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Sex Allocation Patterns across Cooperatively Breeding Birds Do Not Support Predictions of the Repayment Hypothesis

The repayment hypothesis predicts that reproductive females in cooperative breeding systems overproduce the helping sex. Thanks to well-documented examples of this predicted sex ratio bias, repayment has been considered an important driver of variation in sex allocation patterns. Here we test this hypothesis using data on population brood sex ratios and facultative sex allocation from 28 cooperatively breeding bird species. We find that biased sex ratios of helpers do not correlate with production biases in brood sex ratios, contrary to predictions. We also test whether females facultatively produce the helping sex in response to a deficiency of help (i.e., when they have fewer or no helpers). Although this is observed in a few species, it is not a significant trend overall, with a mean effect size close to zero. We conclude that, surprisingly, repayment does not appear to be a widespread influence on sex ratios in cooperatively breeding birds. We discuss possible explanations for our results and encourage further examination of the repayment model.


Introduction
formulated an elegant explanation for why sex ratios are so often equal in nature. Because each offspring has a mother and father, any sex that becomes rarer immediately enjoys a reproductive success advantage, and the associated selection pressure drives population sex ratios toward parity. Exceptions to the general rule of equal sex ratios have fascinated evolutionary biologists since then (West 2009). In these cases, producing one sex confers a cost or benefit that trades off against the benefit of rarity underlying Fisher's prin-ciple (Hamilton 1967). Sex allocation by breeders can be viewed as an adaptive decision in the context of parental investment, with the relative costs and benefits of producing each sex being key to its outcome.
In cooperative breeders, one benefit that has attracted a great deal of attention is the fitness gain that parents receive from offspring that help them in future breeding attempts (Malcolm and Marten 1982;Koenig and Walters 1999;Griffin et al. 2005). Help is usually more likely to come from one sex than the other (Komdeur 2004). The repayment hypothesis predicts that parents should invest more in this helpful sex because of the greater chance that their investment will be repaid through future help (Emlen et al. 1986;Lessells and Avery 1987). The hypothesis rests on the assumption that apparent help provides a genuine fitness benefit to breeders, and so its predictions apply only where this is the case (see "Methods").
The repayment hypothesis yields intuitive predictions about offspring sex ratios in cooperative breeders, and longterm studies of bird populations provide valuable data sets with which to test these. The first general prediction is that offspring sex ratios should be biased toward the helping sex at the population level because of the extra payoff associated with producing this sex. Brood sex ratios in bell miners (Manorina melanophrys) are consistent with this prediction: helping is extremely male biased, and 58% of hatchlings are male (Clarke et al. 2002). The second prediction is that breeders with no or fewer helpers should facultatively adjust the sex ratio of their broods to be more biased toward the helping sex, as they have more to gain from doing so. There is again some empirical support, especially from Seychelles warblers (Acrocephalus sechellensis): helping is female biased in this species, and breeders without helpers produce more females when their territory is of sufficient quality to support the extra philopatric offspring (Komdeur et al. 1997).
Despite these examples, the status of repayment as a widespread driver of sex ratio skew is called into question by a number of negative results. For example, in purple-crowned fairy wrens (Malurus coronatus) and white-banded tan-agers (Neothraupis fasciata) there is no significant bias toward production of the helping sex at the population level and no evidence for facultative adjustment of brood sex ratios in response to any cues (Kingma et al. 2011;Gressler et al. 2014). While the predictions of the repayment hypothesis are intuitively appealing, the adaptive value of producing each sex will also depend on difficult-to-measure components of the direct fitness of both parents and offspring. Long-term data on red-cockaded woodpeckers (Picoides borealis) have been used to estimate direct fitness differentials between the sexes and incorporate them into a repayment model; however, the model still failed to predict brood sex ratios at the population level (Koenig and Walters 1999). A meta-analysis by Griffin et al. (2005) suggests that individuals are more likely to adjust their offspring's sex ratio in systems where the benefits of help are high. This provides some explanation for failures to observe adjustment, but such negative results have proliferated since Griffin et al.'s (2005) study, perhaps because authors realize that they run counter to the prevailing view of adaptive sex allocation (Cockburn and Double 2008).
Here we use a comparative analysis and meta-analysis to test the key predictions of the repayment hypothesis, using data from previously published studies of 28 cooperatively breeding bird species spanning 18 families. We then discuss the usefulness and generality of the concept of repayment in light of our results.

Methods
We collected data from relevant studies identified using the search term "(brood) sex ratio birds" in Web of Science and Google Scholar as well as from Koenig and Dickinson (2016), Komdeur (2004), and references within. We also searched the primary literature using Web of Science for any species identified as a kin-based cooperative breeder by Riehl (2013). We included data only from bird species with kinbased cooperative breeding systems, as production is related to future help only in these cases. Where multiple studies were published for the same species, we chose the one with the largest sample size or, in the case of Seychelles warblers, the one that came from a natural population (Komdeur et al. 1997). Helper sex ratios were obtained from Green et al. (2016) or from the literature directly, where possible from the same population as brood sex ratios. Data are deposited in the Dryad Digital Repository: http://dx.doi.org/10.5061 /dryad.9bk88 .
Breeding females are expected to benefit from biasing their offspring's sex ratios toward the helping sex only if the help actually improves their fitness in turn (Emlen et al. 1986;Griffin et al. 2005). For this reason, from a data set of 32 candidate species we excluded four for which research suggests help has no positive effect on the fitness of breeding females (table A1; tables A1-A3 are available online). We included a further 10 species for which this effect has not been tested because help had a positive effect on breeder fitness in 82% of tested species (n p 22). We checked the influence of including these untested species by carrying out a restricted analysis in which they were removed from the data set.
We investigated the effect of helper sex ratio on logtransformed brood sex ratio across 28 species in the full data set and 18 species in the restricted data set, controlling for phylogeny using a phylogenetic generalized least squares (PGLS) model implemented in R software (ver. 3.2.2). We applied this model across 1,000 trees downloaded from BirdTree .org (Jetz et al. 2012) using the Hackett et al. (2008) backbone ( fig. 1). Following Green et al. (2016), we included data quality as a variance component in the model, using categories of weak, medium, or strong assigned to each study. When assigning these scores, we considered the sample size, the length of study, the sample size for the helper sex ratio estimate, and the point at which brood sex ratio was measured (with closer to the primary sex ratio being considered better quality).
For 16 studies that tested for facultative sex allocation in cooperatively breeding bird species, we used a meta-analysis to investigate the hypothesis that breeders without helpers or with fewer helpers show greater production of the helping sex. This is the strongest prediction made by the repayment hypothesis in the context of facultative allocation. We did not include studies of two species for which research suggests help has no positive effect on the fitness of breeding females, for the reasons given above. We extracted effect sizes of the relationship using equations from Lajeunesse (2013), except for two studies where we obtained effect sizes from Griffin et al. (2005). Brood sex ratio was treated as the response, and the predictor was either whether a nest was helped (categorical; seven studies) or number of helpers (integer; nine studies). We derived confidence intervals (CIs) and sample weights for each study using equations from Lipsey and Wilson (2001), and we calculated a weighted mean and 95% CI using the Hmisc package in R (Harrell 2016).

Results
We included data on helper and brood sex ratios for 28 species of cooperatively breeding bird. The mean brood sex ratio (proportion of males) across species was 0:52 5 0:01 SE (median, 0.51); this value ranged from 0.37 in broods of the black-eared miner (Manorina melanotis) to 0.69 in broods of the splendid fairy wren (Malurus splendens). The mean helper sex ratio across species was 0:80 5 0:05 SE (median, 0.89), ranging from 0.10 in white-throated magpie jays (Calocitta formosa) to exclusively male helpers in 10 species (table A2).
We obtained effect sizes for the relationship between the number of helpers or being helped and brood sex ratios from studies of 16 cooperatively breeding bird species ( fig. 3; table A3). Seven of these effects were in the expected direction, with more of the helping sex produced by unhelped females or those with fewer helpers. Seven were in the opposite direction, and the directions of two small effects were not reported. The weighted mean of the 14 effect sizes whose direction was reported was 0.01 (95% CI, 20.17 to 0.036) in the direction expected. This result was the same (to two decimal places) when both excluded effect sizes were treated as positive, and the weighted mean shifted to 0.00 when they were treated as negative. Effect sizes have been closer to zero Brood sex ratio 0.4 0.5 0.6 Figure 1: Phylogeny showing relationships between the 28 species used in our comparative analysis, with branch lengths from one of 1,000 sampled trees downloaded from BirdTree.org (Jetz et al. 2012). Brood sex ratio for each species is expressed as the mean proportion of males in broods from a studied population. Brood sex ratio is randomly distributed with respect to phylogeny (see "Results"). Myiopsitta monachus, Manorina melanophrys, Manorina melanotis, Manorina melanocephala, Stipiturus malachurus, Malurus leucopterus, Corvus brachyrhynchos, Alophoixus pallidus, Neothraupis fasciata, and Loxioides bailleui were excluded from a restricted analysis because of unconfirmed effects of help on breeder fitness (see "Methods").

Discussion
We investigated two general predictions attributed to the repayment hypothesis. The first is that in kin-based cooperative breeders females produce broods biased toward the helpful sex because the future fitness contribution made by helpers repays some of their investment. Across 28 bird species, we found no evidence that this was generally the case, despite a lack of phylogenetic signal indicating that brood sex ratio is a labile trait. The second prediction was that females in need of help adjust their brood's sex ratios further in favour of the helping sex. We drew together tests of this prediction from 16 studies, and although it was borne out in a minority of cases, there was not a significant directional trend across species. Earlier studies reported greater effect sizes than more recent studies, which may have led to an overestimation of the prevalence of adaptive sex allocation in the literature.

No Overall Bias toward Producing the More Helpful Sex
A predicted global sex ratio skew toward the helping sex in cooperative breeders is the most direct interpretation of the repayment model; in their introduction to the original model, Emlen et al. (1986) proposed that "the sex ratio should achieve an equilibrium in which there is an overproduction of the helper sex." There are two levels at which this prediction may falter: (1) proper accounting of the costs and benefits of producing each sex and (2) empirical observation. Where sexes differ in their tendency to help, they are also likely to differ in other key life-history traits. Although one sex may "repay" investment by helping and thus improving their parents' productivity, this could feasibly be counteracted by enhanced reproductive success in the nonhelping sex improving parents' production of grandoffspring. If this is the case, biased brood sex ratios should not be adaptive. This important point was identified by Koenig and Walters (1999), who incorporated sex differences in survival and reproductive success into an extended repayment model that aimed to predict optimal brood sex ratios in red-cockaded woodpeckers. Their results were interesting in two respects: (1) the predicted optimal brood sex ratio in this species with male-biased help was still male biased and was little affected There is no relationship between these two variables (see "Results"), in contrast to the predictions of the repayment hypothesis. Circle sizes represent our assessment of data quality (with large circles representing the strongest data). Filled circles correspond to species for which benefits of help to breeders are unconfirmed; these were removed from a restricted analysis (see "Methods"). by considering differences in the direct fitness achieved by male and female offspring and (2) the predicted optimal brood sex ratio was significantly different from observed sex ratios, which were close to parity. Here we were unable to account for the relative influence of offspring and grandoffspring production on expected sex ratios because very few species in our sample have been studied in as much detail as the red-cockaded woodpecker. Instead, we used helper sex ratio, the key driver of expected brood sex ratio bias in Koenig and Walters (1999), and similarly found that observed brood sex ratios do not fit expectation. This does not necessarily mean that the extended repayment model as applied to red-cockaded woodpeckers also fails in other systems; it is still possible that this species is exceptional and that in most cases including sex differences in future productivity may better explain observed patterns (but see Koenig et al. 2001). For example, the benefits of rarity identified by Fisher (1930) may be much greater than the marginal fitness ben-efits associated with the likelihood of helping. Nevertheless, in general our results suggest that females biasing production toward the helping sex, which is the most intuitive prediction of repayment models, is not a valid generalization. The repayment hypothesis makes predictions opposite to those of the local resource competition hypothesis, which suggests that females may benefit from overproducing the dispersive (generally nonhelping) sex, to reduce competition for resources (Clark 1978). Costs of competition could explain the discrepancy between our predictions and results, although there are reasons to doubt this interpretation. First, in most systems the benefits of help appear to compensate for any costs because helped nests are usually provisioned more frequently (Hatchwell 1999) and are generally more productive (Dickinson and Hatchwell 2004;Koenig and Dickinson 2016). Furthermore, if competition provided the main constraint to adaptively biasing the sex ratio, we would expect biases toward the helping sex to be especially pro- nounced in species like riflemen (Acanthisitta chloris), where most helpers had previously dispersed from their natal territory and the sexes do not differ significantly in their dispersal distances (Preston 2012). It is noteworthy, therefore, that the observed sex ratio is close to parity in this species (Khwaja 2017). Nevertheless, competition may limit the adaptive value of biased sex allocation in other species. A third possible explanation is simply that biasing brood sex ratios is constrained or costly, although again this has little support. Mechanisms of biased sex allocation are currently unknown, and some suggestions rely on potentially taxon-specific characteristics, such as size dimorphism in the centromeres of sex chromosomes (Rutkowska and Badyaev 2008). However, our models showed a complete lack of phylogenetic constraint on brood sex ratios. Although across species these average around parity, some studies with convincingly large sample sizes show significantly biased population brood sex ratios (Clarke et al. 2002;Cockburn and Double 2008). There may be a mechanistic barrier to biasing sex ratios in some species, but as this is clearly not globaland phylogenetically random-it is not a well-supported interpretation (West and Sheldon 2002). While a combination of the three explanations we have suggested may underlie our results, none are especially convincing for the reasons discussed. We would welcome a theoretical reevaluation of the repayment model, which may make sense of its uneasy fit with empirical data.

Rarity of Facultative Production of the More Helpful Sex
A final candidate explanation for this lack of populationlevel brood sex ratio biases is that biases may be context dependent rather than consistent (Pen and Weissing 2000). Females may bias their broods' sex ratios only when they have fewer or no helpers (for such facultative manipulation, the local resource competition and repayment hypotheses make the same rather than opposite predictions). In contrast to the lack of evidence for population-level sex ratio biases, a few studies do provide strong support for facultative control of sex ratios. In Seychelles warblers, females show extraordinarily sophisticated control of their broods' sex ratios, with females (the more helpful sex) overproduced on good-quality territories without existing helpers (Komdeur et al. 1997. This does not, however, result in an overall population-level bias toward the production of females because males (the more dispersive sex) are overproduced on poor-quality territories, where supernumeraries are likely to be costly. Thus, in this case an unbiased population sex ratio is consistent with the repayment hypothesis because females across different contexts adaptively allocate their offspring's sex. Western bluebirds (Sialia mexicana) also show evidence of facultative control (Dickinson 2004), but in general our meta-analysis shows that these species are the exception rather than the rule (with an average effect size close to zero). There is no general tendency across species to produce the helping sex when breeders are deficient of help. This picture emerges strongly with the inclusion of more recent publications documenting negative results, providing a contrast to the mainly positive findings published by the time of Griffin et al.'s (2005) previous meta-analysis and leading us to somewhat different conclusions ( fig. 4). We hope this encourages publication of negative results, which are essential for the validity of comparative work.
Our findings raise the question of why helpers are apparently not facultatively produced in response to "need" in other species, where there may be a plausible benefit to doing so; or, what is exceptional about Seychelles warblers? One unusual feature of this species's breeding system is that although females are more likely to become helpers than males, they are also more likely to become subordinate cobreeders that lay their own egg in the nest of the dominant pair (Richardson et al. 2001(Richardson et al. , 2002. This provides an additional selection pressure against producing philopatric females on poorquality territories, as their potential reproduction would place a further strain on resources; it is conceivable that without this additional pressure the benefits of manipulation may not outweigh its costs (see Pen et al. 1999). In addition to other species lacking such a dual selective pressure on sex ratio manipulation, we outline four suggestions below that may explain why the helping sex is elsewhere rarely overproduced in response to apparent need.
Unpredictable Environments. Adaptive sex allocation in Seychelles warblers relies on assessment of environmental quality. Philopatric females are overproduced only on territories with sufficient food (Komdeur et al. 1997). Cooperatively breeding birds are commonly associated with unpredictable environments, with extra care thought to buffer against stochasticity (Jetz and Rubenstein 2011; but see Griesser and Suzuki 2016). Species living in such conditions may lack adaptive cues for sex allocation. In acorn woodpeckers (Melanerpes formicivorus), helpers have a generally positive effect on breeders' reproductive success, but this effect becomes negative when conditions are poor (Koenig et al. 2011). A change in environmental conditions may therefore cancel any adaptive benefit of facultatively producing philopatric males.
Unpredictable Help. In species that breed in kin neighborhoods, such as riflemen and long-tailed tits (Aegithalos caudatus), helpers are not permanently affiliated with the breeding pair (Hatchwell 2009). Respectively, helpers in these species begin the breeding season dispersed onto their own territories or attempting to breed themselves, and they start help-ing at a nest partway through the provisioning phase (Preston et al. 2013;Hatchwell 2016). As a result, breeding females may not have good information on the amount of help they will receive (Nam et al. 2011). This constraint is not limited to species in kin neighborhoods: even in cooperative groups formed by delayed dispersal, it is sometimes the case that not all group members help (e.g., Rubenstein 2016), and therefore group size may be an inaccurate cue for assessing future help. Unpredictable help limits the potential for female breeders to make adaptive sex allocation decisions based on need.
Other Cues Influencing Allocation Decisions. Sociable weavers (Philetairus socius) display a surprising sex allocation pattern in which females with helpers produce relatively more rather than fewer males, the helping sex (Doutrelant et al. 2004). In this species, the need for help is clearly not a key driver of allocation decisions; the authors suggest that the inheritance of within-colony rank by philopatric males may select for overproduction of males by high-ranking breeders, which would inevitably correlate with levels of help. In whitewinged fairy wrens (Malurus leucopterus) and superb starlings (Lamprotornis superbus), sex allocation is consistent with the Trivers-Willard hypothesis, where females with better reproductive prospects overproduce males, which have higher potential fitness (Trivers and Willard 1973;Rathburn and Montgomerie 2005;Rubenstein 2007). In these species, allocation decisions based on rank and breeding condition presumably carry more benefit than those based on a need for help.
Insufficient Benefits of Help. Griffin et al. (2005) found that the benefit of help was key to the extent of facultative production of the helping sex. They used helpers' effect on productivity as a measure of this benefit. There are issues with this approach, as in some species helpers improve downstream recruitment rather than breeding productivity and in others they have less effect on productivity but provide direct benefits to breeders through load lightening (Hatchwell 1999;Hatchwell et al. 2004;Preston et al. 2016). Quantifying the total benefit that help provides to breeders is therefore challenging and potentially misleading. Nevertheless, variation in the true value of this effect is likely to explain some of the wide variation in patterns of sex ratio adjustment that we have identified in this study.

Conclusion
The repayment hypothesis is strongly supported in certain species of cooperatively breeding bird, but our study shows that its predictions do not explain variation across species. On a generalized level, we find that its importance is marginal in driving both sex ratio biases and facultative sex allocation. We have suggested several factors that may confound predicted results, but it is surprising that predictions from such an intuitively appealing theory do not fit observed patterns. This contrasts with the majority of work on sex allocation, in which theoretical predictions have matched empirical results with a great deal of success (West 2009). We conclude that repayment is an occasional but not widespread influence on sex allocation in cooperatively breeding birds.