Eusociality is a distinct form of biological organization. A key characteristic of advanced eusociality is the presence of non-reproductive workers. Why evolution should produce organisms that sacrifice their own reproductive potential in order to aid others is an important question in evolutionary biology. Here, we provide a detailed analysis of the selective forces that determine the emergence and stability of non-reproductive workers. We study the effects, in situations where the queen of the colony has mated once or several times, of recessive and dominant sterility alleles acting in her offspring. Contrary to widespread belief based on heuristic arguments of genetic relatedness, non-reproductive workers can easily evolve in polyandrous species. The crucial quantity is the functional relationship between a colony’s reproductive rate and the fraction of non-reproductive workers present in that colony. We derive precise conditions for natural selection to favor the evolution of non-reproductive workers.DOI: http://dx.doi.org/10.7554/eLife.08918.001

Graphical Abstract Highlights d Crossover number is correlated across chromosomes within individual meiotic nuclei d CO covariation results from covariation of chromosome axis lengths within nuclei d CO covariation increases the frequencies of gametes with either many or few COs d Hyper-and hypo-CO gametes aid adaptation in a sporadically fluctuating environment SUMMARY Crossing over is a nearly universal feature of sexual reproduction. Here, analysis of crossover numbers on a per-chromosome and per-nucleus basis reveals a fundamental, evolutionarily conserved feature of meiosis: within individual nuclei, crossover frequencies covary across different chromosomes. This effect results from per-nucleus covariation of chromosome axis lengths. Crossovers can promote evolutionary adaptation. However, the benefit of creating favorable new allelic combinations must outweigh the cost of disrupting existing favorable combinations. Covariation concomitantly increases the frequencies of gametes with especially high, or especially low, numbers of crossovers, and thus might concomitantly enhance the benefits of crossing over while reducing its costs. A four-locus population genetic model suggests that such an effect can pertain in situations where the environment fluctuates: hyper-crossover gametes are advantageous when the environment changes while hypo-crossover gametes are advantageous in periods of environmental stasis. These findings reveal a new feature of the basic meiotic program and suggest a possible adaptive advantage.

Comparative studies in evolutionary genetics rely critically on evaluation of the total amount of genetic shuffling that occurs during gamete production. Such studies have been hampered by the absence of a direct measure of this quantity. Existing measures consider crossing-over by simply counting the average number of crossovers per meiosis. This is qualitatively inadequate, because the positions of crossovers along a chromosome are also critical: a crossover toward the middle of a chromosome causes more shuffling than a crossover toward the tip. Moreover, traditional measures fail to consider shuffling from independent assortment of homologous chromosomes (Mendel’s second law). Here, we present a rigorous measure of genome-wide shuffling that does not suffer from these limitations. We define the parameter r¯ as the probability that the alleles at two randomly chosen loci are shuffled during gamete production. This measure can be decomposed into separate contributions from crossover number and position and from independent assortment. Intrinsic implications of this metric include the fact that r¯ is larger when crossovers are more evenly spaced, which suggests a selective advantage of crossover interference. Utilization of r¯ is enabled by powerful emergent methods for determining crossover positions either cytologically or by DNA sequencing. Application of our analysis to such data from human male and female reveals that (i) r¯ in humans is close to its maximum possible value of 1/2 and that (ii) this high level of shuffling is due almost entirely to independent assortment, the contribution of which is ∼30 times greater than that of crossovers.