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Spatial proximity determines post-speciation introgression in Solanum

An increasing number of phylogenomic studies have documented a clear ‘footprint’ of post-speciation introgression among closely-related species. Nonetheless, systematic genome-wide studies of factors influencing the likelihood of introgression remain rare. Here, we use an a priori hypothesis-testing framework, and introgression statistics, to evaluate the prevalence and frequency of introgression. Specifically, with whole genome sequences from 32 lineages of wild tomato species, we assess the effect of three factors on introgression: genetic relatedness, geographical proximity, and mating system differences. Using multiple trios within the ‘ABBA-BABA’ test, we find that one of our factors, geographic proximity, is consistently associated with evidence for recent introgression between species. Of 14 species pairs with ‘proximate’ versus ‘distant’ population comparisons, 12 showed evidence of introgression; in ten of these cases, this was more prevalent between geographically-closer populations. We found no evidence that introgression varies systematically with increasing genetic divergence between lineages or with mating system differences, although we have limited power to address the latter effect. While our analysis indicates that recent post-speciation introgression is frequent in this group, estimated levels of genetic exchange are modest (0.05-1.5% of the genome), so the relative importance of hybridization in shaping the evolutionary trajectories of these species could be limited. Regardless, similar clade-wide analyses of genomic introgression would be valuable for disentangling the major ecological, reproductive, and historical determinants of post-speciation gene flow, and for assessing the relative importance of introgression as a source of evolutionary change. IMPACT STATEMENT The formation of new species is traditionally viewed as a tree-like branching process, in which species are discrete branches that no longer share an ongoing genealogical connection with other, equally discrete, species. Recently this view has been challenged by numerous studies examining genealogical patterns across entire genomes (all the DNA of an organism); these studies suggest that the exchange of genes between different species (known as ‘introgression’) is much more common than previously appreciated. This unexpected observation raises questions about which conditions are most important in determining whether species continue to exchange genes after they diverge. Factors such as physical proximity, differences in reproductive mechanisms, and time since species shared a common ancestor, might all contribute to determining the prevalence of introgression. But to evaluate the general importance of these factors requires more than individual cases; many species comparisons, that differ systematically in one or more of these conditions, are needed. Here we use whole-genome information from 32 lineages to evaluate patterns of introgression among multiple species in a single, closely related group—the wild tomatoes of south America. We contrast these patterns among pairs of lineages that differ in their geographical proximity, reproductive system, and time since common ancestry, to assess the individual influence of each condition on the prevalence of introgression. We find that only one of our factors—geographical proximity—is consistently associated with greater evidence for recent introgression, indicating that this is largely shaped by the geographical opportunity for hybridization, rather than other plausible biological processes. Our study is one of the first to systematically assess the influence of general ecological and evolutionary conditions on the frequency of post-speciation introgression. It also provides a straightforward, generalizable, hypothesis-testing framework for similar systematic analyses of introgression in groups of other organisms in the future.


IMPACT STATEMENT 44
The formation of new species is traditionally viewed as a tree-like branching 45 process, in which species are discrete branches that no longer share an ongoing 46 genealogical connection with other, equally discrete, species. Recently this view has 47 been challenged by numerous studies examining genealogical patterns across entire 48 genomes (all the DNA of an organism); these studies suggest that the exchange of 49 genes between different species (known as 'introgression') is much more common than 50 previously appreciated. This unexpected observation raises questions about which 51 conditions are most important in determining whether species continue to exchange 52 genes after they diverge. Factors such as physical proximity, differences in reproductive 53 mechanisms, and time since species shared a common ancestor, might all contribute to 54 determining the prevalence of introgression. But to evaluate the general importance of 55 these factors requires more than individual cases; many species comparisons, that 56 differ systematically in one or more of these conditions, are needed. Here we use 57 whole-genome information from 32 lineages to evaluate patterns of introgression among 58 multiple species in a single, closely related group-the wild tomatoes of south America. 59 We contrast these patterns among pairs of lineages that differ in their geographical 60 proximity, reproductive system, and time since common ancestry, to assess the 61 individual influence of each condition on the prevalence of introgression. We find that 62 only one of our factors-geographical proximity-is consistently associated with greater 63 evidence for recent introgression, indicating that this is largely shaped by the 64 geographical opportunity for hybridization, rather than other plausible biological 65 processes. Our study is one of the first to systematically assess the influence of general 66 ecological and evolutionary conditions on the frequency of post-speciation introgression. 67 It also provides a straightforward, generalizable, hypothesis-testing framework for 68 similar systematic analyses of introgression in groups of other organisms in the future. 69

INTRODUCTION 70
The prevalence of hybridization among species, and the importance of 71 introgression for shaping species evolution, are historically contentious questions 72 (Mallet, 2008(Mallet, , 2005. Although traditionally viewed to be more common among plants 73 (Anderson, 1968;Stebbins, 1970), evidence of hybridization and introgression is 74 emerging for an increasingly broad range of organisms (Mallet et al., 2016). Perhaps 75 the most famous contemporary example involves Neanderthal and modern human 76 lineages (Mallet et al., 2016), in which ~1 -4% of Neanderthal genome is inferred to 77 have introgressed into some human populations. Quantifying the frequency and amount 78 of introgression is important for understanding the historical dynamics of closely-related 79 lineages, as well as the potential sources of genetic variation that could fuel ongoing 80 evolutionary change. For example, if sufficiently common, gene flow between species 81 could act as a significant source of adaptive loci, as has been observed for mimicry 82 pattern alleles in Heliconius butterflies (The Heliconius Genome Consortium et al., 83 2012). Adaptive introgression is likely to be especially important among recently 84 diverged lineages, where the accumulation of hybrid incompatibilities is not so 85 advanced that it prevents the exchange of unconditionally adaptive loci when lineages 86 come into contact. Nonetheless, the clade-wide prevalence of introgression events, and 87 therefore their relative importance in shaping the evolutionary trajectory of close 88 relatives, is only now beginning to be assessed (Folk et al., 2018). 89 From a genomic perspective, introgression leaves a detectable 'footprint': 90 introgressed regions show distinctive patterns of historical relatedness that differ from 91 non-introgressed regions, because they are most closely related to the donor species 92 rather than the recipient genome in which they are found (Payseur and Rieseberg, 93 2016). Accordingly, genome-wide data is ideal for characterizing the prevalence of 94 hybridization because it provides a detailed picture of phylogenetic relationships at loci 95 across the genome, including in genomic regions that show patterns of relatedness 96 inconsistent with the species as a whole. Beyond the human and butterfly examples, 97 genome-wide data has been used to infer past introgression events among species in 98 groups as diverse as Saccharomyces yeast (Morales and Dujon, 2012) Anopheles 99 mosquitoes (Fontaine et al., 2015), wild tomatoes (Pease et al., 2016), and Drosophila 100 (Turissini and Matute, 2017). However, while revealing the extent and timing of gene 101 flow events is interesting in individual cases, there are few tests of the generality of 102 introgression across whole groups of closely related species, including whether it 103 systematically varies in frequency or extent under different biological conditions. 104 Some of the factors that could influence the frequency of hybridization and 105 subsequent introgression include phylogenetic relatedness (i.e., genetic distance), 106 geographical proximity, and biological factors that affect the likelihood and direction of 107 reproductive events, such as differences in mating system. In the first case, 108 because the strength of reproductive isolation is expected to accumulate with the 109 amount of time since lineages diverged (Coyne and Orr, 1989), more genetic exchange 110 might be expected to occur between more closely-related species, with diminishing 111 rates accompanying increasing lineage differentiation. Second, genetic exchange is 112 more likely to occur among species in close geographic proximity, where they can 113 potentially come into physical and therefore reproductive contact (Harrison, 2012). 114 Determining the level of spatial proximity that allows gene exchange can be challenging, 115 as it likely depends upon numerous biological factors (e.g., dispersal mechanisms) and 116 abiotic factors (e.g., physical barriers to dispersal). Nonetheless, a general expectation 117 is that hybridization is more likely when biological or abiotic factors do not hinder contact 118 between lineages. For example, numerous hybrid zone studies demonstrate that the 119 proportion of individuals with mixed ancestry usually decreases with geographic 120 distance from the hybrid zone (Harrison andLarson, 2014, 2016). 121 Third, factors that specifically influence the timing and success of reproductive 122 events are also expected to influence the likelihood of hybridization and introgression. 123 For example, mating system variation can influence introgression, either directly by 124 affecting the likelihood of successful mating between species or indirectly by influencing 125 the longer-term likelihood that introgressed loci will persist in the recipient lineage. In the 126 first instance, mating system differences can cause predictable asymmetries in the 127 success of initial crosses between species. This can occur either via differences in the 128 size or shape of reproductive organs that can lead to asymmetric mechanical isolation 129 between lineages (e.g. where outcrossing species can fertilize inbreeding species, but 130 not vice versa; Brothers and Delph, 2017;Levin, 1978) 131 or-especially in plants-via differences in the presence/absence of genetically 132 determined self-incompatibility systems, whereby pollen from self-incompatible species 133 can fertilize ovules of self-compatible species, but self-incompatible plants actively 134 reject pollen from self-compatible species (e.g. in Nicotiana (Anderson and de Winton, 135 1931), Petunia (Mather and Edwardes, 1943) and Solanum (McGuire and Rick, 1954)). 136 In both mechanical and active-rejection cases, outcrossing species are more likely to 137 donate alleles to more inbreeding species compared to the reciprocal direction of gene 138 flow, reducing the potential for gene flow specifically between species with unalike 139 mating systems. Similarly, the longer-term likelihood that introgressed loci will persist in 140 recipient lineages can vary based on the mating system of the donor and recipient 141 lineages, because mutational load and the efficacy of selection is expected to differ 142 between species with histories of more or less inbreeding and different effective 143 population sizes (N e ) (Busch, 2005;Charlesworth et al., 1990;Harris and Nielsen, 2016;144 Juric et al., 2016;Lande and Schemske, 1985). In particular, introgression from 145 outbreeding to inbreeding populations should be especially disfavored both because 146 donor alleles are expected to have stronger deleterious fitness effects (due to genetic 147 load that can persist in outbreeders) and because the smaller N e recipient population is 148 less effective at disassociating these from other non-deleterious loci before they are 149 purged (Brandvain et al., 2014;Ruhsam et al., 2011). In comparison, the exchange of 150 alleles between lineages with similar mating systems should be less constrained by 151 these considerations. In general, then, no matter whether affected by initial crossing 152 differences (from mechanical or active rejection asymmetries) or differences in the 153 historical factors determining genetic load and effective population size, gene flow 154 between lineages that differ in their mating system might be expected to be more 155 constrained than gene flow between lineages with similar mating systems. 156 While these factors are expected to influence the rate and likelihood of gene flow 157 between species, there are few systematic tests of their general importance in shaping 158 the prevalence of post-speciation introgression. Here we use whole genome data to 159 systematically evaluate the effects of genetic distance, geographical proximity, and 160 mating system differences, on genome-wide patterns of post-speciation introgression 161 across a closely related clade of species. To assess introgression, we use the 'ABBA-162 BABA' test (also known as the D-test; Durand et al., 2011;Green et al., 2010). This test 163 detects introgression by comparing the frequency of alternate ancestral ("A") and 164 derived ("B") allele patterns among four taxa, where the species tree has the allele 165 pattern BBAA (Figure 1 in a 4-taxon tree, so that P2 and P3 are always predicted to experience more 176 introgression than P1 and P3 ( Figure 1). For example, if geographic proximity per se 177 affects the amount of introgression between two species, in a case where P1 and P2 178 are populations of one species but P2 is more geographically proximate to populations 179 of a second species (P3), then our a priori expectation is that elevated introgression will 180 be observed as an excess of ABBA (i.e. evidence of gene flow between P2 and P3) 181 rather than BABA (gene flow between P1 and P3; Figure 1). Multiple different four-taxon 182 tests with the same structure can then be used to evaluate whether geographically 183 proximity is systematically more frequently associated with evidence of post-speciation 184 introgression. A similar structure can be used to test the a priori expectation that gene 185 flow is expected to be more frequent between lineages with shared versus different 186 mating systems. More generally, 4-taxon tests that involve increasing evolutionary 187 divergence between the P1/P2 and P3 lineages, can be used to evaluate evidence that 188 introgression is on average more prevalent between more closely related taxa. 189 Here we use this a priori hypothesis-testing framework to assess the prevalence 190 and frequency of introgression among wild tomato lineages (Solanum section 191 Lycopersicum) depending upon a) geographical proximity, b) differences in mating 192 system, and c) evolutionary distance. In addition to high-quality, whole-genome data for 193 multiple wild genotypes of known provenance (Aflitos et al., 2014;Lin et al., 2014), this 194 group has well-curated historical records of geographic coordinates for hundreds of wild 195 populations from across the clade. Moreover, prior evidence of introgression events 196 between specific lineages (e.g. Beddows et al., 2017;Pease et al., 2016), and the ability 197 to generate F1 and later-generation hybrids in the greenhouse (e.g., Moyle, 2008;Rick, 198 1979), indicate the possibility that introgression could shape genomes in this group. 199 Using whole-genome data from 32 closely related accessions across 12 species of wild 200 tomato, our goal here was to systematically test hypotheses about the prevalence of 201 introgression, to make general inferences about the role and importance of particular 202 factors in the frequency of cross-species hybridization, and to begin to assess the 203 potential importance of introgression in shaping genome content and evolutionary 204 trajectories in this clade. 205

METHODS 206
Sequencing data and mapping to reference genome 207 Our analyses used data from three whole genome-sequencing projects (Aflitos et 208 al., 2014;Hardigan et al., 2016;Lin et al., 2014). Specifically, we obtained raw reads 209 either as fastq or SRA files for genomes of 32 wild Solanum individuals from the tomato 210 clade (Solanum section Lycopersicum), each from a different accession (historical 211 population collection), along with Solanum tuberosum (potato; Hardigan et al., 2016) 212 which we used as the outgroup in all comparisons (Supplemental Table 1 values indicate more gene exchange between P1 and P3 (an excess of BABA). We 227 used multiple replicate 4-taxon tests to evaluate three a priori expectations: 228 1) Post-speciation introgression is more prevalent between geographically closer 229 versus more distant lineages. Four-taxon tests were structured so that P1 and P2 were 230 taken from populations of the same species, but P2 was spatially closer to the P3 231 species and P1 was more distant (Figure 1). In this case, we expect a systematic 232 excess of positive values of the resulting D-statistics. Species comparisons and specific 233 P1, P2, and P3 accessions were identified for these tests based on known species 234 ranges and geographical locations of the sequenced accessions (see Supplemental text 235 for our specific criteria). Because these analyses are constrained by the available 236 sequenced genotypes, the actual geographic distances involved vary broadly between 237 4-taxon tests (Supplemental Table 2), so that this analysis is an imperfect reflection of 238 close spatial proximity; however, the structure of each test means we are still able to 239 systematically compare the effect of greater ('proximate') versus less ('distant') 240 geographic proximity on detected patterns of introgression. 241 2) Post-speciation introgression is more prevalent between lineages that share 242 mating system. Here, four-taxon tests were structured so that P1 and P2 were again 243 taken from populations of the same species, but P2 was self-compatible (SC) and P1 244 was self-incompatible (SI); in every test, P3 was the same accession of an SC species. 245 In this case, we also expect a systematic excess of positive D-statistics. Within our 246 dataset there are only three species for which we had whole genome sequence data 247 from both SI and SC accessions: S. arcanum, S. habrochaites, and S. peruvianum. 248 3) Post-speciation introgression is more prevalent between lineages that are 249 more closely related. In this case, we expect that the estimated magnitude of D should 250 decrease as evolutionary (genetic) distance between (P1, P2) and P3 increases within 251 the 4-taxon test. We calculated pairwise genetic distance for each comparison by taking 252 the average genetic distance for the two comparisons within the focal trio (i.e. P1 with 253 P3 and P2 with P3), based on genome-wide site differences between accessions. In 254 this case, there is no expectation of either positive or negative D-values, as P1 and P2 255 are equally closely related to P3. Instead, the comparison is among D-values taken from 256 different 4-taxon combinations. 257 The supplemental text provides a more detailed description of how these factors 258 were defined and determined for individual 4-taxon tests. analyses reported in the main text, we used only 100 kb windows that had >20 variable 267 sites (~4200 windows on average per test, depending upon the specific trio analyzed; 268 Supplemental Table 3); this eliminated windows in which no or few single nucleotide 269 polymorphisms (SNPs) were found, as these have low power to accurately estimate D. 270 For completeness, we also performed analyses on D estimated from all 100 kb windows 271 in the genome and found the same qualitative results as the higher power dataset 272 (Supplemental Table 4). For each four-taxon test, we performed a chi-squared 273 goodness-of-fit test, to determine if our genome-wide estimate of mean D was 274 significantly different than zero. Across all four-taxon tests, we determined whether the 275 number of tests supporting a higher incidence of introgression in the predicted direction 276 was greater than expected by chance, using a sign test. All statistical analyses were 277 performed in RStudio version 1.1453 (2015). 278 To determine if post-speciation introgression is associated with quantitative 279 differences in geographical proximity between populations of two species, for every trio 280 we also determined the geographic distance (in km) between P1 and its nearest P3 281 accession, and between P2 and its nearest P3 accession (using our georeferenced 282 location data for all population accessions, see supplemental text), to generate an 283 estimate of their relative proximity to any population from P3 (i.e. the difference between 284 these two distances; Supplemental Table 5). For all four-taxon tests, we regressed our 285 mean genome-wide estimate of D on this relative geographic distance estimate 286 (Supplemental Figure 1). To determine if evidence for post-speciation introgression is 287 more prevalent for recently diverged lineages, we evaluated the association between 288 the absolute values of our estimates of genome-wide D and genome-wide genetic 289 distance, using regression across all four-taxon tests. 290 Finally, to provide a general estimate of the fraction of the genome inferred to 291 have come from introgression in each trio, we calculated the number of varying sites 292 that support evidence of differential introgression (i.e. the excess of sites that support 293 one minority topology over the other, or (|ABBA sites -BABA sites|) and expressed 294 these as a proportion of total variable sites in this trio (i.e. |ABBA -BABA| / (ABBA + 295 BABA + BBAA)). These estimates were calculated for all four-taxon combinations 296 included in our analyses, and used only data from 100 kb windows with >20 SNPs 297 (Supplemental Table 6). While these estimates are not precise measures of the 298 proportion of the genome that has experienced introgression (for example, they could 299 underestimate total introgression if there has been gene flow both between P1 and P3, 300 and between P2 and P3), they provide a set of rough global estimates with which to 301 compare different four-taxon tests. These estimates were regressed onto mean genetic 302 distance for all trios to evaluate whether the amount of inferred introgression between 303 species was associated with the time since their divergence (Supplemental Figure 2). 304

RESULTS 306
We generated genome-wide D estimates for 17 four-taxon combinations, 14 that 307 could address the effects of geographical proximity on introgression, and three 308 addressing the effects of mating system variation. All 17 combinations were used to 309 assess the effect of genetic distance. Across all 17 tests, the genome-wide average 310 estimates of D ranged from -0.08 to 0.15, based on 100kb windows with >20 variable 311 sites (Table 1; estimates of D from all windows were similar, Supplemental Table 4). 312 The fraction of the genome estimated to be differentially introgressed ranged from 0.05 313 -1.5 (Supplemental Table 6). 314 For our tests of geographical proximity, of 14 testable four-taxon combinations, 315 ten had average D values significantly greater than zero-indicating that our 316 geographically closer lineages (P2 and P3) share a higher proportion of sites-whereas 317 two were significantly less than zero (chi-squared goodness-of-fit tests, with Bonferroni 318 correction; Figure 2, Table 1a). A two-sided sign-test indicated that the number of 319 significantly positive versus negative mean values of D was different (p = 0.038), 320 consistent with a systematic excess of introgression between species pairs when their 321 populations are geographically closer versus more distant. Because there is non-322 independence in our dataset (that is, some individual accessions/genome sequences 323 are used in more than one four-taxon test), we evaluated the influence of this non-324 independence by paring our dataset down to trios (of P1, P2, P3) that only used unique 325 accessions. Of our twelve trios with significant positive or negative D statistics, we could 326 evaluate combinations of up to six different trios that shared no accessions in common. 327 In all eight unique alternative combinations of six trios, five tests had a positive D and 328 one had a negative D; that is, we found evidence for an excess of introgression 329 consistently more frequently when populations of a species pair were geographically 330 closer versus more distant. This directionality is non-significant in each of the reduced 331 datasets (p = 0. 2188; Supplemental Table 7) as the two sided sign test is 332 underpowered to detect a systematic difference in direction when n=6. Finally, across all 333 14 four-taxon tests, mean genome-wide D was not significantly associated with the 334 relative geographical proximity of the P1 versus P2 population to the closest population 335 from the P3 species (R-squared = 0.055, p-value = 0.42, Supplemental Figure 1a), 336 suggesting that, while geographical proximity influences the possibility of introgression, 337 other factors likely determine the quantitative amount of introgression that occurs. 338 For our evaluation of mating system effects, of three testable trios, two genome-339 wide mean D values were significantly positive and one was significantly negative, 340 regardless of the specific accession used as the P3 taxon in our tests (Table 1; Figure  341 3). Note that relative geographical proximity does not explain the sign of D in any of 342 these cases; for the two instances where D was positive (P1 and P2 from S. arcanum or 343 from S. habrochaites, respectively: Supplemental Table 5), our SI accessions are 344 geographically closer to a P3 accession compared to their conspecific SC accessions, 345 and the opposite is observed in the case where mean D was negative. In addition, 346 mean genome-wide D is not negatively associated with the relative difference in 347 geographic proximity for these mating system trios (Supplemental Figure 1b). Overall, 348 then, our evidence in support of mating system effects is equivocal: 2 of 3 tests support 349 the expectation that introgression is more prevalent between species pairs when their 350 populations share the same mating system, but one does not. The prevalence of introgression is one pattern emerging from contemporary 363 genome-wide studies in many groups of closely related species, including in groups not 364 traditionally associated with post-speciation gene flow. However, there have been few 365 attempts to systematically assess the influence of different factors in shaping the 366 frequency and extent of this gene flow. Here we used directionally structured, four-taxon 367 ABBA-BABA tests to examine the influence of three factors-genetic distance, 368 geographical proximity, and mating system differences-on genome-wide patterns of 369 introgression among wild tomato species. We found that recent introgression was 370 commonly detected among these species, that consistent patterns of post-speciation 371 introgression depend largely on geographical proximity rather than the other two factors, 372 and that the estimated fraction of the genome differentially introgressed between 373 species was modest. These findings have interesting implications for interpreting the 374 contexts in which introgression might play the greatest role in shaping evolutionary 375 trajectories in this and other similar clades, and for assessing the potential contribution 376 of introgression to adaptive phenotypic evolution. 377 378

Recent introgression occurs frequently but is modest in scope among wild tomatoes 379
Our analysis indicates that, among wild tomato lineages, post-speciation gene 380 exchange is prevalent: of 17 total four-taxon tests across all our analyses, 15 had mean 381 D values significantly different from zero. Prior studies have detected evidence for 382 introgression among specific wild tomato lineages (Beddows et al., 2017;Pease et al., 383 2016), and our findings expand and illuminate these observations in several key 384 respects. First, our analyses preferentially assessed evidence for recent, rather than 385 more ancient (Pease et al., 2016), introgression events because in every case we 386 contrasted populations (P1 and P2) from a single species when looking for evidence of 387 introgression with a second species (P3). Accordingly, any inferred introgression must 388 have occurred after the evolutionary split of these two (P1 and P2) conspecific 389 populations. Despite this, we find repeated evidence that populations from different 390 species have exchanged genes recently, including species that are estimated to have 391 diverged >2 million years ago (e.g., S. pimpinellifolium and S. pennellii; Pease et al., 392 2016). 393 Our results suggest there is broad potential for cross-species hybridization 394 across the clade, a finding consistent with other observations that indicate premating 395 isolation is likely to be incomplete between lineages in nature: all species share general 396 floral morphology (rotate, yellow, five-petaled flowers), all are buzz-pollinated, and 397 multiple species pairs are found in sympatry (Rick, 1950). Nonetheless this finding is 398 intriguing as few natural hybrids have been observed in the wild in this group (Taylor, 399 1986), and some of these species are known via crossing and genetic studies to 400 express moderate to strong postmating and postzygotic reproductive isolation under lab 401 conditions (Hamlin et al., 2017;Moyle andNakazato, 2010, 2008). These later-acting 402 barriers might be important in limiting the amount of introgression that results from 403 hybridization events. Indeed, a second general observation of our analysis is that 404 despite evidence for relatively frequent hybridization, the amount of the genome 405 exchanged between species is likely to be limited: the proportion of the genome 406 estimated to be differentially exchanged between species is on the order of 0.05-1.5% 407 of all variable sites (Supplementary Table 8). Further, when D-statistics are examined 408 chromosome-by-chromosome within each four-taxon test (Supplementary Figure 3), in 409 most cases introgression is inferred on some chromosomes but not others; this variation 410 among chromosomes might be due to variation in the presence of loci contributing to 411 reproductive isolation. Overall, the amount and distribution of inferred introgression 412 suggests that current species reproductive barriers are sufficiently incomplete to allow 413 detectable recent introgression among diverged species in the field, but also that 414 genomes are not completely or uniformly porous to gene flow among lineages, even in 415 cases where there is an opportunity for gene exchange. 416

417
Introgression frequency varies with spatial proximity between species pairs, 418 rather than overall genetic relatedness or mating system differences 419 Importantly, the structure of our analyses also allowed us to explicitly evaluate 420 the influence of several factors on these detected patterns of introgression. We found 421 that repeated patterns of recent post-speciation hybridization were consistently 422 associated with only one of our factors: geographical proximity. This suggests that the 423 propensity for post-speciation gene exchange is most often dependent on the simple 424 opportunity for reproductive contact-geographic proximity per se between populations 425 of different species allows greater gene flow. In contrast, although there were few 426 comparisons available, we found that mating system differences were not consistently 427 associated with reduced (or elevated) patterns of introgression; two tests were 428 consistent with our a priori prediction (including the strongest case) but one test 429 indicated more introgression between lineages that differed in mating system. While we 430 currently have too few four-taxon tests to draw definitive conclusions, these 431 idiosyncratic observations could be due to additional biological factors. For example, the 432 transition to self-compatibility within each of our polymorphic (SI/SC) species might be 433 too recent to yet see consistent differences in crossing asymmetry or genetic load that 434 are expected between long-standing SC versus SI populations. Regardless, because 435 there are clear predictions about associations between mating system, genetic load, the 436 efficacy of selection, and the propensity and direction of introgression (Busch, 2005;437 Charlesworth et al., 1990;Harris and Nielsen, 2016;Juric et al., 2016;Lande and 438 Schemske, 1985)-some of which appear to be supported in individual cases (e.g., 439 Mimulus; Brandvain et al., 2014)-testing the generality of these effects with a larger set 440 of comparisons remains a goal in the future. Within the limitations of the data available 441 here, however, mating system difference alone is an equivocal predictor of overall 442 patterns of recent genomic introgression in this group. 443 Interestingly, we also did not detect an association between the magnitude of 444 evolutionary divergence (genetic distance), and either the occurrence or the amount of 445 inferred introgression. Species are expected to accumulate reproductive isolation with 446 increasing evolutionary divergence (Coyne and Orr, 1997), and this pattern has been 447 observed among wild tomatoes for loci involved in postzygotic reproductive isolation 448 (hybrid pollen and seed sterility; Moyle and Nakazato, 2010), suggesting that 449 introgression should become attenuated with increasing evolutionary age between 450 species. Nonetheless, the total number of loci estimated to contribute to postzygotic 451 isolation in this group is relatively modest, even among the oldest species pairs (Moyle 452 andNakazato, 2010, 2008). In addition, mean sequence divergence between all 453 lineages analyzed here is low-0.1-4.0%-consistent with the recent, rapid origin of 454 species in this clade (Pease et al., 2016). Using data from a very broad range of taxa, a 455 recent meta-analysis inferred that divergence of just a few percent results in barriers 456 that can effectively suppress gene flow (Roux et al., 2016)  Our analyses join a growing consensus of studies that suggest gene flow among 481 distinct lineages might be common, especially those that have rapidly diverged, have 482 incomplete isolating barriers, and that maintain some regions of geographical overlap 483 (Brawand et al., 2014;Jónsson et al., 2014;Lamichhaney et al., 2015 if the associated variants have very large but local fitness consequences, as is 501 observed for locally adaptive mimicry alleles in Heliconius for example. While not a 502 primary goal of our analyses here, we did not observe any obvious analogous cases at 503 mating-system loci in our genomes (see Supplementary Text). A prior analysis using 504 transcriptome data did detect limited regions of introgression among some Solanum 505 species pairs, with indirect evidence that these might have adaptive functions 506 associated with local ecological conditions ￼ ￼ definitely demonstrating adaptive 507 function requires knowing the fitness effects of alternative alleles under ecologically 508 realistic conditions, these remain hypotheses. For now, the observation that a low level 509 of gene exchange frequently occurs between lineages suggests that introgression could 510 be a significant source of adaptive genetic variation, certainly in comparison to lineages 511 where there is no evidence of gene flow. 512 Overall, while genetic exchange in any particular instance is likely to be 513 influenced by both ecological and genomic contexts, only via systematic tests of 514 introgression patterns across multiple cases can we start to disentangle the major 515 determinants of post-speciation gene flow. One of our goals here was to demonstrate 516 that structured a priori tests, across multiple species pairs in a diverse clade, provides 517 one method for assessing the relative influence of several general factors on the 518 frequency and amount of post-speciation introgression. By going beyond individual 519 cases to generate general and quantitative evaluations, these tests should provide 520 insight both into the main determinants of post-speciation introgression across a 521 diversity of organisms and contexts, and the relative importance of introgression as an 522 engine of evolution.