Sexual antagonism evolves when autosomes influence offspring sex ratio

Sex allocation theory generally assumes maternal control of offspring sex and makes few predictions for populations evolving under paternal control. Using population genetic simulations, we show that maternal and paternal control of the sex ratio lead to different equilibrium sex ratios in structured populations. Sex ratios evolved under paternal control are more female biased. This effect is dependent on the population subdivision; fewer founding individuals leads to both more biased sex ratios and a greater difference between the paternal and maternal equilibria. In addition, sexual antagonism evolves in simulations with both maternally- and paternally-acting loci. Maternally-acting loci continuously accumulate ever more female-biasing effects as male-biasing effects accumulate at paternally-acting loci. The difference in evolved sex-ratio equilibria and the evolution of sexual antagonism can be largely explained by differences in the between-group variance of maternal and paternal effects in the founding generation. These theoretical results apply to any system with biparental autosomal influence over offspring sex, opening up an exciting new line of questioning.

(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint

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Evolved sex ratios reach different equilibria for each condition 146 We performed simulations for each of three conditions representing three different 147 autosomal modes of regulating sex allocation: maternal effect, paternal effect, or both 148 simultaneously, across a range of founder numbers. As expected, female-biased sex 149 ratios evolved in every case. Evolved sex ratio varied significantly by simulation 150 condition (p < 10 -15 ; analysis of deviance from a linear regression). Across all founder 151 numbers tested, sex-ratio equilibria in simulations with paternally-acting loci were more 152 female biased than those in simulations with maternally-acting loci ( Fig. 2A,B). In 153 simulations with both maternally-and paternally-acting loci, the evolved equilibrium was 154 intermediate, though closer to the maternal condition ( Fig. 2 A,B). The rate of evolution 155 was different between the three conditions, with the maternal-only condition slower to 156 evolve than the other two conditions ( Fig. 2A). As expected from theory, the evolved sex 157 ratios approach 0.5 as the number of founders in our simulations increases (Fig. 2B). 158 We also see the differences between conditions shrink as the number of founders 159 increases. Note that a small brood size constrains sex-ratio equilibria. This is most 160 apparent in the two-founder paternal case where the equilibrium for a brood size of 10 is  (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint

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. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint Sex ratio loci are sexually antagonistic. 172 When both maternally-and paternally-acting loci are segregating in a population  (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint

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. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint The effects of overlapping generations. 200 An important metapopulation parameter is generational overlap. When generations 201 overlap, founding individuals are able to mate with their offspring. We hypothesized that 202 by producing more female-biased broods, founding fathers increase the probability of greater than six, we see no significant difference in the rate of sexual antagonism 215 evolution for overlapping and discrete simulations (p < 10 -15 , p < 10 -15 , p < 10 -9 , p < 10 -5 216 p < 0.67; t-test for two, three, four, five, and six founders respectively). For the two-     Patches with more female-biased sex ratios have a population growth advantage and 232 will be overrepresented during migrant selection. When the variance among patches in 233 migrant production is zero all patches will be equally represented in the migrant 234 population and frequency-dependent forces will drive sex ratios to equality (Charnov,  However, it does not totally explain the phenomenon. QST in the two-founder scenario is 248 the same in overlapping and discrete simulations while the sex ratio in discrete 249 simulations is less biased (Fig. 5B,D). This likely represents constraint at the first 250 generation of offspring production on a patch. In the overlapping scenario a single male 251 founder can assure mating for the second generation and is therefore free to evolve a 252 more biased sex ratio. This constraint is likely not limited to just two founders. Sex ratios 253 evolved under maternal-only conditions are also overall more biased with discrete 254 generations (Fig. 5B,D). In both overlapping and discrete conditions, QST explains the 255 majority of the variation in sex ratios (overlapping, R 2 = 0.8864; discrete, R 2 = 0.8576).

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For conditions with both maternal and paternal loci, QST is larger for paternal effects and 257 smaller for maternal effects (Fig. 5E,F). Sex ratios across all simulation conditions and 258 founder numbers evolved less-biased sex ratios than predicted by Hamilton's model  (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint

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. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint Effects of multiple generations and mating before and after dispersal.

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As predicted by the haystack model, sex ratios became more female biased as a 286 function of the number of generations in a patch for all three models (Fig. 6). As 287 expected, sex ratios do not evolve a bias with single-generation patches in either of the 288 models with mating after dispersal, as they are equivalent to constant panmictic 289 conditions. Overall, the inheritance mode did affect the evolved sex ratio for all models 290 (p < 10 -4 , p < 10 -11 and p < 10 -15 ; deviance from linear regression for mating after 291 colonization, mating in pool and mating before dispersal). In addition, we observed the 292 evolution of sexual antagonism for each of the three models (Supp. Fig. 1).

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For the mating-before-dispersal model there was no difference in the evolved sex 294 ratios between the inheritance modes with a one-generation patch, which is equivalent 295 to the canonical LMC model (p = 0.90; deviance from linear regression). Similarly, we 296 saw no difference in the evolved sex ratios between inheritance modes for the single-297 founder scenario across all numbers of generations in a patch for the mating-before-298 dispersal model (p = 0.96; deviance from linear regression). This was also true for 299 mating after colonization for a founder number of two (p = 0.78; deviance from linear 300 regression, see Fig. 4 for comparison). However, we did see a marginally significant 301 difference when looking at the mating-in-pool model (p = 0.03; deviance from linear 302 regression). These tests may be limited by simulation sample size, as we do observe 303 . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint

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. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint the evolution of sexual antagonism for one and two founders in the mating-after-311 colonization and mating-in-pool models (Sup. Fig. 1).

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We show for the first time that maternal or paternal autosomal control of the sex ratio drives sex ratios to equality (Charnov, 1982). The mechanism producing this among-335 patch variation is sampling error in the migrant selection process, which causes sex-336 ratio genotypes to be distributed unevenly among patches. Sampling error increases as 337 founder number decreases, leading to more biased sex ratios. As a consequence of the 338 selection for a female-biased sex ratio, the population of males is smaller than the 339 population of females. It follows that the average patch will have fewer male founders 340 . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted June 15, 2023. ; https://doi.org/10.1101/2023.06.14.544982 doi: bioRxiv preprint than female founders. Sampling error for males and their paternal genetic effects will 341 consequently be higher, leading to greater variance among patches in population 342 growth and eventually migrant production. Another way to describe this is that paternal-343 effect loci experience selection under a smaller "effective founder number" than 344 maternal-effect loci given the same census founder number.

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A second new result is that sexual antagonism evolves when maternal and paternal 346 sex-ratio loci are acting in the same population. In this case, paternal loci that are 347 female biasing are fixed continuously while maternal loci that are male biasing are fixed.

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The rate of sexual antagonism evolution is dependent on the number of founding 349 individuals and peaks at six founders. These results can also be explained by QST;  The within-patch differences between maternal and paternal control of the sex ratio can be illustrated with a simple numerical example involving a patch with three male and three female founders. In each patch, an allele that shifts offspring sex ratio from 0.5 to 0.35 to 0.2 with each additional allele in the parental genotype starts at frequency 0.5 in the founding generation. Each female has 10 offspring.