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Abstract Many animal species are haplodiploid: their fertilized eggs develop into diploid females and their unfertilized eggs develop into haploid males. The unique genetic features of haplodiploidy raise the prospect that these systems can be used to disentangle the population genetic consequences of haploid and diploid selection. To this end, sex-specific reproductive genes are of particular interest because, while they are shared within the same genome, they consistently experience selection in different ploidal environments. However, other features of these genes, including sex-specific expression and putative involvement in postcopulatory sexual selection, are potentially confounding factors because they may also impact the efficacy of selection asymmetrically between the sexes. Thus, to properly interpret evolutionary genomic patterns, it is necessary to generate a null expectation for the relative amount of polymorphism and divergence we expect to observe among sex-specific genes in haplodiploid species, given differences in ploidal environment, sex-limited expression, and their potential role in sexual selection. Here, we derive the theoretical expectation for the rate of evolution of sex-specific genes in haplodiploid species, under the assumption that they experience the same selective environment as genes expressed in both sexes. We find that the null expectation is that reproductive genes evolve more rapidly than constitutively expressed genes in haplodiploid genomes. However, despite the aforementioned differences, the null expectation does not differ between male- and female-specific reproductive genes, when assuming additivity. Our theoretical results provide an important baseline expectation that should be used in molecular evolution studies comparing rates of evolution among classes of genes in haplodiploid species. 

In holometabolous insects, larval nutrition affects adult body size, a life history trait with a profound influence on performance and fitness. Individual nutritional components of larval diets are often complex and may interact with one another, necessitating the use of a geometric framework for elucidating nutritional effects. In the honey bee, Apis mellifera, nurse bees provision food to developing larvae, directly moderating growth rates and caste development. However, the eusocial nature of honey bees makes nutritional studies challenging, because diet components cannot be systematically manipulated in the hive. Using in vitro rearing, we investigated the roles and interactions between carbohydrate and protein content on larval survival, growth, and development in A. mellifera. We applied a geometric framework to determine how these two nutritional components interact across nine artificial diets. Honey bees successfully completed larval development under a wide range of protein and carbohydrate contents, with the medium protein (∼5%) diet having the highest survival. Protein and carbohydrate both had significant and non-linear effects on growth rate, with the highest growth rates observed on a medium-protein, low-carbohydrate diet. Diet composition did not have a statistically significant effect on development time. These results confirm previous findings that protein and carbohydrate content affect the growth of A. mellifera larvae. However, this study identified an interaction between carbohydrate and protein content that indicates a low-protein, high-carb diet has a negative effect on larval growth and survival. These results imply that worker recruitment in the hive would decline under low protein conditions, even when nectar abundance or honey stores are sufficient.