Stochastic linkage

In many species with heritable sex determination, the sex chromosomes are heteromorphic. Furthermore, in most systems with large non-recombining regions, the heteromorphic chromosome has accumulated a high number of deleterious alleles. Finally, it is well established that many loci that exist on the X have been completely lost from the Y (Ohno 1967). In phylogenetic analysis, sex chromosome heteromorphism is associated to sex ratio (Pipoly et al. 2015) and reproductive isolation (Lima 2014). In this section, I review the body of literature considering the degeneracy of the Y chromosome. Currently, the single factor best able to explain the accumulation of deleterious mutations is the absence of recombination on Y chromosomes. Similar to the degeneration of asexual species, the reduced efficacy of selection caused by selection at linked sites can account for the degeneracy of the Y.

In 1914, Muller proposed that the heteromorphic chromosome was actively degenerating (Hermann J. Muller 1914). Considering the accumulating evidence that the Y carried  disproportionately low numbers of genes, Muller suggested that Y heteromorphism was not an optimized product of natural selection, but rather that somehow selection was not able to act effectively on the Y.  In other words, as paraphrased by Haldane, the “Y chromosome ‘empties’ in the course of evolution” (Haldane, 1933, p.13). Perhaps, Muller proposed, the same process that could cause genes on the Y to be completely lost led genes could also lead to a disproportionately accumulation of deleterious mutations on the Y. In support of his hypothesis, by 1918, Muller had found substantial evidence showing an accumulation of deleterious and lethals variants on the Y. However, these deleterious variants were sheltered because any Y mutant could be masked by the X chromosome (H. J. Muller 1918).

Given Y-Y genotypes do not arise, the Y chromosome is always heterozygous. Westergaard’s model, build from Corren’s hypothesis, established that the best Mendelian interpretation of sex chromosomes suggests Xs carry recessive male sterility allele and Ys carry dominant female sterility allele. Any individual with an Y chromosome is female sterile and therefore must mate with an individual that is female fertile. Matings between Y-bearing individuals should be rare, as both individuals would be female-sterile, causing Y-Y genotypes also to be rare or even absent. Following this reasoning, Muller proposed that the masking of Y alleles by X alleles could allow deleterious recessive alleles to build up on the Y, thus accounting for its degeneracy (Hermann J. Muller 1914). While dominant deleterious mutations on the Y would be removed by selection, recessive deleterious mutations on the Y could be masked by their X counterpart. Recessive deleterious mutations on the X would be purged in females, but those on the Y would never be subject to selection. Over time, Y-Y genotypes would be further purged as begins the unmasking of recessive deleterious mutations build-up.

However, masking of deleterious recessive alleles is not enough to account for a disproportionate degeneration of the Y. Unless mutations are accumulating faster on the Y, mutations at the same loci on the X will uncover recessive mutations on the Y (R. A. Fisher 1935), yet, we expect the X and the Y to have equal rates of mutation. While it is true that because females carry two X chromosomes while males carry one X and one Y, and therefore the effective population size of the Y is ⅓ that of the X, causing the rate of mutations on Ys population-wide to be ⅓ that of the X as Y’s are three times rarer in the population. We also expect drift to fix alleles more slowly on the X as it has a larger effective population size. Therefore, as expected under mutation-drift balance, we expect new mutations to fix at the same rate on the X as on the Y. To be tenable, Fisher showed Muller’s model required another force account for the higher fixation rate of mutations on the Y than on the X (R. A. Fisher 1935). Unless the rate of mutation is significantly higher for the Y specifically, a change in the efficacy of selection is necessary to explain the accumulation of mutations on the Y.

The maintenance of the Y as heterozygous has another effect besides masking: the Y chromosome never has the opportunity to recombine. Because the X and the Y do not recombine and Y-Y genotypes never occur, Y chromosomes are never in a situation where they have a homolog with which to crossover. The absence of recombination on the Y chromosome places it center stage in the debate on the evolution of sex. Since the body of work on the evolution of sex considers asexuality explicitly as the absence of recombination, uncovering the cost of asexual reproduction may explain the degeneration of non-recombining chromosomes such as the Y (Brian Charlesworth 1978; Darlington 1937).

At first glance, the maintenance of sex as a reproductive strategy is counter-intuitive, and has shown to be a challenging conundrum to resolve (Maynard Smith 1978). Only half of the genome of sexual organisms is passed on to the next generation in contrast to the whole genome that is passed to offspring of asexual organisms. All else being equal, asexual genotypes should spread in a population twice as fast as a sexual one. However, the degeneration of large non-recombining Y chromosomes provides evidence that there may be a cost to the loss of recombination. The current best explanation is the sex breaks down random associations between alleles.

In 1886, Weissman proposed a verbal argument for why sex should be favoured by natural selection over asex (Weismann 1889). Weissman’s main postulate was that sex, by shuffling inherited materials, offered more variance on which selection could act. “Sexual reproduction will readily afford such combinations of required characters, for by its means the most diverse features are continually united in the same individual, and this seems to me to be one of its most important results” (Weissman, 1886, p.281). Similar ideas were proposed by Fisher (Ronald A. Fisher 1930), Wright (Wright 1931), Darlington (Darlington 1937) and Muller (H. J. Muller 1932). In general, their theories proposed that the efficacy of selection will be hindered by chance associations between alleles with different fitness effects (Felsenstein 1974).

The integration of chance and of stochasticity into models of evolution has been broad and its study has been rewarding (Lenormand, Roze, and Rousset 2009), especially for understanding the benefits of recombination. A classic example of the incorporation of chance into models of evolution is S. Wright’s concept of genetic drift, fluctuations in allele frequency between generations caused by chance (Wright 1931). By switching to populations that were composed of a finite number of individuals rather than a hypothetical infinite population, random events mattered and their chance of having an effect depended on their frequency in the population. In 1964, Muller proposed that disadvantageous mutations can accumulate in asexuals by the stochastic loss of the group which have the smallest number of deleterious mutation (H. J. Muller 1964). With each loss of the least loaded class, the mean fitness of the population would decrease (Haigh 1978; B. Charlesworth and Charlesworth 1997).

Furthermore, stochastic processes can cause linkage disequilibrium (LD), which will affect the efficacy of selection (Robbins 1918). For example, the random addition of alleles into a population by mutation, or their loss by drift (Ohta and Kimura 1969), will cause unpredictable, and often undesirable, correlations between alleles. Without recombination, selection must choose between one of these blocks of alleles rather than choosing each allele individually. In 1966, Hill and Robertson using computer simulations found that selection was less effective when accounting for random associations between alleles (Hill and Robertson 1966). In his 1974 review on the topic, J. Felsenstein concluded that Muller’s hypothesis (which he named ‘Muller’s ratchet’), the simulations of Hill and Robertson (‘the Hill-Robertson effect’) and, more generally, models considering the effects of chance, were the most promising resolution to the question of the maintenance of sex by natural selection (Felsenstein 1974; Felsenstein and Yokoyama 1976). “Those authors who have allowed finite-population effects into their models have been the ones who found an advantage to having recombination” (Felsenstein, 1974, p. 738).

[disentangle signal and action: signal is a neutral sites but action is at non-neutral sites. With linked selection, you can’t find the signal of the other.]

The study of the effect of selection at linked sites lead to the development of models of genetic hitchhiking and of background selection. Genetic hitchhiking proposed that alleles near sites under positive selection could rapidly spread and fix, or ‘sweep’, through a population (Smith and Haigh 1974), and that sweeps could happen even when the linked allele had slightly deleterious effects on the organism’s fitness. By being linked by chance to beneficial alleles, the nearby alleles were predicted to increase in frequency along with the locus under positive selection. Similarly, background selection proposed that strong negative selection reduced the number of viable haplotypes in a population, such that many linked alleles never get to spread; because less haplotypes last on evolutionary timescales, selection has less to choose from and is less effective (B. Charlesworth, Morgan, and Charlesworth 1993).

Disentangling each strain of linked selection has been troublesome empirically because the effects of hitchhiking and of background selection produce similar expectations. However, the general predictions of reduced polymorphism in regions of low recombination have been found in Drosophila (Begun and Aquadro 1992; Elyashiv et al. 2016), C. elegans (Cutter and Choi 2010; Rockman, Skrovanek, and Kruglyak 2010) as well as most other systems studied. While the relative effects of either sweeps or background selection remains debated, the effects of linked selection generally are well supported. It is in the interference zone that you get degeneration, within the assumptions of background selection you only get reduction in diversity at linked neutral sites.

Since the body of work on the evolution of sex considers asexuality explicitly as the absence of recombination, stochastic LD building processes offer a practical mechanism for explaining the degeneration of non-recombining chromosomes such as the Y (Brian Charlesworth 1978; Darlington 1937). Essentially, this conceptual transition views that the degeneration of the Y can be anticipated by considering the effects of selection on sexual vs asexual regions of a same genome. For example, to predict the effects Muller’s ratchet on sex chromosomes, we expect the fittest Y haplotypes in a population to eventually be lost by chance, and to never be recovered. With each loss of the best Y haplotypes, the mean fitness of Y haplotypes in the populations falls further behind the mean fitness of Xs or of the autosomes in the population (B. Charlesworth and Charlesworth 1997). Similarly, hitchhiking on the Y chromosome is predicted to allow the spread of deleterious variants dragged along by selection on linked beneficial site and hence to cause degeneration (Rice 1987), while background selection on the Y can lower the effective selection on linked slightly deleterious mutation and therefore increase their probability of fixation (B. Charlesworth 1996). Finally, linked selection can reduce the probability of fixation of beneficial alleles on the Y compared to the X due to the reduced efficacy of selection (Peck 1994). Depending on the number of loci under selection and the strength and direction of selection (Kaiser and Charlesworth 2009; Good et al. 2014), all these processes could contribute to Y chromosome degeneration.

Early studies of fixed differences between X and Y find credence to the idea that, as predicted, alleles on the Y have less efficient selection. The most common quantification of reduced selection is the ratio of non-synonymous substitutions to synonymous substitutions (dn/ds). Indeed, the Y chromosome has often been observed to have a significantly higher dn/ds ratio. While a high dn/ds ratio could also be caused by positive selection, further studies using within population polymorphisms have confirmed that the higher rate of evolution on the Y is due to less efficient selection rather than to positive selection. Finding less non-synonymous polymorphism than non-synonymous substitutions suggests more new mutations fix than are expected, a signal indicative of reduced efficacy of selection (McDonald and Kreitman 1991). In accordance with predictions from linked selection within populations, studies in humans (Wilson Sayres, Lohmueller, and Nielsen 2014) and in Rumex (Hough et al. 2017), among others, observed reduced polymorphism on the Y. Together, these results suggest linked selection played a significant role in the evolution and degeneration of large sex chromosomes.

 

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