (DNA nucleotides, AA and rDNA nucleotides plus AA) was interpreted as follows in the Results and Discussion: 100% MLB = maximal clade support, ≥ 95% and <100% = strong clade support, ≥75 and <95% = moderate clade support, ≥50 and <75% = weak clade support, and <50% = negligible clade support.

Divergence time estimates
Bayesian analyses were implemented in the program beast v1.8.0 (Drummond et al., 2006;Drummond & Rambaut, 2007) on an .xml file produced in the program beauti v1.7.5 (Drummond et al., 2006(Drummond et al., , 2012a from the concatenated DNA sequence data, fossil priors and monophyly constraints (see Tables 1 and S2). The beast analyses (uncorrelated lognormal relaxed clock, Yule prior) employed temporal information from 15 fossils as priors and used a starting tree randomly selected from among the top 25 trees obtained from the unconstrained ML search in GARLI. The ML tree was prepared for use as a starting tree in beast by transforming the branch lengths to ultrametric using NPRS (Sanderson, 1997(Sanderson, , 2003 in the program TreeEdit X version 0.5 (Page, 1996). The branches were then scaled to be compatible with the fossil constraints by using the minimum age of the earliest known unequivocal fossil crown group archostematan (Table 1) to scale the tree. The resulting chronogram was then imported into beauti as a user-specified starting tree for inclusion in the .xml file that was later executed in beast.
Monophyly constraints were placed on nodes in the phylogeny corresponding to fossil constraints on node age and on select suprafamilial nodes with indication of monophyly based on the ML tree and/or previous studies (Table S2). We conservatively selected fossils and applied age constraints as priors based on a review of the literature and our collective knowledge of the fossil record of Coleoptera (Table 1). The boundaries of geological stages and associated terminology used are consistent with the International Commission on Stratigraphy (Cohen et al., 2012). Except for the root, prior estimates of divergence dates were specified using lognormal distributions, with a mean of 30 and log (stdev) of 0.75. All age-specific priors were applied to stem groups, except for constraints on the age of the root. We applied a normal prior distribution to the age of the root, with initial and mean values of 302 Ma and a standard deviation of 30 Ma based on the age of fossilized galls on the fronds of tree ferns that are proposed to have been caused by holometabolous insects (Carboniferous, Gzhelian Stage; Labandeira & Phillips, 1996). We established an upper boundary on the prior distribution of the age of the root (truncated to 396 Ma) based on the age of the Table 1. Fossils and corresponding references used in the node dating analyses implemented in beast, along with the minimum and mean age for the offset-lognormal priors on node ages. Character evidence in support of the placement of these fossils can be found in the references cited.
The oldest reported fossil Staphyliniformia (family Staphylinidae) are from North American Upper Triassic Period deposits (Carnian stage: 225-230 Ma) (Fraser et al., 1996;Chatzimanolis et al., 2012). However, attribution of these fossils to Staphylinidae has been questioned (Grebennikov & Newton, 2012). earliest known fossil insect, Rhyniognatha Tillyard (Engel & Grimaldi, 2004). The lower boundary on the prior distribution was conservatively truncated to 270 Ma based on the earliest known unambiguous fossil stem group Coleoptera [Tshekardocoleidae from the Lower Permian of Obora, Czech Republic, and Tshekarda, Russia (Ponomarenko, 1963;Kukalová, 1969;Grimaldi & Engel, 2005;Beckemeyer & Engel, 2008;Kukalová-Peck & Beutel, 2012)]. These boundaries readily accommodate the ages of several additional relevant fossils that were not specifically used as constraints, including: Stephanastus polinae  Ma), a proposed stem group representative of Coleopterida (Coleoptera + Strepsiptera)   Nel et al., 2007), a proposed Carboniferous Mecopteran. We conducted three separate analyses of the combined DNA sequence data in beast with partitions as determined by PartitionFinder (see Data Partition and Model Selection), estimated base frequencies and four gamma categories -the same partitioning scheme and analytical conditions used in the ML analyses. Posterior distributions were estimated via MCMC sampling, with tree and parameter values sampled every 1000 generations for 100 million generations per run. To diagnose convergence, determine an appropriate burn-in, and otherwise check performance and accuracy of the beast analyses, we performed graphical and statistical analyses on the resulting log files in the program Tracer v1.5 (Rambaut et al., 2011). This included an examination of: (i) the frequency distribution, mean, standard deviation, confidence intervals and other statistics for each logged analysis parameter, (ii) the Bayesian posterior density plot for each analysis parameter, (iii) a trace of each parameter against generation number (to check mixing, choose a suitable burn-in and to look for trends that might suggest problems with convergence), and (iv) estimated sample sizes of combined traces (to show cases where individual traces are sampling different distributions) (Rambaut, 2009).

Diversification rates
medusa (Alfaro et al., 2009;Harmon et al., 2011) was used to integrate information about the timing of splits along the backbone of the beetle phylogeny with taxonomic richness data (described species), in order to estimate diversification rates in Neuropteroidea and Coleoptera. Analyses were executed using the MCC timetree modified so that terminals reflected monophyletic family-level (or nearest possible equivalent) groupings of taxa within Coleoptera ( Figure S1; Table S3). In some cases this required forming terminals from groupings of taxa that have not previously been treated as families or monophyla. We used R (R Development Core Team, 2011) to perform these analyses using the packages Ape (Paradis et al., 2004), Geiger (Harmon et al., 2008(Harmon et al., , 2011 and Laser (Rabosky, 2007), following the methods of Alfaro et al. (2009).
We established the background tempo of diversification for Neuropteroidea as a whole and for its constituent group Coleoptera using estimates for described extant family-level species diversity within Coleoptera fromŚlipiński et al. (2011). We used estimates for ordinal-level species diversity for Neuropterida and Strepsiptera (Grimaldi & Engel, 2005) because these groups were not sampled at the family-level in our study. Other sources were consulted when sub-familial taxon numbers were needed to provide taxonomic richness estimates for families of Coleoptera that were split apart or lumped together in the MCC tree along infrafamilial lines (see Table S3). However, when a family was split into two groups (none were split into more than two), the extent of the resulting groups was typically uncertain (establishing this would require sampling additional taxa), so, to avoid introducing unnecessary bias, the total number of described species in the family was split evenly between the two separately-recovered lineages for the analysis of diversification rates. medusa was then used to determine which family-level clades within Coleoptera are too species-rich (increase in rate) or species-poor (decrease in rate) to result from the estimated background diversification rate for the order.

Phylogenetic trees and clade support
The phylogenetic hypothesis for Coleoptera in Fig. 2 shows relationships resulting from a Bayesian analysis (with monophyly constraints; see also Table S2 and Figure S9. Relationships and clade support (BPPs) estimated under Bayesian inference should therefore be interpreted cautiously) of concatenated nucleotides from all eight nuclear genes. The ML tree shown in Figure S2 resulted from an unconstrained partitioned likelihood analysis of the same dataset. Clade support values resulting from ML bootstrap (MLB) analyses of nucleotides alone  [unconstrained ( Figure S3) and with Strepsiptera constrained to the OG ( Figure S7)] and rDNA nucleotides + AAs from the six NPC genes ( Figure S4) are summarized on the ML tree. The topologies obtained from Bayesian (Fig. 2) and ML analyses ( Figure S2) are summarized and compared in detail in Figs 3-15. MLB values from analysis of the AAs alone ( Figure  S5) are not shown in Figure S2 because taxa with data for less than 50% of the AA positions were excluded from the analysis, resulting in a smaller taxon sample (see Materials and methods). The same applies to the MLB analysis of nucleotides from the six NPC genes alone, for which the same taxa were excluded from analysis on account of missing data ( Figure S6). The MLB analysis of AAs alone ( Figure S5) and the MLB analysis of NPC nucleotides alone ( Figure S6) therefore cannot be directly compared to the results from the other MLB analyses because they contain different numbers of species. We only compare and contrast these results with the results of the other analyses (below) when specifically noted.

Higher-level relationships and near relatives of beetles
Coleoptera was monophyletic in the ML tree (−lnL = 871077.08) resulting from analysis of the concatenated nucleotide sequences alone ( Figure S2), and Strepsiptera (Mengenilla) was its sister group. These orders together formed the clade Coleopterida (Strepsiptera + Coleoptera; Kukalová-Peck & Lawrence, 2004). Likelihood trees with Strepsiptera recovered within the beetle suborder Myxophaga (63% MLB nucleotides alone, Figure S3; 57% MLB rDNA nucleotides + AAs, Figure S4), or with Strepsiptera sister to the beetle suborder Archostemata, had likelihood scores only slightly worse than the ML tree (<25 units higher). Clade support for Coleopterida was moderate in the MLB analyses of nucleotides alone ( Figure S3), rDNA nucleotides plus AAs ( Figure S4), and AAs alone ( Figure S5), weak in the MLB analysis of nucleotides alone with Strepsiptera constrained to the OG ( Figure S7), and lacking in the analysis of NPC nucleotides alone ( Figure S6). MLB support increased for many relationships when Strepsiptera was constrained to the OG ( Figures S2 and S7). For example, in the analysis of nucleotides alone, MLB support for the sister-group relationship between Archostemata and Myxophaga increased from 51% ( Figure S3) to 90% ( Figure S7). Coleopterida was sister to Neuropterida [comprising Megaloptera (Sialis), Raphidioptera (Agulla) and Neuroptera (Plega)], forming the clade Neuropteroidea (containing Coleoptera + Strepsiptera + Neuropterida) in all analyses (Figs 2, 3; Figure S2). MLB support for Neuropterida was moderate in the analysis of nucleotides alone ( Figure S3), the analysis of rDNA nucleotides plus AAs ( Figure S4) and the analysis of AAs alone ( Figure S5), strong (99%) in the analysis of nucleotides alone with Strepsiptera constrained to the OG ( Figure S7), and lacking in the analysis of NPC nucleotides alone ( Figure S6). Within Neuropterida, Neuroptera and Megaloptera were sister taxa, and these together were sister to Raphidioptera in all analyses (Figs 2, 3; Figure S2). Neuropteroidea was sister to Hymenoptera (Apis and Cephus), the most distant OG in our analyses. These relationships are the same as in the BI tree (Fig. 2).

Interrelationships of the suborders of beetles
The subordinal relationships recovered in the ML and BI trees were the same -Polyphaga (Adephaga (Myxophaga, Archostemata)) (Figs 2, 3; Figure S2) -and each of the suborders of Coleoptera was monophyletic. MLB support for the suborders varied among analyses. Archostemata received strong to maximal MLB support in all analyses ( Figure S2). MLB support for Myxophaga was weak in the analyses of nucleotides alone ( Figure S3) and rDNA nucleotides plus AAs ( Figure S4), negligible in the analysis of AAs alone ( Figure S5), and lacking in the analysis of NPC nucleotides alone ( Figure S6) (in all of these Strepsiptera was included). However, MLB support for Myxophaga increased substantially (from 63 to 93%) in the analysis of nucleotides with Strepsiptera (Mengenilla) constrained to the OG ( Figures S3 and S7). MLB support for Adephaga was moderate in the analysis of nucleotides alone ( Figure S3), strong in the analyses of rDNA nucleotides plus AAs ( Figure S4) and AAs alone ( Figure S5), maximal in the analysis of nucleotides with Strepsiptera constrained to the OG ( Figure S7), and weak in the analysis of NPC nucleotides alone ( Figure S6). MLB support for Polyphaga was weak in the analyses of rDNA nucleotides plus AAs ( Figure S4) and AAs alone ( Figure S5),

Fig. 2.
Maximum clade credibility timetree for beetles (367 species representing 171/183 families) and OGs (six species representing five orders), resulting from partitioned Bayesian analyses of DNA sequences from eight nuclear genes in the program beast. Note that the top/right row/column entries are interdigitated between the bottom/left ones, as connected by the broken lines. Statistical measures of Bayesian posterior probability (BPP) support are shown along branches (an asterisk indicates nodes with maximal BPP support of 1.0) and 95% confidence intervals around node age estimates (series, superfamilies, and select other higher-level groups mentioned in the text) are shown as grey bars. Background colours: black/white = OGs; red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga. Monophyly constraints from the beast analysis are shown as black ovals, with node ages constrained by fossil priors indicated by letters within the ovals (A-O; see Table S3). White stars mark species of Derodontoidea. Black stars mark species of Cucujoidea s.l. (Biphyllidae and Byturidae) recovered in positions separate from other members of the superfamily. Numbers of extant species for superfamilies (in parentheses) are fromŚlipiński et al. (2011). The timing and taxonomic location of increases or decreases in diversification rate in beetles are marked in the phylogeny with boxes numbered 1-23, with individual net diversification rates (r = b − d) and relative extinction rates ( = d/b) summarized by number in Table 3. Clades showing an inferred significant increase in diversification rate are marked with red boxes, whereas clades showing a significant decreases in rate are marked with blue boxes. Photo credits: ©David R. Maddison (DRM), ©Duane D. McKenna (DDM), ©Piotr Naskrecki (PN), and ©Alex Wild (unlabelled). A high-resolution version of this figure is available in Figure S8. 95% confidence intervals for all nodes are shown in Figure S9. † = Plus Derodontoidea: Nosodendridae. . Partitioned ML bootstrap support under various analytical schemes is noted by coloured boxes along branches in the ML tree (see embedded legend). Background colours: gray = OGs; red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga. Monophyly constraints from the beast analysis are shown as black ovals [Note, monophyly constraints on taxa shown as terminals are not marked (see Table S2)]. Photo credit for Cicindela Linnaeus: Alex Wild. lacking in the analysis of NPC nucleotides alone ( Figure S6), and moderate in the analyses of nucleotides alone with and without Strepsiptera constrained to the OG ( Figures S3 and S7).

Relationships within Archostemata and Myxophaga
Within Archostemata, internal relationships were recovered with variable (moderate to maximal, but mostly strong to maximal) MLB and BPP support, except for the sister-group relationship between Cupes Fabricius and Distocupes Neboiss (Cupedidae), which had weak to negligible support in MLB analyses but strong support under BI (Fig. 4). Micromalthus Leconte (Micromalthidae) formed a clade with Tetraphalerus Waterhouse (Ommatidae) with strong to maximal MLB and BPP support, sister to Cupedidae. Myxophagan relationships were the same in the ML and BI trees ( Fig. 4; Figure S2). The monophyly of Torridincolidae (three exemplars) received strong to maximal support in all analyses ( Fig. 2

Relationships within Adephaga
Adephaga comprised two large clades in the ML and BI trees, corresponding to the traditional Hydradephaga and Geadephaga (Figs 2, 5; Figure S2). MLB support for Hydradephaga was mostly weak in unconstrained analyses ( Figures S2-S4); however, in the analysis of nucleotides alone with Strepsiptera  Table S3).  Table S3).
(Mengenilla) constrained to the OG ( Figure S7), MLB support for Hydradephaga increased substantially -from 61 to 85%. Geadephaga received strong to maximal support in all ML analyses, and had the same internal relationships under ML (nucleotides alone) and BI. Support for the internal relationships of Hydradephaga and Geadephaga was variable, but mostly moderate to maximal; relatively few clades within Adephaga had weak or negligible support. At the family level within Hydradephaga, Dytiscidae and Gyrinidae were strongly to maximally supported as monophyletic. Aspidytes Ribera, Beutel, Balke & Vogler (Aspidytidae) was sister to Amphizoa Leconte (Amphizoidae) in all analyses, and had moderate to strong MLB support and maximal BPP support. Meru Spangler & Steiner (Meruidae) was recovered sister to Noteridae (Noterus Schellenberg and Notomicrus Sharp) with moderate to maximal MLB support and maximal BPP support. Within Geadephaga,  maximum-likelihood (ML) summary trees for Staphyliniformia and Scarabaeiformia (plus Jacobsoniidae) resulting from partitioned phylogenetic analyses of DNA sequences from eight nuclear genes (see Materials and methods). We included data from all extant families except Belohinidae (Scarabaeoidea). Statistical measures of Bayesian posterior probability (BPP) support are shown along branches in the Bayesian tree (an asterisk indicates nodes with maximal BPP support of 1.0). Partitioned ML bootstrap support under various analytical schemes is noted by coloured boxes along branches in the ML tree (see embedded legends). Background colours indicate major clades present in both trees. Monophyly constraints from the beast analysis are shown as black ovals (see Table S3).  Table S3). maximum-likelihood (ML) summary trees for Elateroidea, resulting from partitioned phylogenetic analyses of DNA sequences from eight nuclear genes (see Materials and methods). We included data from all extant families of Elateroidea except Rhinorhipidae and Plastoceridae. Statistical measures of Bayesian posterior probability (BPP) support are shown along branches in the Bayesian tree (an asterisk indicates nodes with maximal BPP support of 1.0). Partitioned ML bootstrap support under various analytical schemes is noted by coloured boxes along branches in the ML tree (see embedded legends). Background colours indicate major clades present in both trees. Monophyly constraints from the beast analysis are shown as black ovals (see Table S3).
Calosoma Weber (Carabidae) was sister to Trachypachidae (Systolosoma Solier in Gay and Trachypachus Motschulsky), and these together were sister to the remaining Carabidae plus Rhysodidae (Clinidium Kirby and Omoglymmius Ganglbauer), thereby rendering Carabidae paraphyletic. However, the sister relationship between Trachypachidae and Calosoma had negligible to weak MLB and BPP support, except in the analysis of AAs ( Figure S5; 83% MLB, moderate support).
Calosoma was sister to all other Carabidae plus Rhysodidae in some likelihood tree searches, but these trees had slightly worse likelihood scores (<25 units higher) than the ML tree.
Carabidae plus Rhysodidae minus Calosoma received moderate nodal support in most MLB analyses, and maximal BPP support. Rhysodidae was recovered well within Carabidae, in a position sister to Paussinae (Arthropterus MacLeay in Smith and Metrius Eschscholtz) under both ML and BI. Cicindelinae was recovered within Carabidae under both ML and BI.

Series and superfamily-level relationships within Polyphaga
Scirtoidea was rendered paraphyletic under ML both by the inclusion of Derodontidae (Derodontoidea; three exemplars), Background colours indicate major clades present in both trees. Monophyly constraints from the beast analysis are shown as black ovals (see Table S3). Background colours indicate major clades present in both trees. Monophyly constraints from the beast analysis are shown as black ovals (see Table S3). and by its separation into two clades that were successive sister taxa to all other Polyphaga. However, the basal splits forming these clades had negligible to weak MLB support in most analyses (Figs 3, 6; Figure S2). Under BI, Scirtoidea plus Derodontidae formed a clade with moderate BPP support (Figs 2, 3, 6), sister to the remaining Polyphaga. Derodontoidea sensu Lawrence et al. (2010a) was therefore polyphyletic in all analyses ( Fig. 2; Figure S2), and the remaining two families of Derodontoidea -Jacobsoniidae (Derolathrus Sharp and Saphophagus Sharp) and Nosodendridae (Nosodendron Latreille) -formed two additional clades under both ML and BI, which were recovered in separate positions elsewhere within Polyphaga. Jacobsoniidae was recovered within Staphyliniformia in close relation to Staphylinoidea, and Nosodendridae was recovered sister to Dascilloidea (ML) or sister to Elateriformia (BI). Polyphaga minus Scirtoidea and Derodontidae received variable MLB support and maximal BPP support (Figs 2, 3; Figure S2). Many of the series and superfamilies of Polyphaga, and several other major clades, received MLB and BPP support in most analyses (not counting the BI analysis in cases where a clade was constrained to be monophyletic) (Figs 3; Figure S2). These included Buprestoidea (Fig. 7), Buprestoidea + Byrrhoidea + Elateroidea  Monophyly constraints from the beast analysis are shown as black ovals (see Table S3). maximum-likelihood (ML) summary trees for Cleroidea (including Biphyllidae and Byturidae) resulting from partitioned phylogenetic analyses of DNA sequences from eight nuclear genes (see Materials and methods). We included data from all extant families of Cleroidea except Mauroniscidae, Phloiophilidae, and Rhadalidae. Statistical measures of Bayesian posterior probability (BPP) support are shown along branches in the Bayesian tree (an asterisk indicates nodes with maximal BPP support of 1.0). Partitioned ML bootstrap support under various analytical schemes is noted by coloured boxes along branches in the ML tree (see embedded legends). Background colours indicate major clades present in both trees. Monophyly constraints from the beast analysis are shown as black ovals (see Table S3).  Table S3).  Figure S2).
Scarabaeoidea was sister to Hydrophiloidea s.l. in the BI tree (with maximal BPP support), and these together were sister to Staphylinoidea (including Jacobsoniidae), rendering series Staphyliniformia paraphyletic. This large clade (Staphyliniformia + Scarabaeoidea + Jacobsoniidae) received maximal BPP support (Figs 2, 7). However, in the ML tree, Staphyliniformia (including Jacobsoniidae, which was sister to Staphylinoidea) was sister to Scarabaeoidea. This large clade had negligible support in all MLB analyses. Within this clade, superfamilies Histeroidea and Hydrophiloidea s.s. were sister groups under ML and BI, (Fig. 7; Figure S2). Staphyliniformia and Staphylinoidea, though both present in the ML tree (Staphylinoidea, but not Staphyliniformia, was present in the BI tree as a monophyly constraint) received negligible MLB support in all analyses. MLB support for Scarabaeoidea was weak in all analyses.
Series Elateriformia (Figs 2,8,9; Figure S2), containing the superfamilies Buprestoidea, Byrrhoidea, Dascilloidea and Elateroidea, was monophyletic including Nosodendron (Nosodendridae), but had negligible MLB support in all analyses. Under ML, Nosodendridae was sister to a strongly to maximally supported superfamily Dascilloidea, and these together were sister to the remaining Elateriformia. Under BI, Nosodendron was sister to the traditional Elateriformia, and Dascilloidea was sister to a clade containing the other superfamilies of series Elateriformia, the latter with negligible MLB support. Superfamily Buprestoidea was monophyletic and received strong to maximal MLB support in all analyses (Fig. 8) Table S3).
Series Cucujiformia was recovered in the ML tree with mostly weak to moderate MLB support (Figs 2, 3; Figure  S2). Most Cucujoidea (in the traditional broad sense of the superfamily) were recovered in one of two large clades. One clade contained the Cerylonid Series of families (Akalyptoischiidae, Alexiidae, Bothrideridae, Cerylonidae, Coccinellidae, Corylophidae, Discolomatidae, Endomychidae and Latridiidae) (Figs 2, 11; Figure S2), here called Coccinelloidea, following Robertson et al. (2015) and the other clade contained the remaining Cucujoidea (Figs 2, 12; Figure S2; here called Cucujoidea s.s.), except Biphyllidae and Byturidae, which were recovered within Cleroidea (Figs 2, 13; Figure S2) (see below for more information). Coccinelloidea was monophyletic in both the ML and BI trees, with mostly moderate MLB support. Coccinelloidea was sister to Tenebrionoidea under ML, and these together were sister to the remaining Cucujiformia, but with negligible MLB support. Under BI, Coccinelloidea was sister to the remaining Cucujiformia, and Tenebrionoidea was sister to the clade Cleroidea + Cucujoidea s.s. + Curculionoidea + Chrysomeloidea, with maximal BPP support. Tenebrionoidea (including Lymexyloidea) was monophyletic in the ML and BI trees. However, MLB support for Tenebrionoidea was negligible in all analyses (Figs 2, 14; Figure S2). The monophyly of Cleroidea plus the traditional cucujoid families Biphyllidae and Byturidae received negligible to moderate MLB support (Figs 2, 13; Figure S2). The main cluster of Cucujoidea (Cucujoidea s.s.) contained those taxa that do not belong to Coccinelloidea or Cleroidea. Its monophyly was recovered in the ML and Bayesian trees, but MLB support for Cucujoidea s.s. was negligible in all analyses (Figs 2, 12; Figure S2). A subset of Cucujoidea s.s. [Nitidulidae, Kateretidae (Amartus Leconte), Monotomidae (Bactridium Kunze and Rhizophagus Herbst), Boganiidae (Paracucujus Sen Gupta & Crowson) and Hobartiidae (Hobartius Sen Gupta & Crowson), or Paracucujus and Smicrips Leconte, or Paracucujus alone] was recovered sister to Phytophaga (forming a paraphyletic grade of Cucujoidea s.s.) in some likelihood trees. These trees had only slightly worse likelihood scores than the ML tree (<25 units higher), in which Cucujoidea s.s. was monophyletic.
The clade Phytophaga (the sister superfamilies Chrysomeloidea and Curculionoidea) was sister to Cucujoidea s.s. in both the ML and Bayesian trees, with mostly moderate MLB support and maximal BPP support (Figs 2, 15; Figure S2). Phytophaga was monophyletic and received weak to moderate MLB support. Chrysomeloidea and Curculionoidea were each monophyletic. MLB support for Chrysomeloidea was mostly weak. MLB support for Curculionoidea was strong in the analysis of nucleotides alone, and varied from weak to moderate in the other MLB analyses.

Internal relationships of the series and superfamilies of Polyphaga
The scirtoid families Clambidae, Eucinetidae and Scirtidae were each monophyletic and moderately to maximally supported in all analyses. Declinia Nikitsky, Lawrence, Kirejtshuk & Gratshev (Decliniidae) was strongly to maximally supported as sister to Scirtidae. The relationships of Clambidae and Eucinetidae to Derodontidae (Derodontoidea) differed between the ML and BI trees, but had negligible to weak nodal support in all analyses. Jacobsoniidae, previously assigned to superfamily Derodontoidea, was recovered within Staphylinoidea, sister to a clade formed by Hydraenidae (three exemplars) + Ptiliidae (Acrotrichis Motschulsky and Nossidium Erichson) under ML ( Fig. 7; Figure S2), but with negligible MLB support for both its inclusion in Staphylinoidea and its position as sister to Hydraenidae + Ptiliidae. Jacobsoniidae was sister to Staphylinoidea under BI (Figs 2, 7). Among staphylinoid subgroups, the Ptiliid group and its constituent families (Ptiliidae and Hydraenidae) were recovered with strong BPP (Figs 2, 7) and variable MLB support (except Ptiliidae in the unconstrained analysis of nucleotides alone; Figures S2 and S3).
The internal relationships of Hydrophiloidea s.s. differed under ML and BI and had mostly negligible MLB support and moderate to strong BPP support (Figs 2, 7; Figure S2). Under ML, Spercheidae (Spercheus Kugelann) was sister to the remaining Hydrophiloidea s.s.; in contrast, under BI, Helophoridae (Helophorus Fabricius) and Georissidae (Georissus Latreille) were together sister to a clade comprising Spercheidae plus Hydrophilidae (Andotypus Spangler and Tropisternus Solier). The sister relationships between Georissidae and Helophoridae and between the two Hydrophilidae were supported in all analyses. Syntelia Westwood (Synteliidae) was the sister taxon to all other Histeroidea in the ML and BI analyses, and Sphaerites Duftschmid (Sphaeritidae) was consistently recovered sister to Histeridae (four exemplars). The internal relationships of Histeroidea (Fig. 7) were the same under ML and BI and had mostly strong to maximal BPP and MLB support.
Neither the Leiodid group (Leiodidae + Agyrtidae) nor Leiodidae (four exemplars) was recovered under BI because of the odd separation of Colon Herbst (Leiodidae: Coloninae) from the remainder, although the group was recovered in the ML tree, where it received negligible nodal support ( Fig. 7; Figure  S2). Agyrtidae (three exemplars), in contrast, was moderately to maximally supported in all analyses. The Staphylinid group (Silphidae + Staphylinidae including Scydmaeninae) was recovered in the ML tree, but received negligible MLB support. Silphidae (Necrophila Kirby & Spence and Nicrophorus Fabricius) (ML and BI) and Colon (BI only) rendered Staphylinidae paraphyletic (Fig. 7). Silphidae was moderately to maximally supported in all MLB analyses. Within Staphylinidae (nine exemplars), sparse taxon sampling limits testing of the four subfamily groupings of Lawrence & Newton (1982, 1995, but Scydmaeninae (three exemplars) was consistently recovered sister to Creophilus Samouelle (Staphylininae) (Fig. 7), as expected for those sole representatives of the Staphylinine group. The omaliine (Paraphloeostiba Steel and Glypholoma Jeannel) and osoriine (Renardia Motschulsky and Scaphidium Olivier) groups were each recovered under ML, but not under BI (Fig. 7). The single included member of the Tachyporine group (Leucotachinus Coiffait & Sáiz) was sister to Silphidae in both the ML tree (negligible to weak MLB support) and BI tree (moderate BPP support).
The deep nodes within Scarabaeoidea were all recovered with negligible MLB support and negligible to weak BPP support (Fig. 7). The three species of Geotrupidae sampled were recovered in the same three separate clades in the ML and Bayesian trees. Geotrupes Latreille (Geotrupinae) was recovered sister to Trox Fabricius (Trogidae) with negligible to weak MLB support and maximal BPP support, Taurocerastes Philippi (Taurocerastinae) was sister to Lucanidae + Diphyllostoma Fall (Diphyllostomatidae) with negligible MLB and BPP support, and Odonteus Samouelle (Bolboceratinae) was recovered along with Pleocoma Leconte (Pleocomidae) and Passalus Fabricius (Passalidae) in a clade with negligible MLB and BPP support that was otherwise composed of Scarabaeidae. Therefore, the topologies are different, but in both trees Scarabaeidae is not monophyletic. The sister-group relationship between the dung beetle subfamilies Scarabaeinae (Scarabaeus Linnaeus) and Aphodiinae (Aphodius Illiger) was maximally supported in all analyses. A clade comprising Lucanus Scopoli (Lucanidae: Lucaninae), Nicagus Leconte (Lucanidae: Nicaginae) and Diphyllostoma (Diphyllostomatidae) was recovered in the ML and BI trees, with weak to moderate MLB support and maximal BPP support. Overall, relatively few internal relationships in Scarabaeoidea had >50% MLB support or >0.75 BPP support.
Within Elateriformia (also see above section Series and Superfamily-level Relationships within Polyphaga), Schizopodidae (Schizopus Leconte) was moderately to maximally supported as sister to Buprestidae (four exemplars). We recovered strong to maximal MLB and BPP support for inclusion of the elateroid Podabrocephalus (Podabrocephalidae; Fig. 8) in the byrrhoid family Ptilodactylidae (Anchycteis Horn and Ptilodactyla Illiger), which also included Cneoglossa Guérin-Ménéville (Cneoglossidae). Callirhipis Latreille in Cuvier (Callirhipidae) was sister to all other Byrrhoidea under ML, with weak MLB support. Callirhipis was nested within early-divergent Byrrhoidea under BI, sister to a clade comprising Dryopidae (Helichus Erichson) and Lutrochidae (Lutrochus Erichson), with moderate BPP support. Within Elateroidea, most relationships were recovered with moderate to strong MLB and BPP support (Fig. 9). Lissomus Dalman (Lissominae) was unexpectedly recovered with strong to maximal support in a position sister to Lycidae (Dictyoptera Latreille and Lycus Fabricius) -and not in Elateridae -in both the ML and BI trees (Fig. 9).
The family-level relationships of Bostrichoidea were mostly moderately to strongly supported under ML and BI. Dermestidae (three exemplars) was recovered in both the ML and BI trees as sister to the remaining Bostrichoidea (Bostrichidae and Ptinidae). The superfamily as a whole was sister to Cucujiformia in both the ML and BI trees ( Fig. 2; Figure S2). MLB support for this placement was maximal under BI, and negligible to weak under ML.
Nodal support was negligible for most (especially deep) nodes in Tenebrionoidea. Tetratomidae (three exemplars) was polyphyletic, with Eustrophopsis Champion (Eustrophinae) and Penthe Newman (Penthinae) sister to a clade containing Sirrhas Champion (Promecheilidae) + Ulodidae (Meryx Latreille and Syrphetodes Pascoe) + Chalcodrya Redtenbacher (Chalcodryidae) (Figs 2, 14; Figure S2). Monommatini) was recovered within Scraptiidae with mostly weak MLB support and moderate BPP support, and the combination was well removed from other Zopheridae, which were sister to Tenebrionidae in both analyses. Lymexyloidea (Atractocerus) was sister to Aderus (Aderidae) in a large clade with overall negligible MLB backbone support and moderate to mostly strong/maximal BPP support (see above). This clade was sister to the rest of the Tenebrionoidea, and overall its internal relationships had negligible BPP and MLB support, and differed markedly between the ML and BI trees (Fig. 14).
Superfamily Cucujoidea (in the former broad sense of the superfamily) was polyphyletic, forming three clades (i) the newly recognized grouping Coccinelloidea   (Fig. 11), (ii) Biphyllidae (Diplocoelus Guérin-Ménéville) and Byturidae (Dascillocyphon Everts and Xerasia Lewis) within Cleroidea (Fig. 13), and (iii) the remaining Cucujoidea s.s. (see above section Series and Superfamily-level Relationships within Polyphaga; Fig. 12). Within Coccinelloidea (Fig. 11), two major clades were recovered: (i) a strongly supported clade with Latridiidae (Corticaria Marsham and Eufallia Muttkowski), Cerylonidae (four exemplars, not monophyletic), Bothrideridae (three exemplars, not monophyletic), and Discolomatidae (Aphanocephalus Wollaston and Fallia Sharp), and (ii) a weakly supported clade comprising the rest of the Cerylonid Series. Bothrideridae and Cerylonidae were intermingled, and these together were rendered paraphyletic by Discolomatidae in both the BI and ML trees (Fig. 11). The two exemplars of Latridiidae, representing the two described subfamilies, were recovered together with strong nodal support. Endomychidae (four exemplars) was polyphyletic. In the BI tree, Bystus Guérin-Méneville (Anamorphinae) and Holoparamecus Curtis (Merophysiinae) form a monophyletic group within a larger clade including Corylophidae and Alexiidae. In the ML tree, Bystus and Holoparamecus are rendered paraphyletic by the other two families. The remaining endomychid exemplars, Endomychus Panzer (Endomychinae) and Epipocus Germar (Epipocinae), form a monophyletic group that, with Akalyptoischiidae, form the sister taxon to Coccinellidae (eight exemplars). MLB and BPP support for these relationships is mostly negligible to weak. Corylophidae (four exemplars) was monophyletic in both the ML and BI trees, but with negligible MLB support and moderate BPP support. Coccinellidae was monophyletic and received strong to maximal MLB and BPP support in all analyses. The lone representative of Microweiseinae (Delphastus Casey) was sister to the seven other coccinellid exemplars (whose internal relationships were the same in the ML and BI trees but had mostly negligible to weak MLB and BPP support), all representing subfamily Coccinellinae. This arrangement received strong to maximal MLB and BPP support.
Nearly all of the backbone relationships in Cucujoidea s.s. had negligible MLB support (Fig. 12) Cleroidea plus the cucujoid families Biphyllidae and Byturidae was monophyletic in the ML and BI trees (see above section Series and Superfamily-level Relationships within Polyphaga; Figs 2, 13; Figure S2). We recovered maximal BPP support and mostly moderate MLB support for Cleroidea minus the trogossitid Rentonellum Crowson, which was sister to all other Cleroidea (plus Biphyllidae and Byturidae). The cleroid family Trogossitidae (six exemplars) was polyphyletic. Temnoscheila Westwood (Trogossitinae) was sister to Isoclerus Lewis (Thanerocleridae). Rentonellum Crowson (Rentoniinae) was, as noted above, sister to all other Cleroidea plus Biphyllidae and Byturidae. The trogossitids Acalanthis Erichson in Germar (Trogossitinae) and Thymalus Latreille, Grynoma Sharp, and Eronyxa Reitter (all Peltinae) were recovered in a clade along with Acanthocnemus Perris (Acanthocnemidae). Phycosecis Pascoe (Phycosecidae) was sister to a clade containing Idgia Laporte (Prionoceridae) and Melyridae (four species sampled) as sister taxa.
Chrysomeloidea and Curculionoidea formed the clade Phytophaga, with weak to moderate MLB support (Figs 2, 15; Figure S2). Within Chrysomeloidea, we recovered two major clades. One clade corresponded to the family Chrysomelidae (seven exemplars), which had negligible to moderate MLB support and maximal BPP support. Chrysomelidae contained three clades: (i) Bruchinae Genn. spp. + Crioceris Geoffroy (Criocerinae), (ii) Chrysomela Linnaeus (Chrysomelinae) + Diabrotica Chevrolat (Galerucinae) Figure S2), but a basal dichotomy between a clade comprising Nemonychidae + Anthribidae and a clade containing the remaining weevil families was recovered in the analysis of 18S and 28S nucleotides plus amino acids ( Figure S4). Attelabidae (Rhynchitinae Gen. sp. and Merhynchites Sharp) was sister to the clade (Caridae (Brentidae, Curculionidae)) under BI (Figs 2, 15) though with negligible BPP support, and sister (with mostly negligible MLB support) to the clade formed by Nemonychidae + Anthribidae under ML. The sister-group relationships of Car Blackburn (Caridae) to the clade Brentidae (Cylas Latreille and Eurhynchus Kirby) + Curculionidae (ten exemplars), and between the latter two families, were recovered with moderate to maximal support in most analyses (Figs 2, 15; Figure S2). The terminals of the subfamilies of Curculionidae sampled were related as follows: Ocladius Schönherr (Brachycerinae) sister to all other Curculionidae, Sphenophorus Schönherr (Dryophthorinae) sister to a clade comprising Mecopelmus and Platypus Herbst (both Platypodinae), and Notaris Germar (Brachycerinae) sister to the 'Higher Curculionidae,' here represented by six terminals currently classified in the subfamilies Cossoninae, Curculioninae, Entiminae, Molytinae and Scolytinae. Brachycerinae was therefore polyphyletic. Within Higher Curculionidae, the clade containing Cossoninae, Curculioninae, Molytinae and Scolytinae had overall mostly negligible to weak MLB and BPP support and very short internal branches.

Timing the diversification of beetles
The split between Neuropteroidea (Coleoptera + Neuropterida + Strepsiptera) and Hymenoptera was reconstructed via BI to have occurred ∼298 Ma (319 to 282 Ma) (Fig. 2  majority of the most species-rich families, were estimated to have originated during the Cretaceous (Figs 2, 16).

Diversification rates
The background family-level diversification rate in beetles and the timing and taxonomic location of increases or decreases in diversification rate resulting from the medusa analyses are summarized in Fig. 2. The background diversification rate for Neuropteroidea as a whole was estimated at 0.025 lineages per Ma, with a significant increase in diversification rate at the node representing crown group Coleoptera (0.037 lineages/Ma; Table 3). Within Coleoptera, 10 clades were identified as too species-rich to result from the background diversification rate ( Fig. 2; Figure S1; Table 3), and are therefore proposed to have experienced significant increases in diversification rate. These were: the Phytophaga (Chrysomeloidea + Curculionoidea), Scarabaeidae + Pleocomidae, Cucujoidea s.s. + Phytophaga, a subset of Tenebrionoidea (Polypriinae to Ulodidae), Tenebrionidae (including Trachelostenus: Trachelostenidae), Laemophloeidae + Phalacridae and Propalticidae, Buprestidae in part (Acmaeoderinae + Agrilinae), Elateridae in part (= Elateridae 2 in Figure S1 and Table S3), Meloidae + Mordellidae, and Scirtidae. Another 12 clades, widely distributed across the phylogeny of Coleoptera, were identified as too species-poor to result from the background diversification rate in beetles, and are therefore proposed to have experienced significant decreases in diversification rate or significantly higher extinction rates Fig. 16. Superimposed plots of crown group divergence times for beetle families 1 and cumulative totals of described extant species diversity showing that most Modern beetle diversity has its origins in the Cretaceous. White circles: species diversity modelled as accruing at a constant rate over time, w/out extinction, from time of family origin to present (5 Ma intervals; actual time-specific rates unknown). Black circles: species diversity modelled as accruing immediately (without extinction) at the time of origin (5 Ma intervals; actual time-specific rates unknown). The irregular pattern of diversification shown in this plot (black circles) is therefore due in part to a lack of information about diversification rates within families. Note that the small difference in total species between the plots is due to rounding effects. Photo credits (used by permission): ©Alex Wild (unlabelled), ©Ted C. MacRae (TM), and ©Nick Porch (NP). than other clades ( Fig. 2; Figure S1; Table 3). These were: Archostemata + Myxophaga, Derodontidae + Scirtoidea, Amphizoidae + Aspidytidae and Hygrobiidae, Meruidae, Artematopodidae + Omethidae and Telegeusidae, Boganiidae + Hobartiidae and Smicripidae, Caridae, Rhizonium, Oxypeltidae, Jacobsoniidae, Trachypachidae, and Phloeostichidae and allied families. Six to seven of the 10 total increases in diversification rate we identified in beetles occurred in the Cretaceous, three to four in the Jurassic, and one in the Cenozoic ( Fig. 2; Figure S1; Table 3). The overall rate increase identified for Coleoptera occurred at or near the Permian/Triassic Boundary. Seven of the twelve decreases in diversification rate that we identified occurred in the Cretaceous, two in the Jurassic, one in the Triassic and two in the Cenozoic (Fig. 2; Table 3).

Higher-level relationships and near relatives of beetles
The interrelationships and internal relationships of our OGs are consistent with other recent studies (e.g. Wiegmann et al., 2009a,b;McKenna & Farrell, 2010;Beutel et al., 2011;Ishiwata et al., 2011;Niehuis et al., 2012;McKenna, 2014;Peters et al., 1 Monophyletic family-level groupings of taxa used to estimate diversification rates (see Materials and methods; Figure S1 and Table S3). 2014). For example, Neuropteroidea was sister to Hymenoptera, as expected, because Mecopterida (caddisflies, butterflies, scorpionflies, fleas, true flies), which would otherwise be sister to Neuropteroidea, were not included in our OG taxon sample. Mecopterida is the established sister group of Neuropteroidea, and Hymenoptera is the sister group of all other endopterygote insect orders. Within Coleoptera, our results broadly confirm existing knowledge of relationships, with departures from the expected relationships either poorly supported in our study, or falling mostly among clades without an existing consensus (poorly supported or with varying resolutions in other studies to date).
Strepsiptera have long been difficult to place in the insect tree of life due to their extreme sexual dimorphism, bizarre life histories, unusual morphological and developmental characteristics, and high rates of molecular evolution (e.g. Carmean & Crespi, 1995;Niehuis et al., 2012). Several recent molecular phylogenetic studies containing small samples of beetles have shown that Strepsiptera are part of Neuropteroidea (Wiegmann et al., 2009a,b;Longhorn et al., 2010;McKenna & Farrell, 2010;Ishiwata et al., 2011). The largest morphological cladistic analysis of Coleoptera performed so far  included one exemplar from Strepsiptera (Mengenillidae: Eoxenos Peyerimhoff), which was recovered sister to Coleoptera. The extensive morphological study of Holometabola by Beutel et al. (2011) also recovered Strepsiptera sister to Coleoptera. Recent studies using very large molecular (phylogenomic) datasets (Niehuis et al., 2012;McKenna, 2014;Peters et al., 2014) confirm the higher-level phylogeny of Neuropteroidea, including the sister-group relationship between Strepsiptera and Coleoptera. Results from the present study are compatible with this view, recovering Strepsiptera (here represented by Mengenilla) as the sister group of a monophyletic order Coleoptera (only in some analyses, in others Strepsiptera falls within non-polyphagan Coleoptera). However, this placement had negligible MLB support, and other placements had similar (though not better) likelihood scores and weak nodal support (see Results). Therefore, although analyses of morphological data Lawrence et al., 2011) and (separately) phylogenomic data (Niehuis et al., 2012;McKenna, 2014;Peters et al., 2014) containing relatively few exemplars recover a sister-group relationship between beetles and Strepsiptera, nodal support for this placement is still lacking in studies (like the present one) containing a broad and representative sample of beetle families and subfamilies, and Strepsiptera. The long terminal branches that characterize Strepsiptera, and to a lesser degree certain early-divergent Coleoptera, contribute to the difficulty of resolving these relationships. A sister-group relationship between Strepsiptera and beetles nonetheless seems highly likely. Beetles and Strepsiptera thus share features including posteromotorism, an enlarged metathorax and a pupa with immobile mandibles due to common ancestry. Certain tenebrionoid beetles, particularly certain Ripiphoridae, have additional features in common with Strepsiptera, including active host-seeking first instar larvae, flabellate antennae and hypermetamorphosis; however, these features are the result of evolutionary convergence Niehuis et al., 2012;McKenna, 2014). Clades showing an inferred significant increase in diversification rate are marked in red, whereas clades showing a significant decreases in rate are marked in blue. The timing and taxonomic location of increases or decreases in diversification rate in beetles are shown in Fig. 2. Misof et al. (2014) sampled eight terminals representing the four suborders of Coleoptera, two genera of Strepsiptera and 134 other taxa from groups outside Coleopterida. Phylogenetic analyses of data from their preferred matrix (AA sequences from 1478 orthologous genes), recovered Polyphaga sister to a clade containing the other three suborders. Adephaga was sister to Archostemata (Priacma Leconte), and these together were sister to Myxophaga (Lepicerus). These relationships are compatible with the results of Peters et al. (2014), who sampled transcriptomic data from five Coleoptera and one Strepsiptera (among many other non-Coleopterida), but did not include any Myxophaga. The subordinal relationships in Misof et al. (2014) differ from the relationships recovered herein, only in the placement of Myxophaga, and the results of Peters et al. (2014;although lacking Myxophaga) are fully compatible with the present study. Notably, these studies recover a basal split between Polyphaga and the other suborders. These subordinal relationships have not otherwise been recovered in a phylogenetic analysis of molecular or morphological data.

Monophyly and interrelationships of the suborders of beetles
All of the suborders of Coleoptera were monophyletic in our study, in contrast to previous molecular phylogenetic studies containing hundreds to thousands of taxa, where Archostemata was recovered in Myxophaga or was otherwise not consistently recovered as a clade (e.g. Hunt et al., 2007;Bocak et al., 2014). The subordinal relationships we recovered were the same under both BI and ML (Fig. 3), but differ from other arrangements proposed to date. However, none of the subordinal relationships that have been proposed in molecular or morphological studies to date has consistently strong nodal support or has otherwise emerged as the consensus topology (e.g. Shull et al., 2001;Hughes et al., 2006;Hunt et al., 2007;McKenna & Farrell, 2010). Lawrence et al. (2011) in a large companion study of morphological data containing most of the same higher taxa as the present study (both were part of the BToL Project), recovered Archostemata and Adephaga as sister groups, and Myxophaga and Polyphaga as sister groups, but the subordinal relationships lacked strong statistical support (as here). The morphological studies of Beutel & Haas (2000), Beutel et al. (2008) and Friedrich et al. (2009) suggest a sister-group relationship between Archostemata and the remaining three suborders (Adephaga and a clade comprising Polyphaga and Myxophaga). An aspect in common between the recent analysis of morphological data by Lawrence et al. (2011) and the present molecular study is that Adephaga share a more recent common ancestor with Archostemata than with Polyphaga (Fig. 2). The molecular study of Bocak et al. (2014) was rooted with Archostemata. In contrast with Bocak et al. (2014) and recent morphological studies, there was no evidence in our analyses for a sister-group relationship between Archostemata and the other three suborders.
Some differences between our results and the results of previous studies, particularly at higher taxonomic levels, are clearly due to differences in rooting and outgroups (or lack thereof) (e.g. Yang & Rannala, 2012). However, differences in the numbers and kinds of genes analysed are likely also important (e.g. McKenna, 2014). Although it would be interesting to investigate extensively the relative contributions of different subsets of genes (for example, only NPC genes), the limited data available within any subset makes this problematic. For example, in our matrices, 54 taxa (∼15% of the total, including OGs) contain less than half of the NPC AA sequences, making the results from analyses of these data alone difficult to compare to the results from combined analyses. For this reason, the analyses herein are focused on the combined 8-gene dataset. Comparative analyses of the results from different groups of genes will be more fruitfully done once genomic methods yield more extensive data.
A sister-group relationship between Polyphaga and the other suborders of Coleoptera, as recovered herein, implies that extensive simplifications of the thoracic skeleto-muscular system took place independently in the non-archostematan suborders, especially in Myxophaga and Polyphaga (Beutel & Haas, 2000;Friedrich et al., 2009). The archostematan families Ommatidae and Cupedidae have preserved the most ancestral condition of this character system (Friedrich et al., 2009) and also exhibit elytral window punctures and a tuberculate surface structure, which likely belong to the groundplan of Coleoptera in the widest sense (e.g. Beutel, 1997). A sister-group relationship between Archostemata and Myxophaga, as recovered herein, is not currently supported by any morphological characters, except perhaps certain features of wing folding in repose (e.g. Crowson, 1981;Grimaldi & Engel, 2005), and these small relict groups differ strikingly in their life habits, the former being associated with wood (larvae, to the extent known, are xylophagous) and the latter with hygropetric or riparian habitats. Nonetheless, the separation of Polyphaga from the other beetles in our study is supported by data from wing venation (Kukalová-Peck & Lawrence, 1993, 2004, and is compatible with Peters et al. (2014) who analysed transcriptomic data from exemplars of Holometabola and outgroups (1343 genes; their small sample of beetles did not include Myxophaga). The congruent subordinal-level topologies recovered in the present study under BI and ML, and the reciprocal monophyly of the suborders in our study -also monophyletic in the morphological study of Lawrence et al. (2011) -are similarly encouraging. Nonetheless, except for the sister-group relationship between Archostemata and Myxophaga [also recovered in several other recent molecular phylogenetic studies, e.g. Farrell (2010)], the interrelationships of the suborders lack consistently strong nodal support in the present study and should therefore be viewed as tentative. The relationships we recovered among series, superfamilies and families, are similar in many respects to those reported in other recent molecular and morphological phylogenetic studies, but show improvements in resolution and nodal support. However, the interrelationships of series and superfamilies in the present study varied somewhat between the ML and BI trees. Clade support was similarly variable, and often negligible or weak in the ML tree, which lacked monophyly constraints.
The low MLB and BPP values recovered for many deep nodes, for example between suborders, series and superfamilies, in this and other higher-level molecular phylogenetic studies of beetles to date are likely a result of some combination of insufficient/weak phylogenetic signal, conflicting phylogenetic signal, rogue taxa (due to the other factors noted here), missing data, short internal branches and/or extreme variation in evolutionary rates among taxa. Strepsiptera clearly contributed to reduced nodal support at multiple depths within our trees, perhaps most notably at deep nodes, as evidenced by comparing the results of unconstrained analyses with results from analyses where Strepsiptera was constrained to the OG (see Results; Fig. 2; Figures S2 and S3). Subordinal relationships in Coleoptera have not yet been comprehensively assessed by analysing a phylogenomic dataset, such as one containing Strepsiptera and at least one exemplar from each of the suborders, series and superfamilies of Coleoptera, and a large number of nucleotide and AA characters from NPC genes. Myxophaga and most series and superfamilies of Polyphaga are lacking from all such studies to date (Niehuis et al., 2012;McKenna, 2014;Peters et al., 2014). However, preliminary analyses of such a dataset (D.D. McKenna, unpublished data) suggest that unambiguously resolving subordinal relationships will be a persistent challenge.

Relationships within Archostemata
Limited representation of Archostemata (by taxa and/or data) has been the norm in all otherwise broadly taxon-sampled studies to date. Hunt et al. (2007) sampled a single archostematan, Distocupes varians Lea, for one gene (18S).  included two genera/species of Archostemata and one gene (18S). Bocak et al. (2014) sampled six species of Archostemata for up to four genes, but data were missing in their study for more than half of the taxon-by-gene combinations for Archostemata. In the present study, seven species of Archostemata were sampled for up to eight genes, with relatively few (16%) missing data. Eight percent (half) of the missing data for Archostemata in the present study was from the difficult NPC gene alpha-spectrin. Our study thus provides the most robust insights to date into: (i) the internal phylogeny of Archostemata and (ii) the phylogenetic placement of Archostemata relative to the other three suborders of beetles, based on molecular phylogenetic analyses. Nonetheless, two extant archostematan families -Crowsoniellidae and Jurodidae -both monospecific in the living fauna and known only as type specimens, were not available for our analysis. The placement of Priacma sister to the remaining Cupedidae is consistent with the morphological study of Beutel & Hörnschemeyer (2002). An ommatid-micromalthid clade (containing Tetraphalerus and Micromalthus in the present study) is in contrast to a strongly supported cupedid-micromalthid clade found in morphology-based studies (Beutel & Hörnschemeyer, 2002;Beutel et al., 2008;Friedrich et al., 2009;. However, neither Ommatidae nor Cupedidae were monophyletic in the results of Lawrence et al. (2011), and reconstructing the phylogeny of Archostemata using morphological data is impeded by the miniaturization and highly aberrant adult morphology of Micromalthidae and by the possibly secondary soil-dwelling habits of larvae of Ommatidae (Lawrence, 1999(Lawrence, , 2001, which may have resulted in convergent structural modifications. Thus, the present phylogenetic hypothesis should be viewed as a suitable starting point for additional investigations, whether morphological or molecular.

Relationships within Myxophaga
Considering morphological data and the similar habits/habitats of Myxophaga (hygropetric or riparian habitats, algophagy) a monophyletic origin of the suborder is highly likely (Beutel et al., 1998;Beutel, 1999). Notably, the branching patterns within Myxophaga resulting from BI and ML analyses of the nucleotide sequence data alone are identical (Hydroscaphidae (Torridincolidae (Sphaeriusidae, Lepiceridae))). Nonetheless, this topology contrasts with the results of morphology-based analyses, which suggest the relationships (Lepiceridae (Torridincolidae (Sphaeriusidae, Hydroscaphidae))) (Beutel et al., 1998;Beutel, 1999). A basal position of Lepiceridae is also suggested by plesiomorphies retained in a putative larva of Lepicerus, such as the presence of six stemmata (five or less in the other families), the absence of spiracular gills (present in the other families) and an abdomen distinctly longer than the thorax (equally long or shorter in the other families) (Lawrence et al., 2013). Previous analyses of molecular data have mostly recovered Torridincolidae and Hydroscaphidae as sister groups (e.g. Hunt et al., 2007), with varying placements for the other families. The presence of an unique type of tracheal gill in Myxophaga strongly suggests a clade of all Myxophaga except Lepiceridae, and semi-entognathous mouthparts and rows of lancet-shaped tergal setae suggest a sister-group relationship of Sphaeriusidae and Hydroscaphidae (Beutel et al., 1998;Beutel, 1999;Lawrence et al., 2013).

Relationships within Adephaga
Our analyses support the reciprocal monophyly of the aquatic Hydradephaga (containing the families Amphizoidae, Aspidytidae, Dytiscidae, Gyrinidae, Haliplidae, Hygrobiidae, Meruidae and Noteridae) and terrestrial Geadephaga (containing the families Carabidae, Rhysodidae and Trachypachidae). The monophyly of Hydradephaga is in contrast with the recent morphological study of Beutel et al. (2013) (and many other earlier studies, e.g. Kavanaugh, 1986), which suggests a sister-group relationship between Gyrinidae (here placed in a clade with Haliplidae) and the remaining adephagan families, but is consistent with several other molecular phylogenetic studies (e.g. Shull et al., 2001;Ribera et al., 2002;Vogler, 2005;Hunt et al., 2007;Wild & Maddison, 2008;). The widely accepted Dytiscoidea (e.g. Beutel et al., 2013) were confirmed in the present study, but only under BI . The miniaturized monospecific Meruidae were recovered sister to Noteridae, corroborating some earlier studies based on morphological or molecular data Balke et al., 2008;Dressler et al., 2011;Bocak et al., 2014), but conflicting with others based only on morphology (Dressler & Beutel, 2010;Alarie et al., 2011;Short et al., 2012) which placed Meruidae in a position sister to the remaining Dytiscoidea. The monogeneric Aspidytidae were sister to Amphizoidae, consistent with Balke et al. (2008). The monophyly of Geadephaga is strongly supported in our analyses and its internal relationships are consistent with recent studies using 18S (Shull et al., 2001) or 18S + 28S + WG . The placement of Trachypachidae is unclear in our study. Its appearance as sister to Calosoma in some analyses (with weak BPP support and mostly negligible MLB support) is similar to that seen in some other analyses (e.g. . Trachypachidae is nonetheless the sister group of the remaining Geadephaga in our analyses, either alone, or in combination with Calosoma and perhaps other Carabini. The phylogenetic placement of Rhysodidae has long been uncertain. It has been placed well outside Carabidae (e.g. Regenfuss, 1975;Deuve, 1988) or as a relative of the scaritine or clivinine carabids (Bell, 1967;Baehr, 1979;Beutel, 1990). We recovered Rhysodidae well within Carabidae, consistent with other molecular phylogenetic studies (e.g. . The sister-group relationship between Haliplidae and Gyrinidae was unexpected. We recovered Cicindelinae within Carabidae, in contrast to the results of Bocak et al. (2014) who recovered this group outside of Carabidae.

Interrelationships and internal relationships of the series and superfamilies of Polyphaga
Most of the traditionally recognized series and superfamilies of Polyphaga were monophyletic or were recovered in arrangements consistent with recent studies (Fig. 3). However, the interrelationships and internal relationships of the series and superfamilies of Polyphaga generally lack consistently strong nodal support in this study in the absence of monophyly constraints, consistent with previous studies. Nonetheless, even in the absence of strong nodal support and fully compatible resolution in the Bayesian MCC tree and ML tree (from analysis of nucleotides), some relationships are consistent with most other recent studies. For example, superfamily Scirtoidea and the family Derodontidae are either together sister to the remaining Polyphaga (present study, BI), or form a paraphyletic grade subtending the remaining Polyphaga (present study, ML; Hunt et al., 2007;Bocak et al., 2014). Series Staphyliniformia (including Jacobsoniidae, a family previously considered to be related to Derodontidae), series Elateriformia, and superfamily Scarabaeoidea form the earliest-diverging branches in Polyphaga other than Scirtoidea and Derodontidae. The interrelationships of Staphyliniformia (including Jacobsoniidae), Elateriformia, and Scarabaeoidea remain uncertain, although Elateriformia (including Nosodendridae, a family previously considered to be related to Derodontidae) is most likely outside of the other two groups. The placement of superfamily Bostrichoidea, although not among early-divergent or highly derived Polyphaga, is uncertain in the present study on account of negligible to weak nodal support. Although it is probably the sister group of the species-rich series/clade Cucujiformia (as found herein), other molecular phylogenetic studies have recovered Bostrichoidea in different, rather distant positions. Relationships among the superfamilies of Cucujiformia also remain uncertain. However, Cucujoidea in the traditional broad sense is clearly polyphyletic, consistently forming three clades: (i) Coccinelloidea, (ii) Biphyllidae + Byturidae (an early-divergent clade within Cleroidea) and (iii) Cucujoidea s.s., which may be monophyletic or paraphyletic, likely forming the sister group of the Phytophaga (Chrysomeloidea and Curculionoidea) or a paraphyletic grade subtending the Phytophaga. In the present study, Coccinelloidea is either sister to all other Cucujiformia (under BI) or sister to Tenebrionoidea (under ML). Other molecular phylogenetic studies also recover the polyphyly of Cucujoidea, for example Hunt et al. (2007), Marvaldi et al. (2009), Robertson (2010 and Robertson et al. (2015). Although the extensively taxon-sampled studies of Hunt et al. (2007) and Bocak et al. (2014) recover a polyphyletic or paraphyletic Phytophaga, it appears highly likely that this informal grouping is monophyletic (as in the present study), and its constituent superfamilies (Chrysomeloidea and Curculionoidea) are monophyletic sister groups.

Polyphaga: Derodontoidea and Scirtoidea
The same or similar placements for Scirtoidea and Derodontidae relative to the remaining Polyphaga have been recovered in other recent studies (e.g. Hunt et al., 2007;Bocak et al., 2014). However, the derodontoid family Jacobsoniidae has not been included in any other molecular phylogenetic studies to date. It is worth noting that McKenna et al. (2014) included the same species of Jacobsoniidae examined in the present study in their preliminary phylogenetic analyses of Staphyliniformia and Scarabaeiformia based on DNA sequence data from 28S rDNA and the NPC gene CAD, recovering Jacobsoniidae as a clade within Staphyliniformia in close relation to Staphylinoidea (as in the present study) in most analyses. Jacobsoniidae were ultimately excluded from the analyses in McKenna et al. (2014) because the lack of sampling of beetle taxa outside of Staphyliniformia and Scarabaeiformia made justifying inclusion of Jacobsoniidae difficult, particularly because the two species we sampled are on long terminal branches and their placement within Staphyliniformia thus could have resulted from long-branch attraction or some other artefact. However, the present study includes many other non-staphyliniform beetles, including many other long-branched taxa, and Jacobsoniidae are still recovered within Staphyliniformia (see below for more discussion of this placement). Nosodendridae was ambiguously placed in Bocak et al. (2014), although always part of a clade containing Scarabaeiformia, Bostrichiformia and Elateriformia. The placement of Nosodendron (Nosodendridae) in the present study as either the sister group of Elateriformia, or within Elateriformia in a position sister to Dascilloidea, is therefore compatible with Bocak et al. (2014), but more localized (though lacking nodal support). Nonetheless, placement far from other Derodontoidea further suggests that Derodontoidea as classified in Bouchard et al. (2011) is polyphyletic, as also found by Lawrence et al. (2010aLawrence et al. ( , 2011. Notably, Böving & Craighead (1931) associated Nosodendridae with Dascilloidea.

Polyphaga: series Staphyliniformia
With respect to higher-level relationships of and within Staphyliniformia (excluding Scarabaeiformia, discussed below), the ML and BI trees are largely compatible with each other and with several other recent studies (e.g. Caterino et al., 2005;Beutel & Leschen, 2005bHunt et al., 2007Lawrence et al., 2011;Bocak et al., 2014;McKenna et al., 2014), although the deepest divergences remain ambiguous. A monophyletic Staphyliniformia (containing Hydrophiloidea s.l. and Staphylinoidea) is sometimes recovered (e.g. McKenna et al., 2014;BI only;present study, ML only). However, Bocak et al. (2014) recovered Staphyliniformia as a paraphyletic grade and recovered a polyphyletic Staphylinoidea. Scarabaeiformia, Hydrophiloidea s.s. and Histeroidea are each nearly always supported as monophyletic, and a clade uniting them is strongly supported by the present Bayesian analyses (in which there were some monophyly constraints on the constituent superfamilies; Table S2). Such an arrangement has been previously proposed on the basis of morphological characters (Beutel & Leschen, 2005b). The reciprocal monophyly of Histeroidea and Hydrophiloidea s.s., together forming the clade Hydrophiloidea s.l. in both analyses, was unsurprising. A clade comprising Histeroidea + Hydrophiloidea (s.s.) was found in McKenna et al. (2014), in addition to all of the analyses reported herein. In contrast, Lawrence et al. (2011) and Bernhard et al. (2009; except for their Bayesian analysis) failed to recover a monophyletic Hydrophiloidea s.s., instead recovering Histeroidea as sister to part of Hydrophiloidea s.s.; Short & Fikácěk (2013) assumed but did not test the monophyly of Hydrophiloidea s.s.
(Andotypus + Tropisternus) were each also well-supported in other recent studies, such as Bernhard et al. (2006, 2009), Short & Fikácěk (2013 and McKenna et al. (2014). In contrast, the position of Spercheidae (Spercheus) in relation to these two clades varies widely: as sister to Hydrophilidae s.s. in the present BI analyses (Spercheidae + Hydrophilidae within Hydrophiloidea s.s.), Bernhard et al. (2009, Bayesian analysis), Lawrence et al. (2011) andMcKenna et al. (2014); part of a trichotomy with the other two clades in Short & Fikácěk (2013); sister to all other Hydrophiloidea s.s. in the present ML tree and in Bernhard et al. (2006); sister to Histeroidea in Bernhard et al. (2009, parsimony analysis), or even sister to all other Hydrophiloidea s.l. in Bernhard et al. (2009, bootstrap consensus). Lawrence et al. (2011) recovered the clade Georissidae + Helophoridae as the sister group to Histeroidea, with Spercheidae + Hydrophilidae s.s. as sister to this larger clade. The clade Spercheidae + Hydrophilidae, which we recovered within Hydrophiloidea s.s., and Hydrophiloidea s.s. sister to Histeroidea, is in agreement with earlier studies based on morphology [e.g. Hansen, 1991 (preferred cladogram);Beutel & Komarek, 2004], and the clade Georissidae + Helophoridae [part of the helophorid lineage of Hansen (1991)] is in agreement with results from a recent molecular study of Hydrophiloidea s.s. (Short & Fikácěk, 2013). Within Histeroidea, we recovered Synteliidae (Sphaeritidae + Histeridae) -although  found Sphaeritidae sister to the other two and Lawrence et al. (2011) found weak support for Histeridae sister to a clade comprising the others. Staphylinoidea found support only in McKenna et al. (2014) and the current study, although in the current study with Jacobsoniidae (Derodontoidea) included within it under ML, and as sister to it under BI.
Within Staphylinoidea, the leiodid genus Colon oddly fell outside the Leiodid group in McKenna et al. (2014;ML only) and the current study (BI only). The Staphylinid group (Staphylinidae, including Silphidae and Scydmaeninae) is monophyletic in most studies [but not in Hunt et al., 2007, where Scydmaeninae (as Scydmaenidae) strangely fell outside as sister to Histeroidea], but with only weak nodal support in Lawrence et al. (2011) and with Colon misplaced within it in the Bayesian analysis (herein). Silphidae and Staphylinidae: Scydmaeninae (following Grebennikov & Newton. 2009; formerly treated as a separate family] were each monophyletic, and in most studies fell within some part of Staphylinidae, which (because of Silphidae) was not monophyletic. Staphylinidae was consistently paraphyletic with respect to Silphidae, which was sister to the staphylinid Leucotachinus (Tachyporinae: Tachyporini). Within Staphylinidae, sparse taxon sampling limits the testing of the four-subfamily groupings of Lawrence & Newton (1982, 1995, but Scydmaeninae were consistently recovered as sister to Creophilus (Staphylininae), as expected for those sole representatives of the Staphylinine group. The representatives of the Omaliine (Paraphloeostiba and Glypholoma) and Osoriine (Renardia and Scaphidium) groups were each recovered as monophyla under ML but not BI. The single included member of the Tachyporine group (Leucotachinus) was unexpectedly recovered with strong support as sister to Silphidae, consistent with the unexpected results of McKenna et al. (2014). Silphidae was recovered or otherwise considered to belong within Staphylinidae in other recent studies [e.g. Lawrence & Newton, 1982;Newton & Thayer, 1995;Hansen, 1997;Ballard et al., 1998;Grebennikov & Newton, 2009 (molecular data only); Bocak et al., 2014], but without clear placement.
The inconsistent position of the leiodid Colon, and the placement of Jacobsoniidae are among the most unexpected results within Staphyliniformia, and require further investigation. The position of Jacobsoniidae as sister of Ptiliidae + Hydraenidae under ML, or as sister of all Staphylinoidea under BI, echoes its surprising association with Staphylinoidea in Lawrence et al. (2011); based on analyses of morphological data, the two genera of Jacobsoniidae came out as successive sister groups to (((Ptiliidae)(Hydraenidae)) (Leiodidae + Agyrtidae)). Crowson (1959) commented on a larval feature (fimbriate galea) occurring in Jacobsoniidae and in some Staphylinoidea. He also noted (Crowson, 1960) that Saphophagus (Jacobsoniidae) wing venation is 'completely staphylinoid'. However, the inconsistency of placement and low levels of nodal support recovered herein and in Lawrence et al. (2011) leave it uncertain whether and how Jacobsoniidae is related to Staphylinoidea.

Polyphaga: superfamily Scarabaeoidea
Scarabaeoidea is a well-established monophyletic group (Scholtz, 1990;Browne & Scholtz, 1999;Grebennikov & Scholtz, 2004;Hunt et al., 2007). However, its sister group has long been uncertain. Proposed sister taxa include the Dascilloidea, Hydrophiloidea + Staphylinoidea + Histeroidea (= Haplogastra; Kolbe, 1908) or Hydrophiloidea s.l. Our results support a sister relationship with either Hydrophiloidea s.l. (under ML; Figure S2) or Hydrophiloidea + Staphylinoidea (= Staphyliniformia) (under BI; Fig. 2), and are consistent with other molecular and morphological studies (e.g. Caterino et al., 2005;Beutel & Leschen, 2005b;Smith et al., 2006;Hunt et al., 2007) in refuting Dascilloidea as a possible sister group of Scarabaeoidea (e.g. Lawrence et al., 2011). Taxa included in major clades within the superfamily are largely consistent based on the ML and BI trees, but the interrelationships of these taxa within clades differ (Fig. 7). Within Scarabaeoidea, notable differences between our results and other recent studies include the relationship of Passalidae to derived scarabs rather than early-divergent scarabs and inclusion of the Pleocomidae within the derived clade of phytophagous scarabs (Pleurosticti). However, these and other results for Scarabaeoidea should be considered cautiously because of missing DNA sequence data in our matrices (more than for any other superfamily) due to the use of poorly-preserved tissue for DNA extraction of many species of Scarabaeoidea studied.
The sister-group relationship recovered in the present study between the dung-associated Scarabaeinae and Aphodiinae is well established (e.g. Howden, 1982;Browne & Scholtz, 1998;Smith, 2006;Smith et al., 2006;Lawrence et al., 2011;Ahrens et al., 2014). This clade is proposed to have codiversified with mammals in the Cenozoic (e.g. Scholtz & Chown, 1995;Ahrens et al., 2014), a scenario temporally consistent with our results, which suggest a Late Cretaceous to early Cenozoic origin for the clade (Fig. 2). The clade comprising Hybosoridae + Glaphyridae + Ochodaeidae recovered herein was previously proposed by Lawrence & Newton (1982) based on morphological characters, and later also supported by Scholtz et al. (1988), Browne (1993), and Browne & Scholtz (1995. This clade was also recovered by Smith et al. (2006) in a phylogenetic analysis of 18S and 28S rDNA sequence data from a large sample of species of Scarabaeoidea.
The largely phytophagous Pleurostict Clade (= the 'Phytophagous Clade', containing the species-rich scarabaeoid subfamilies Cetoniinae, Melolonthinae, Rutelinae, and Dynastinae) is widely accepted as monophyletic (e.g. Erichson, 1847;Browne & Scholtz, 1998;Smith et al., 2006;Hunt et al., 2007). However, in the present study this large clade contains a few unexpected groups that are typically recovered elsewhere in Scarabaeoidea: Pleocomidae, Passalidae, and Bolboceratinae. Most previous studies have treated Passalidae and Pleocomidae as early-divergent scarabaeoids (e.g. Grebennikov & Scholtz, 2004). The tendency for groups that are usually considered early divergent to belong to the most derived subclades was noted by Lawrence et al. (2011) who also recovered Geotrupidae and Pleocomidae with groups that are usually considered derived scarabs. Bocak et al. (2014) recovered Pleocomidae nested in a derived group of Geotrupidae. Inclusion of these groups renders Scarabaeidae nonmonophyletic, consistent with Ahrens et al. (2014) and Bocak et al. (2014), but contrary to McKenna et al. (2014), Lawrence et al. (2011 and Smith et al. (2006).

Polyphaga: series Elateriformia
The phylogenetic position of Nosodendridae (also discussed above), although almost certainly within or sister to Elateriformia, remains unclear because of negligible nodal support and variable placement in the analyses reported herein. It is nonetheless recovered near the base of Elateriformia, contradicting the concept of Derodontoidea as delimited in Lawrence et al. (2010a). The monophyly and composition of superfamily Dascilloidea were unsurprising. Within Buprestoidea, Schizopodidae was recovered sister to the remaining Buprestidae, consistent with its recognition as a family distinct from Buprestidae as originally proposed by LeConte (1859) and advocated by Nelson & Bellamy (1991) and Bellamy (2008). These results are also consistent with Evans et al. (2014), except that in the present study Agrilus Heyden & Heyden (Agrilinae) and Acmaeodera Eschscholz (Polycestinae) are sister groups and Julodinae and Buprestinae are sister groups, whereas in Evans et al. (2014) Agrilinae and Buprestinae are sister groups and Julodinae and Polycestinae are sister groups. Outside the placement of Schizopodidae, however, these relationships lack strong nodal support under ML (but not BI) in the present study. Podabrocephalus (Elateroidea) was nested within the byrrhoid family Ptilodactylidae, a position consistent with Wittmer (1969) and Lawrence et al. (2010bLawrence et al. ( , 2011. The position of Eulichas Jacobson (Eulichadidae) sister to Elmidae is notable, because phylogenetic placement of the former has long been controversial. The sister-group relationship of Elateroidea and Byrrhoidea in the BI tree is consistent with the results of Kundrata et al. (2014), but under ML we recovered Byrrhoidea and Burprestoidea as sister taxa, and these together sister to Elateroidea. Within Elateroidea, the recovery of Lissominae sister to Lycidae (and not in Elateridae) was unexpected, but is not unprecedented; the recognition of Lissomidae as a family separate from Elateridae or Throscidae was suggested by Burakowski (1973Burakowski ( , 1975. Other relationships within Elateriformia and Elateroidea were in general agreement with previous studies (e.g. Bocakova et al., 2007;Kundrata et al. 2014).

Polyphaga: superfamily Bostrichoidea
The monophyly and family-level relationships of Bostrichoidea were compatible with some analyses in the recent molecular phylogenetic study of Ptinidae by Bell & Philips (2012), which also included exemplars from the families Dermestidae and Bostrichidae. It is worth noting that in the present study insufficient data were available from Endecatomus Mellie (Endecatomidae) to include it in our final analyses. However, exploratory molecular phylogenetic analyses that included this taxon placed it sister to all other sampled Bostrichoidea. Placement of Bostrichoidea sister to Cucujiformia (with cryptonephric Malpighian tubules as a synapomorphy) in both the ML and BI analyses is inconsistent with Lawrence et al. (2011) and recent molecular phylogenetic studies (e.g. Hunt et al., 2007;Bocak et al., 2014), which place Bostrichoidea near or among early-divergent Polyphaga (Staphyliniformia, Scarabaeiformia, Elateriformia). However, none of these studies recovers consistently strong support for the placement of Bostrichoidea within Polyphaga. Crowson (1960) proposed that Cucujiformia originated from a 'dermestoid type'. This view is compatible with the results of our phylogenetic analyses, in which Bostrichoidea is recovered sister to series Cucujiformia. Superfamily Cucujoidea was polyphyletic, consistent with other recent studies (e.g. Vogler, 2005;Hunt et al., 2007;Robertson et al., 2008;Hunt & Vogler, 2008;Marvaldi et al., 2009;Bocak et al., 2014). The superfamily therefore appears to be a convenience group for beetles that share certain features (e.g. clubbed antennae, non-heteromerous tarsi, ring-shaped aedeagus) but do not fit elsewhere. Indeed, no synapomorphies are known to support its monophyly (Leschen et al., 2005). Morphological studies first suggested Cucujoidea was not monophyletic. For example, Leschen et al.'s (2005) cladistic analysis of 'basal Cucujoidea' (i.e. Cucujoidea not including the Cerylonid Series) demonstrated that from a morphological perspective, basal cucujoids could not be separated from Cleroidea. Wanat (2007) studied the male genitalia of Curculionoidea and other beetle groups and noted that not only was the tegmen or parameres of Coccinellidae not homologous to those of the remaining Cucujoidea, but that Cucujoidea may further be paraphyletic with respect to Phytophaga given the inferred homology of tegminal plates between these groups.

Polyphaga: series Cucujiformia
The cucujoid families Biphyllidae and Byturidae were recovered as an early-divergent clade within Cleroidea as in other recent molecular phylogenetic studies (e.g. Hunt et al., 2007;Bocak et al., 2014). They were also suggested by Lawrence & Newton (1995) to belong in Cleroidea based on morphology. Ample support now exists to justify the reclassification of these families to Cleroidea. We consistently recovered a cucujoid clade comprising the Cerylonid Series, a group that was originally proposed by Crowson (1955), recognizable by several larval and adult characters (Robertson et al., 2008). Although the constitution of the Cerylonid Series has been refined since 1955, the currently recognized families have consistently been recovered as a clade in molecular phylogenetic studies (e.g. Hunt et al., 2007;Robertson et al., 2008;Marvaldi et al., 2009;Robertson, 2010;Bocak et al., 2014). However, the morphological study of Lawrence et al. (2011) did not recover a monophyletic Cerylonid Series. Nonetheless, given its relative diversity and the strong, consistent support that it receives in all other phylogenetic studies to date, this clade warrants superfamilial status as 'Coccinelloidea', following Robertson et al. (2015). We recovered the remaining Cucujoidea (not including Byturidae and Biphyllidae) as a clade, again consistent with Robertson et al. (2015). However, other recent molecular phylogenetic studies with dense cucujoid taxon sampling have not recovered this group as a clade (e.g. Hunt et al., 2007;Hunt & Vogler, 2008;Bocak et al., 2014), and the results of some of our analyses were suggestive of its potential paraphyly with respect to Phytophaga (see above and Results). Hunt et al. (2007) supported Silvanidae and Phloeostichidae imbedded within Phytophaga. Nitidulidae, Kateretidae and Passandridae were recovered together forming the sister group to Curculionoidea in Bocak et al.'s (2014) analysis, and Sphindidae + Cybocephalidae were supported as more closely allied to Phytophaga than the remaining Cucujoidea s.s.
Within Coccinelloidea, the division into two major clades is a recurring pattern found in other molecular phylogenetic studies (e.g. Hunt et al., 2007;Robertson et al., 2008;Bocak et al., 2014), with one exception: Latridiidae is often recovered in the clade containing Coccinellidae and allies Robertson, 2010;Bocak et al., 2014), not in the clade with Cerylonidae, Bothrideridae and Discolomatidae (present study; Robertson et al., 2008). Cerylonidae, Bothrideridae and Discolomatidae were also close relatives in Hunt et al. (2007), Robertson et al. (2008) and Bocak et al. (2014). Bothrideridae and Cerylonidae were paraphyletic with respect to each other and to Discolomatidae in the present study. Most previous studies lacked the exemplar diversity needed to rigorously test the monophyly of these families. However, Hunt et al. (2007) and Robertson et al. (2015) reach the same conclusions, and the polyphyly of these families has been suspected based on morphological evidence (Ślipiński, 1990;Lawrence, 1991a;Ślipiński & Pakaluk, 1991). The current definitions of these three families are formally revised in light of these findings in Robertson et al. (2015). The two exemplars of Latridiidae, representing the two recognized subfamilies, were recovered together with strong nodal support. The placement of Latridiidae, be it with Cerylonidae, Bothrideridae and Discolomatidae, or within the clade comprising Coccinellidae, Endomychidae and allies, is not consistent among recent molecular phylogenetic studies. Both Hunt et al. (2007) and Bocak et al. (2014) support the latter placement, whereas the present study strongly supports Latridiidae as forming the sister group to the former clade. The enigmatic genus Akalyptoischion Andrews was not recovered near Latridiidae, supporting the decision by Lord et al. (2010) to remove it from that family and recognize the monogeneric family Akalyptoischiidae.
Endomychidae was polyphyletic; another result that has been suspected based on morphology (Ślipiński & Pakaluk, 1991) and demonstrated with molecular data . A subset of endomychid exemplars appears in a clade where they are rendered paraphyletic with respect to Corylophidae and Alexiidae. The placement of Bystus (Endomychidae: Anamorphinae) closely allied with Corylophidae is not surprising and consistent with previous studies (Robertson et al., 2008(Robertson et al., , 2012. The other endomychid exemplars (Endomychus, Epipocus) appear in a second clade where, with Akalyptoischiidae, they form the sister group to Coccinellidae. These findings are consistent with those of Robertson et al. (2008). Even though the taxonomic representation in the two studies is quite different [e.g. neither Alexiidae nor Akalyptoischiidae were sampled in Robertson et al. (2008)], both studies recover one endomychid clade with Anamorphinae (Endomychidae) and Corylophidae, and a second endomychid clade comprising the 'Higher Endomychidae' of Tomaszewska (2005) with Coccinellidae. Endomychidae was also polyphyletic in Lawrence et al. (2011). Surprisingly, we found only modest support for the monophyly of Corylophidae. The internal relationships are, however, entirely consistent with Robertson et al. (2012), andconsistent withŚlipiński et al. (2009) in the recovery of Periptyctus Blackburn sister to all other taxa sampled. Coccinellidae is a well-supported clade in our analyses, as might be expected given the support found for the group in other studies to date (e.g. Robertson et al., 2008;Seago et al., 2011). In addition, the internal relationships of Coccinellidae are consistent with the two-subfamily classification proposed by Seago et al. (2011Seago et al. ( ) [see alsoŚlipiński (2007]; the lone representative of Microweiseinae (Delphastus) separates from the seven other coccinellid exemplars, all representing Coccinellinae, at the basal split in the family, as expected. All higher relationships between the coccinellids are poorly supported, a recurring pattern for phylogenetic studies of the family (e.g. Giorgi et al., 2009;Magro et al., 2010;Seago et al., 2011).
Within Cucujoidea s.s. [the basal Cucujoidea of Leschen et al. (2005) minus Biphyllidae and Byturidae], all analyses recovered Erotylidae with strong nodal support. These findings confirm previous studies (e.g. W ȩgrzynowicz, 2002;Leschen, 2003b;Robertson et al., 2004;Leschen & Buckley, 2007) that support subsuming Languriidae within Erotylidae. Sphindidae was rendered paraphyletic by Protocucujidae, a family generally considered to be very closely related (Sen Gupta & Crowson, 1979;McHugh, 1993;Ślipiński, 1998;Chiao & McHugh, 2000;Leschen et al., 2005), and also Helotidae under BI. Sphindidae lacks an unambiguous morphological synapomorphy, and adult Ericmodes Reitter and Protosphindus are strikingly similar anatomically. Myxomycophagy was proposed as a potential synapomorphy for Sphindidae, but the biology of Protocucujidae is poorly known. The relationship of these two families should nonetheless be re-examined. The location of the clade Sphindidae + Protocucujidae in the current study is intuitively pleasing because Sphindidae is generally considered to have features of a basal cucujoid. In other recent, deeply taxon-sampled molecular phylogenetic analyses, the placement of Sphindidae has been inconsistent, often puzzling. For example, Hunt et al. (2007) recovered Sphindidae sister to the large clade Lymexyloidea + Tenebrionoidea. In Bocak et al. (2014), and Cline et al. (2014) Sphindidae was recovered in a small clade as the sister group of Cybocephalinae (Nitidulidae). The cause for this instability is not clear. However, these and many of the other branches deep within Cucujoidea s.s. and deep within Cucujiformia as a whole, are among the shortest in the whole beetle tree ( Figure S2).
Laemophloeidae and Propalticidae were recovered as sister taxa, consistent with previous morphological (e.g. Leschen et al., 2005) and molecular studies Bocak et al., 2014). McElrath et al. (2015) found Propalticidae to be deeply nested within Laemophloeidae and formally subsumed the family there. Phalacridae was sister to a clade comprising Laemophloeidae + Propalticidae, consistent with the results of Hunt et al. (2007), Bocak et al. (2014), andMcElrath et al. (2015). There is strong support for the monophyly of Nitidulidae + Kateretidae, as in Lawrence et al. (2011). These families have historically been considered confamilial. Although there is strong support for some clades within Nitidulidae, there is relatively weak support for the family as a whole. Monotomidae has been considered by other authors to be part of a 'nitiduloid assemblage' (Leschen et al., 2005), and its placement sister to Nitidulidae + Kateretidae is consistent with this thinking. It is noteworthy that Smicrips (Smicripidae), which also has been proposed to be part of the 'nitiduloid assemblage', is not recovered in this clade, instead appearing (but with negligible ML support) in a clade with Boganiidae and Hobartiidae. Crowson thought Boganiidae was a potential sister taxon of Chrysomeloidea (Crowson, 1990). However, here Boganiidae (represented by Paracucujus) is embedded in Cucujoidea s.s., suggesting that its peculiar characters (e.g. articulated larval mala, distinct area of microsculpture on the hindwing, etc.) are derived. Nonetheless, the phylogenetic positions of Hobartius, Paracucujus and Smicrips -and to a lesser degree, Nitidulidae, Kateretidae and Monotomidae -were unstable in our analyses, and nodal support for the placement of these taxa, and for the deep splits in Cucujoidea s.s. in general, were mostly negligible, further highlighting the uncertainty surrounding the monophyly and deep splits in Cucujoidea s.s. The ML tree contains a clade of small austral families, including Priasilphidae + Agapythidae, sister to Hymaea (Phloeostichidae). This grouping is not surprising given that all of these families were considered to be members of one family, Phloeostichidae, until recently (Leschen et al., 2005). The polyphyly of both Cryptophagidae (four exemplars) and Silvanidae (two exemplars) was unexpected and is inconsistent with previous analyses of morphological (e.g. Lawrence et al., 2011) andmolecular data (e.g. McElrath et al., 2015), which suggest these families, at least to the extent sampled, are monophyletic.
Tenebrionoidea, with the inclusion of Lymexyloidea: Lymexylidae was monophyletic, but its monophyly and early splits lacked strong nodal support, as in other recent molecular phylogenetic studies (e.g. Gunter et al., 2014). The phylogenetic placement of Lymexyloidea relative to other Tenebrionoidea was unclear in our study because of the lack of nodal support across the backbone of Tenebrionoidea. Nonetheless, Lymexyloidea was recovered within early-divergent Tenebrionoidea in the ML and BI trees. Other molecular phylogenetic studies recover Lymexyloidea within Tenebrionoidea  or sister to Tenebrionoidea Gunter et al., 2014), but they, too, lack nodal support for these relationships. We sampled only one species of Lymexyloidea (Lymexylidae: Atractocerus); therefore, we were unable to assess the monophyly of the superfamily.
Within Tenebrionoidea, Lymexylidae, Aderidae, Anthicidae, Meloidae, Mordellidae, Ripiphoridae and Stenotrachelidae formed a well-supported clade sister to the rest of the superfamily. Similar relationships were recovered in the morphological study of Lawrence et al. (2011) and several other molecular phylogenetic studies Bocak et al., 2014;Gunter et al., 2014;(Kergoat et al., 2014a,b). However, this contrasts with the traditional view that Tetratomidae, Mycetophagidae, Archeocrypticidae, Pterogeniidae and Ciidae represent ancestral forms within the superfamily (Crowson, 1966;Lawrence, 1977). Tetratomidae, Salpingidae, Ulodidae and Promecheilidae were polyphyletic, consistent with the morphological study of Lawrence et al. (2011). Trachelostenus (Trachelostenidae) and Leaus (incertae sedis) were recovered as sister taxa well within Tenebrionidae, as suggested by Matthews & Lawrence (1992). The Bayesian tree strongly supports the monophyly of the Salpingid group (Watt, 1987), which includes Boridae, Pyrochroidae [added by Pollock (1994)], Pythidae, Salpingidae and Trictenotomidae. The three Southern Hemisphere families Chalcodryidae, Promelcheilidae and Ulodidae formed a strongly supported clade under both ML and BI. Polypria (Oedemeridae: Polypriinae) was unexpectedly sister to Mycteridae (Hemipeplus and Lacconotus), contradicting its placement by Lawrence (2005) in the family Oedemeridae. Hyporhagus (Zopheridae: Monommatini) was sister to Scraptiidae, well removed from the other Zopheridae sampled, and in contradiction to the results of morphological studies byŚlipiński & Lawrence (1997Lawrence ( , 1999. However, many apomorphies in the Zopheridae are larval characters that may be convergent. Placement of the Incertae sedis taxon Rhizonium was not strongly supported, but it was recovered in the above-mentioned early-divergent clade in both the Bayesian and ML analyses. This is in contrast with its placement in the Zopheridae: Colydiinae (Lawrence, 1980;Ivie &Ślipiński, 1990), or Zopheridae incertae sedis (Leschen, 2003a). The family-level placement of the enigmatic genus Lagroida Fairmaire & Germain (currently placed in Anthicidae; Lawrence & Britton, 1991;Costa et al., 1995;Lawrence et al., 2010c) was uncertain in our analyses, although none of our molecular phylogenetic analyses recover it within Anthicidae.
Within Cleroidea, the trogossitids Acalanthus, Eronyxa, Grynoma and Thymalus were recovered as a clade, sister to Acanthocnemidae, contradicting Majer (1994) who considered Acanthocnemidae to be part of the melyrid lineage.  suggested a more basal position of Acanthocnemidae within Cleroidea based on the newly discovered larva. The morphological analysis of Lawrence et al. (2011) also supported a relationship of Acanthocnemidae to Trogossitidae and not the melyrid group. The placement of Temnoscheila (Trogossitidae: Trogossitinae) sister to Isoclerus (Thanerocleridae) is inconsistent with the results of the molecular analysis of Gunter et al. (2013), which included only cleroid taxa and resulted in a cladogram in which Thanerocleridae was within the main clerid clade (excluding only Tillinae). Whether these results indicate a further splitting of Trogossitidae into more than two groups [the aforementioned plus Rentonellum (Rentoniinae), which was sister to all other Cleroidea and has not been included in any molecular phylogenetic studies of Cleroidea to date], is not clear. Trogossitidae is nonetheless clearly not monophyletic, as has been observed in other studies Gunter et al., 2013;Bocak et al., 2014). Phycosecidae is placed within the remaining melyrid lineage as suggested by Majer (1987), and the sister relationship between Idgia (Prionoceridae) and Melyridae corroborates results from the recent molecular phylogenetic studies of Bocakova et al. (2012), Gunter et al. (2013) and Bocak et al. (2014). The placement of Rentoniinae (Trogossitidae) sister to the remaining cleroids is similar to the results of Lawrence et al. (2011). Potential long-branch issues aside, doubts have been expressed about the placement of Rentoniinae in Trogossitidae (Lawrence &Ślipiński, 2013a;Gimmel & Leschen, 2014). Although the placement of Biphyllidae + Byturidae sister to the cleroid clade excluding Rentoniinae contradicts the results of most morphological analyses [in particular, Leschen et al. (2005), which places both families within Cucujoidea s.s.], the presence of a cleroid-like aedeagus in both families was noted by Lawrence & Newton (1995) and Lawrence et al. (2014), and this result is consistent with other molecular phylogenetic studies (discussed above).
The informal grouping Phytophaga -superfamily Chrysomeloidea plus its sister taxon, superfamily Curculionoidea -was recovered as a clade in all analyses, corroborating previous studies with fewer genes and (generally) less clade support (e.g. Farrell, 1998;Marvaldi et al., 2009;. This is, however, the first broadly sampled molecular phylogenetic study of Coleoptera to report a monophyletic Phytophaga. In Bocak et al. (2014), Phytophaga was rendered paraphyletic by Nitidulidae (Cucujoidea s.s.), which was sister to Curculionoidea. In Hunt et al. (2007), Phytophaga was rendered paraphyletic by Silvanidae and Phloeostichidae (Cucujoidea s.s.), which were sister to Curculionoidea in their 320-taxon dataset, and Chrysomeloidea was polyphyletic. Within Phytophaga, superfamily Chrysomeloidea contained two major clades: the family Chrysomelidae, and the family Cerambycidae s.l. (plus Megalopodidae and Orsodacnidae), and with internal relationships mostly in agreement with results from other recent molecular or morphological studies (e.g. Reid, 1995Reid, , 2000Farrell, 1998;Farrell & Sequeira, 2004;Gomez-Zurita et al., 2007;Švácha & Lawrence 2014a-d). The polyphyly of Vesperidae was unexpected and is not supported by morphology (e.g. Švácha & Lawrence, 2014a). No molecular phylogenetic studies have sampled more than one species of Vesperidae. Nonetheless, these relationships are not well supported, and the internal branches uniting these taxa are all very short, whereas the terminals are relatively long.
Within Curculionoidea, the unstable placement of Nemonyx, rendering Nemonychidae paraphyletic under BI, and rendering Anthribidae paraphyletic under ML suggests a closer affiliation of Nemonyx (Nemonychinae) with Anthribidae (including Urodontinae) than with other taxa currently placed in Nemonychidae. This (or similar) has been noted in other studies (e.g. Oberprieler et al., 2007;). Certain other family-level relationships, such as the placement of Belidae and Attelabidae, were inconsistent across analyses and with relationships reported in other previously published studies, but lacked strong nodal support. There is nonetheless agreement between the present results and previous studies about the earliest divergence of Curculionoidea leading to nemonychid-like and belid-like weevils. Moreover, our results from analysis of 18S and 28S nucleotides plus AAs ( Figure S4) are concordant with the morphological hypothesis on weevil interfamilial relationships (e.g. Marvaldi et al., 2002;Oberprieler et al., 2007), showing a basal split between the Nemonychidae-Anthribidae clade and the remaining curculionoid families. The sister-group relationship of Caridae to the clade Brentidae + Curculionidae, and the internal higher level relationships of the family Curculionidae are in general agreement with current views on weevil phylogeny based on morphological and/or molecular data (e.g. Marvaldi et al., 2002Marvaldi et al., , 2009Oberprieler et al., 2007;Haran et al., 2013;Gillett et al., 2014). Within Curculionidae, two members of the Brachycerinae appear in separate, though relatively basal, positions, suggesting that this subfamily is not monophyletic, again consistent with other studies (e.g. Gillett et al., 2014). Notably, the platypodines form a clade with the Dryophthorinae, a relationship contentious with traditional views that link platypodines with the Scolytinae (e.g. Kuschel et al., 2000). A close relationship of Platypodinae to Dryophthorinae was, however, originally suggested by Marvaldi (1997) based on morphological evidence from immatures and is now supported by evidence from several molecular phylogenetic studies (e.g. Haran et al., 2013;Bocak et al., 2014;Gillett et al., 2014).

Timing and patterns of diversification in beetles
We report the first timetree for beetles reconstructed using Bayesian methods that co-estimate node ages along with phylogeny (see Materials and methods). The reconstructed timing of the split between Neuropteroidea (comprising Coleoptera + Neuropterida + Strepsiptera) and Hymenoptera at ∼298 Ma (95% HPD: 319 to 282 Ma) is compatible with the fossil record and the developing view (e.g. Nel et al., 2013;Misof et al., 2014) that Holometabola originated in the Carboniferous. The split between Coleoptera and Strepsiptera is estimated to have occurred in the latest Carboniferous or Early Permian at which time all of Earth's major landmasses were united as the supercontinent Pangaea. The largest mass extinction in the Phanerozoic occurred near the end of the Permian, peaking ∼253 Ma (uppermost Permian), approximately the same time as the estimated appearance of crown group Coleoptera. The basal split in Coleoptera produced the clade Archostemata + Adephaga + Myxophaga and the clade Polyphaga in the Early to Middle Triassic, with the split between Archostemata and Myxophaga and the split between Adephaga and Archostemata + Myxophaga occurring shortly thereafter (also in the Triassic). Crown Myxophaga, Adephaga and Archostemata appeared in the latest Triassic or earliest Jurassic. The supercontinent of Pangaea existed until the mid-Triassic, after which it began to gradually rift into Laurasia to the north and Gondwana to the south, with the continental climate eventually shifting from mostly dry (Triassic) to mostly humid (Jurassic and Cretaceous). The implications of such changes for beetles remain unclear, but many of the series and superfamilies that dominate the modern beetle fauna originated during this time, perhaps facilitated by the increase in landscape-level heterogeneity and complexity, latitudinal expansion of characteristically tropical habitats and biotas, and the further development of intimate and coevolved interactions with plants (especially involving flowering plants during the Cretaceous) and animals, not to mention the invasion of beetles into novel arid or aquatic habitats, to which they may have been preadapted by way of elytral covering of the spiracles and other features (Lawrence & Newton, 1982;Beutel, 1997).
We generally recovered slightly younger mean estimated divergence times for most subordinal-, series-and superfamily-level relationships in beetles than previous ordinal-level molecular studies (Table 2; Hunt et al., 2007 2 ;). This may result at least in part from the use of well-established, and therefore typically more conservative fossils for calibration, and/or the misidentification of early fossil Coleoptera used in other studies as belonging to crown groups when they instead belong to stem groups.
For example, proposed crown group Archostemata are known from the Late Triassic (201-235 Ma) (e.g. Ommatidae in Ponomarenko, 1963), suggesting that the estimated age for crown group Archostemata reported herein (median ∼158 Ma, 95% HPD: 192 to 123 Ma) may be too young, and that the real age lies beyond the estimated 95% HPD in our study. However, it is of course also possible that Late Triassic fossil Archostemata actually belong to the archostematan stem group, which is estimated to have split from Myxophaga in the Triassic ∼220 Ma (95% HPD: 237 to 205 Ma), and that the first crown group Archostemata indeed do not appear until the Jurassic.
The two previous estimates of the age of the suborders of beetles based on near-comprehensive molecular phylogenies calibrated with fossil data have been fairly consistent. Hunt et al. (2007) used seven fossil age constraints to calibrate their Bayesian consensus tree, and dated internal nodes via penalized likelihood (Sanderson, 2002). The age of the split between the suborders Myxophaga + Archostemata and the suborders Adephaga + Polyphaga was fixed in their analyses at 285 Ma. , using nonparametric rate smoothing (Sanderson, 1997), estimated that the split between Adephaga and Polyphaga occurred ∼269 to 265 Ma (mean 266.4 Ma), just slightly later than Hunt et al. (2007) (Table 2), who estimated this split to have occurred ∼277 Ma. However, the subordinal-level topologies of Hunt et al. (2007) and  were the same, and differ substantially from the subordinal-level topology reported herein. Further, Hunt et al. (2007) and  were both deeply taxon-sampled, but used data from just 1-3 genes. In the case of the three-gene study , the matrix also had considerable missing data, and both studies incorporated fewer fossils into their analyses than were included in the analyses reported herein.  reported only subordinal divergence times on account of the lack of resolution and nodal support at lower taxonomic levels in their trees. Nonetheless, some comparisons can be made to the present study. For example, in the present study Archostemata and Myxophaga split from their sister group (Adephaga) at ∼242 Ma, whereas in  Archostemata + Myxophaga split from their sister group (Adephaga + Polyphaga) at ∼267 Ma. In the present study, unlike the aforementioned previous studies, only one or two lineages of crown group Coleoptera are proposed to have survived the end Permian extinction, with stem group representatives of all four extant suborders appearing by the end of the Triassic. Misof et al. (2014), which was focused on Hexapoda, but included eight exemplar Coleoptera, estimated the timing of origin of crown Coleopterida (Coleoptera + Strepsiptera) at ∼286 Ma (Permian) and the origin of crown Coleoptera at ∼270 Ma (also Permian). These dates are similar to the estimates reported herein. For example, the timing of origin of Coleopterida was estimated at 278 Ma, 8 Ma younger than the mean estimate of Misof et al. (2014) which falls within its 95% HPD, and the timing of the origin of crown group Coleoptera was estimated at 253 Ma, 17 Ma less than the mean estimate of Misof et al. (2014).
Our results within Polyphaga are generally compatible with the fossil record as characterized by Grimaldi & Engel (2005). One of several notable differences involves the superfamily Staphylinoidea. In the present study, crown group Staphylinoidea are estimated to have originated ∼193 Ma (95% HPD: 210 to 175 Ma). However, a proposed crown group staphylinid, Leehermania prorova, is known from the Carnian (235 to 228 Ma) of southern Virginia, and an undescribed possible staphylinid is known from the Anisian (247 to 242 Ma) of Grès à Voltzia, France (Papier et al., 2005;Chatzimanolis et al., 2012). These fossils are substantially older than the estimated 95% HPD for even stem group Staphyliniformia (+ Scarabaeiformia: Scarabaeoidea) in our study (median 200 Ma, 95% HPD: 217 to 183 Ma). Although attribution of these fossils to Staphylinidae has been questioned 3 [Chatzimanolis et al. (2012) and Grebennikov & Newton (2012), respectively], they highlight the possibility that some of the divergence times in the beast chronogram (Fig. 2) may be underestimated because we used relatively unambiguous, and therefore often conservative, fossil-based ages as priors on node ages in our analyses. Unequivocal crown group staphylinids occur by the Middle Jurassic Period (e.g. Chatzimanolis et al., 2012), consistent with our results.
Convergence between our nodal age estimates and those of most lower-level studies further suggests that our estimates are reasonable. For example, crown group Chrysomeloidea and Curculionoidea are estimated herein to have appeared near the end of the Jurassic (∼145 and ∼150 Ma, respectively), near the first appearance of flowering plants (Bell et al., 2010), and consistent with estimated divergences within Phytophaga and its descendant superfamilies Curculionoidea and Chrysomeloidea, as reported by . A recently described fossil derodontid from the middle Jurassic (∼165 Ma; Cai et al., 2014), is not only the first known for the early-divergent polyphagan family Derodontidae, but also fully consistent with our results, which indicate that crown group Derodontidae first appeared ∼175 Ma. Some estimated ages in our study are much older than select other estimates. For example, Gomez-Zurita et al. (2007) propose a relatively young age for crown Chrysomelidae (∼75 Ma). This is much younger than in the present study (∼130 Ma) and younger than in other molecular timetrees to date (e.g. Hunt et al., 2007;Wang et al., 2013). Most modern families and subfamilies of Coleoptera, including the crown groups of a majority of the most species-rich families, are estimated herein to have Cretaceous origins (Figs 2, 16), in contrast to the results of Hunt et al. (2007), which indicate a Jurassic origin for many such lineages.

Diversification rates
Crown group Coleoptera experienced an increase in diversification rate over Neuropteroidea as a whole (Table 3; Fig. 2). However, these rates, which are 0.025 lineages per million years (Ma) for Neuropteroidea and 0.037 lineages/Ma for Coleoptera, are not unusually high when compared to other animals. For example, Neoaves has an estimated rate of 0.089 lineages/Ma (Alfaro et al., 2009), but that clade is much younger than Coleoptera, highlighting the role of clade age in extant beetle diversity. Hunt et al. (2007) estimated a rate of 0.05-0.07 lineages/Ma for Coleoptera, approximately twice the rate calculated herein. Nonetheless, in the present study 10 clades within Coleoptera were identified as too species-rich to result from the background diversification rate, all belonging to the suborder Polyphaga (Table 3; Fig. 2) and including most major groups of beetles proposed by other authors to have undergone rapid diversification. These include most phytophagous beetles that feed on living or dead plant material (including wood and often also involving fungi), for example the Phytophaga, Buprestidae, Meloidae + Mordellidae and Scarabaeidae, but notably also including groups not typically associated with plants, such as Elateridae and Tenebrionidae + Trachelostenidae. Five of these eleven clades have diversification rates approaching or exceeding the above-mentioned rate for Neoaves. Interestingly, six to seven of the 10 significant increases in diversification rate were in beetle clades that originated in the Cretaceous, which is also when most modern beetle families, including the crown groups of a majority of the most species-rich families, first appeared (Table 3; Figs 2, 16; Figure S1). The Cretaceous Period is well known for the diversification of angiosperms and their rise to ecological dominance (Lidgard & Crane, 1988. Many other groups of organisms also diversified at this time -a phenomenon that has been referred to as the 'Cretaceous Terrestrial Revolution' (Lloyd et al., 2008). However, neither phytophagy, nor specialized associations with angiospermous plants uniquely characterize the groups of beetles that have undergone statistically significant increases in diversification rate -at least to the extent that this can be estimated with extant species numbers. The 12 clades of beetles identified as exhibiting decreases in diversification rate are species-poor in the modern fauna, but collectively exhibit diverse trophic habits, notably including phytophagy -though sometimes the associations are with gymnosperms [e.g. Caridae (Cupressaceae)] rather than with angiosperms. These and most others have relictual, often Gondwanan distributions, suggesting that floral and faunal turnover itself may have played an important role in their present low diversities and limited distributions.

Conclusions
Our results provide a uniquely well-resolved temporal and phylogenetic framework for studying patterns of innovation and diversification in beetles, and a foundation for further sampling and resolution of the Coleoptera tree of life. They also provide much-needed evolutionary context for interpreting observations emerging from the study of beetle life histories, behaviour, morphology, microbiomes, genetics and genomics. However, our results are not definitive, particularly with regard to resolution of the deepest splits in the beetle tree. Furthermore, some of our estimated divergence times are younger than expected based on the Mesozoic beetle fossil record.
Many have proposed explanations for the apparent success of beetles (e.g. Crowson, 1981;Farrell, 1998;Barraclough et al., 1998;Grimaldi & Engel, 2005;Hunt et al., 2007). Some hypotheses, including the evolution of hardened forewings (elytra) which protect the hindwings, thereby facilitating a cryptic lifestyle (Crowson, 1981;Grimaldi & Engel, 2005) and the invasion of arid or aquatic habitats through elytral covering of the spiracles (Lawrence & Newton, 1982), apply to nearly the entire lineage Coleoptera. Other hypotheses only apply to a subset of major lineages. For example, the Phytophaga were proposed by Farrell (1998) to have diversified because of their intimate associations with flowering plants (angiosperms). The large series Staphyliniformia (rove beetles and allies) and Scarabaeiformia (scarab beetles and allies) are proposed to have radiated at least in part as a consequence of (pre)adaptations gained through ecological and evolutionary opportunities and challenges faced as part of life in the ancestral litter environment . Based on the timing discussed above, the increasing humidity of the climate in the early stages of their evolution may also have contributed to their rapid and dramatic diversification. There are numerous additional lineage-specific hypotheses that warrant mention. Hunt et al. (2007) concluded that the success of beetles is not readily explained by 'exceptional net diversification rates nor by a predominant role of herbivory and the Cretaceous rise of angiosperms'. Instead, they proposed that the success of beetles is due to low extinction rates and 'sustained diversification in a variety of niches', observations consistent to some degree with the results of the present study. Beetles as a whole have, however, experienced a statistically significant increase in diversification rate over their near relatives (Fig. 2). Furthermore, descendant lineages of polyphagan beetles that are associated with plants, especially angiosperms, are frequently (but not always) species rich (Farrell, 1998;Evans et al., 2014;McKenna et al., 2014) 4 and were identified as among those clades in the phylogeny exhibiting statistically significant increases in diversification rate, for example Phytophaga, Meloidae + Mordellidae, Acmaeoderinae + Agrilinae. In fact, some of these clades exhibit diversification rates ( Table 3) that can reasonably be characterized as 'exceptional' in the context of other groups of animals (see Alfaro et al., 2009).
Flowering plants and beetles both apparently underwent extensive taxonomic diversification during the Cretaceous, a phenomenon seen in other groups of organisms. Six to seven of the 11 significant increases in diversification rate that we identified in beetles occurred during the Cretaceous (Table 3; Fig. 2), although not all are among plant-associated beetle groups. Most modern beetle families, including the crown groups of a majority of the most species-rich families, also originated in the Cretaceous (Figs 2, 15). Thus, the apparent success of beetles, as measured by species numbers, may ultimately result from their associations with widespread and 'diverse' substrates -including plants, of which, flowering plants are most diverse, (Farrell, 1998;Ahrens et al., 2014), fungi (Robertson, 2010;Robertson et al., 2015) and leaf litter  -but what facilitated these associations in the first place or has allowed these associations to flourish likely varies within and between lineages. Proximate explanations for the apparent success of beetles therefore might most profitably be sought on a lineage-specific basis, for example by identifying and characterizing features of beetle morphology, genomes, microbiomes, etc. that facilitate ecological and taxonomic diversification and likely also promote temporal persistence via increased diet breadth, range size and/or dispersal ability. These are, of course, not new ideas (e.g. Harnik et al., 2012;Jablonski et al., 2013). The lineage-specific 'features' that facilitate diversification are unlikely to be the same in disparate clades of beetles, although certain general patterns of innovation may emerge, such as specialized interactions with endosymbionts (e.g. Scully et al., 2014), and lateral gene transfer from plants and/or microbes to beetles (e.g. Kirsch et al., 2014), both facilitating access to 'new' ecological adaptive zones. The extraordinary collective ecological breadth, apparent evolutionary plasticity, and morphological, taxonomic and ecological diversity of the lineage Coleoptera not surprisingly appears to result from multiple factors, each with relevance to different numbers of beetle clades at or over different geographic and temporal scales.

Supporting Information
Additional Supporting Information may be found in the online version of this article under the DOI reference: 10.1111/syen.12132 Figure S1. Maximum clade credibility timetree from beast with OGs removed and terminals collapsed to reflect monophyletic family-level (or nearest possible equivalent 5 ) groupings of taxa for use in estimating diversification rates in the program medusa (see Materials and methods and Table S3). Figure S2. Maximum-likelihood (ML) phylogenetic tree for 367 species of beetles representing 171/183 extant families, plus OGs (six species representing five orders), resulting from an unconstrained partitioned analysis of concatenated DNA sequence data from eight nuclear genes, implemented in Garli (see Materials and methods). Note that the top/right row/column entries are interdigitated between the bottom/left ones, as connected by the broken lines. ML bootstrap support ≥50% from partitioned analyses in RAxML (see Materials and methods) is indicated along branches using coloured squares, as shown in the graphical key. The embedded phylogram shows branch lengths proportional to the number of nucleotide substitutions. ML bootstrap support from the analysis of AA sequences alone is not shown because of differences in taxon sampling (see Figure  S5). AR, Archostemata; MY, Myxophaga; OG, outgroups.
White stars mark species of Derodontoidea. Black stars mark species of Cucujoidea s.l. (Biphyllidae and Byturidae) recovered in positions separate from other members of the superfamily. Figure S3. (In three parts) 50% majority-rule consensus tree for 367 species of beetles plus OGs (six species in five orders), resulting from a partitioned maximum-likelihood bootstrap (MLB) analysis of aligned nucleotide sequences from eight nuclear genes, implemented in the program RAxML (see Materials and methods). MLB support is shown along branches. Background colours indicate suborders and OGs (red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga; white = OGs). These data are summarized on the ML tree in Figure S2. Figure S4. (In three parts) 50% majority-rule consensus tree for 367 species of beetles plus OGs (six species in five orders), resulting from a partitioned maximum-likelihood bootstrap (MLB) analysis of nucleotide sequences from 18S and 28S rDNA, plus AA sequences from six nuclear protein-coding genes. Analyses were implemented in the program RAxML (see Materials and methods). MLB support is shown along branches. Background colours indicate suborders and OGs (red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga; white = OGs). These data are summarized on the ML tree in Figure S2. Figure S5. Fifty percent majority-rule consensus tree for 313 species of beetles plus OGs (six species representing five orders), resulting from a partitioned maximum-likelihood bootstrap (MLB) analysis of AA sequences from six nuclear protein-coding genes, implemented in RAxML (see Materials and methods). MLB support is shown along branches. Beetles for which ≥50% of AA positions had data were excluded from the analysis; therefore, these results are not summarized in Figure S2 (which contains data from all 373 taxa). Background colours indicate suborders and OGs (red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga; white = OGs). Figure S6. Fifty percent majority-rule consensus tree for 313 species of beetles and OGs (six species representing five orders), resulting from a maximum-likelihood bootstrap (MLB) analysis of nucleotide sequences from six NPC genes. Analyses were implemented in RAxML (see Materials and methods). MLB support is shown along branches. Background colours indicate suborders and OGs (red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga; white = OGs). Figure S7. Fifty percent majority-rule consensus tree for 367 species of beetles and OGs (six species representing five orders), resulting from a partitioned maximum-likelihood bootstrap (MLB) analysis of nucleotide sequences from eight nuclear genes, with Strepsiptera (Mengenilla moldryzki) constrained to the OG, i.e. constrained to fall outside Coleoptera, but not constrained in its placement outside of Coleoptera. Analyses were implemented in RAxML (see Materials and methods). MLB support is shown along branches. Background colours indicate suborders and OGs (red = Myxophaga; orange = Archostemata; blue = Adephaga; green = Polyphaga; white = OGs). These data are summarized on the ML tree in Figure S2.  Figure S9. Maximum clade credibility timetree for beetles and OGs from Fig. 2 showing 95% confidence intervals around node age estimates as red bars, and estimated node ages (see Fig. 2 for more information). Table S1. Taxonomic placement, DNA code(s), and collection and GenBank DNA sequence accession numbers for all taxa included in this study. Species marked with an asterisk (*) were excluded from analyses of AA sequences alone (these contained <50% of the targeted AA positions). Families marked with a pound sign (#) have not previously been included in higher-level studies of beetle phylogeny. Italicized GenBank accession numbers indicate previously published DNA sequences obtained from GenBank. Table S2. Monophyly constraints applied in the beast analysis. Table S3. Estimated total numbers of described extant species for monophyletic family-level (or nearest possible equivalent 6 ) groupings of taxa (see Materials and methods, Figure S1). Species numbers were obtained fromŚlipiński et al. (2011) except when sub-familial taxon numbers were needed to provide estimates for groups that were split apart or lumped together along sub-familial lines (cited individually in the table). However, typically when a family was split into two or more groups, the extent of the resulting groups was unclear, so the total number of described species in the family was split evenly between the two separately recovered lineages. Estimated species numbers for Neuropteroidea other than Coleoptera were obtained from Grimaldi & Engel (2005).
File S2. Supermatrix containing the concatenated masked nucleotide sequence alignments for the eight nuclear genes included in this study. The supermatrix contains 8377 aligned nucleotide positions for 373 species.
File S3. Supermatrix containing the concatenated masked AA sequence alignments for the six NPC genes included in this study. All taxa that were missing data from more than 50% of the aligned AA positions (marked with * in Table S1) were removed from the supermatrix. The resulting supermatrix contains 1747 aligned AA positions for 319 species.