Low rates of crossover between the X and the Y seems to be one of the defining characteristic of sex chromosomes (Harkess et al. 2017; Vicoso, Kaiser, and Bachtrog 2013). One hypothesis can adequately explain limited crossovers on part of the sex chromosomes: if the appearance of separate males and females in a population of hermaphrodites involves a sterility mutations for each sex, offspring which inherited both sterility mutations would be completely sterile and therefore selection can favour the restriction of crossovers between sex-specific sterility mutations. Yet, given this model requires only two mutations, can it explain the wide variation in recombination rate between sex chromosomes that is observed across different species: in some species recombination is completely absent in one sex (for example, Drosophila (Morgan 1910) or the amphipod crustacean Gammarus chevreuxi (Huxley 1928)), while in others the non-recombining region of the sex chromosomes is limited to between two loci (for example, fugu pufferfish (Kamiya et al. 2012) and asparagus (Harkess et al. 2017)). A whole suite of differences between these extremes in recombination rate variation exists (Bachtrog et al. 2014). In this section, I review models that explain the evolution of recombination rate on the sex chromosomes and the observations for which those models should be able to account.
The rate of recombination describes the probability that two alleles are inherited independently. In practice, recombination can be used to model both the independent assortment of chromosomes and/or crossover events (Muller 1932; C. D. Darlington 1939). The distinction between assortment and crossover can be important in some cases. For example, in Drosophila there are no crossovers on any chromosomes during meiosis in males. However separate chromosomes are still independently assorted at meiosis, and therefore there is a distinction between chromosomes that never experience crossover events because they segregate with maleness (the Y) and chromosomes that can crossover because they are occasionally in females (the autosomes and the Xs). Models have often been developed to broadly ask whether and under which circumstances recombination modifiers can evolve, and the unique considerations of independent assortment are subsequently compared to those of changes to crossover rate. These models assume recombination rate could evolve if under selection.
Recombination rate is both variable and heritable, and therefore is predicted to evolve under selection. Both independent assortment and crossover rate have been observed to be polymorphic within populations and to have diverged between related taxa. In some species, chromosome number is polymorphic. Chromosome number can change when chromosomes fuse with each other or when one chromosome splits into separate parts (Schubert and Lysak 2011). Fused chromosomes no longer segregate independently, which can affect the rate of recombination between alleles on previously separate chromosomes. Similarly, recent work on a gene participating in establishing crossover location in mammals, PRDM9, has shown it to be polymorphic within populations, and that individuals with different genotypes at the PRDM9 locus have different rates of recombination (Kono et al. 2014). Chromosomal inversions have also been documented to have a significant role in recombination modification (Noor et al. 2001; Rieseberg 2001). Together, this evidence suggests recombination should be able to evolve when under selection. The question remains as to under which conditions recombination rate on the sex chromosomes could be under selection.
In 1937, Darlington proposed low rates of crossover were essential to sex chromosome ontogeny (Cyril Dean Darlington 1937). From his study of sex chromosome cytotypes, Darlington concluded that the evolution of sex chromosomes was inseparable from the evolution of separate sexes from hermaphroditic populations, assuming that sex was heritable and followed Mendelian patterns of inheritance (Westergaard 1958; Cyril Dean Darlington 1937). Phylogenetic analysis suggests the transition between hermaphroditism and seperate sexes is common in plants (Goldberg et al. 2017) and in animals (Pennell, Mank, and Peichel 2018). At the very least, Darlington proposed, the complete transition to seperate male and female individuals from a hermaphroditic population required two mutations. Individuals in a hermaphroditic population with a male sterility mutation would exhibit female phenotypes and individuals with a female sterility mutation would exhibit male phenotypes. Darlington predicted that, in the transition to separate sexes, each sterility mutation must arise on different haplotypes as to avoid the deleterious fitness consequences of double-sterile haplotypes, therefore the recombination rate between these two haplotypes must be low or evolve to be low. Darlington’s verbal argument was formalized by Westergaard in 1958 (Westergaard 1958).
Darlington and Westergaard’s sex chromosome ontogeny model seems to be supported by empirical evidence. Young sex chromosomes contain an over-representation of alleles that cause substantial deformity or complete sterility of the sex organs (Harkess et al. 2017; Tennessen et al. 2018). How sterility mutations might spread or be maintained in a population, given these mutations are likely to be deleterious in any other context, has been subject to much speculation. Their maintenance is best explained by frequency dependent selection, but the cause of their spread is still subject to debate.
Sex-specific sterility mutations can be maintained by selection. Once one sterility mutation for each sex is maintained in the population, the transition to seperate male and female individuals has begun. When all hermaphrodites are lost and any individual can be categorized as either male or female, the population is known as dioecious. In stable dioecious populations, both sterility alleles can be maintained by frequency-dependent selection, as first stated by R.A. Fisher (Fisher 1930). If a genotype creates sex-biased progeny, that sex will become more frequent in the population in the next generation. As that sex is more common in the next generation, the sex-ratio-bias genotype becomes less successful: because the population develops a biased sex ratio, and the bias leans towards the sex overproduced by that genotype, individuals with the genotype causing the bias have less opportunities to mate as they are the most common sex. The sex-ratio-bias genotype is less successful any time it is present in more than half the population and therefore can never fix. This mode of frequency-dependent selection is expected to keep the sex ratio even and therefore allow for the maintenance of both sex-specific sterility mutations at equal frequency in the population. This model assumes sterility mutations have already invaded the population.
Sex-specific sterility mutations can sometimes invade a hermaphroditic population. Most models explaining the spread of sex-specific sterility mutations often aim to answer a related question: when is the transition from hermaphroditism to dioecy favourable? Contexts proposed to favour the transition from hermaphroditism to dioecy include optimization of sex-specific resource allocation (Charnov, Bull, and Smith 1976), evasion of constraints to seed dispersal or of pollen limitation (Lloyd 1982), or purging of deleterious mutational load (Agrawal 2001), but the most well-developed model in plants is that the evolution of dioecy helps avoid the cost of inbreeding depression (B. Charlesworth and Charlesworth 1978; Darwin 1877; Thomson 1981; Baker 1959). Self-fertilization has been predicted (Kamran-Disfani and Agrawal 2014; S. Wright 1921) and shown (eg. (Thornhill 1993)) to have important deleterious fitness consequences. Because population with separate sexes prevent the option for individuals to self-fertilize, the transition to dioecy is most beneficial when the cost of inbreeding is high, or when the cost of inbreeding is intermediate but the rate of selfing is very high. Further models have been developed to include the effects of inbreeding depression into models of the optimization of sex-specific resource allocation (Deborah Charlesworth 1999). While the relative roles of each process in the spread of sterility mutations in nature remains unclear, it is generally accepted that some combination of these models should be able to account for the transition to dioecy and the birth of non-recombining sex chromosomes (Geber and Dawson 1999).
A corollary of the two-sterility model of sex chromosome ontogeny is that sex chromosomes evolve from regular chromosomes. As any chromosome could harbour the pair of sex-specific sterility mutations, the loss of recombination, favoured by selection to avoid the cost of double-sterile individuals, will create sex chromosomes. The loss of recombination itself has further consequences on the alleles within the non-recombining region. The loss of recombination between X and Y is expected to allowed the sex chromosomes to diverge from each other. Indeed, ancient homology between X and Y genes for many species supports this hypothesis (Ohno 1967).
Recombination suppression allows for divergence, by selection and/or drift, between the X and the Y, in a form analogous to evolution in separate species. The methods used to estimate divergence times between related species (Motoo Kimura 1983; Brookfield and Li 1997) can and have (Lahn and Page 1999) been repurposed to estimate the time since recombination arrest between the X and Y. Studies of divergence time between the X and Y found that, while groups of genes which are physically close to each other on the X have similar divergence times, the divergence times across the entire sex chromosomes are best explained by discrete clusters of divergence rather than by one chromosome-wide divergence time (Pandey, Wilson Sayres, and Azad 2013). Discrete clusters of divergence times suggest several different evolutionary events have caused the loss of recombination between the sex chromosomes. Using the word borrowed from geology, the clusters of divergence times have been termed ‘evolutionary strata’ to invoke a sequential discrete process of additions where each stratum represent an older evolutionary period. First observed by Lahn and Page in humans (Lahn and Page 1999), strata have subsequently been observed in many other organisms including rodents (Sandstedt and Tucker 2004), birds (A. E. Wright, Moghadam, and Mank 2012) and the plant Silene latifolia (Bergero et al. 2007) to name but a few. The observation of evolutionary strata suggests that recombination loss across the sex chromosomes is more complex than can be expected from Darlington and Westergaard’s model of evolution to avoid double-sterile individuals, as strata are observed to be added to the sex chromosomes long after the dioecy has fixed.
One way to explain evolutionary strata is that the invasion of the sterility mutations is just one step in the evolution of sex chromosomes, and that subsequent to the transition to dioecy more genomic regions can become locked into segregating with the sex-specific sterility mutations. This hypothesis proposes that the sex chromosomes can grow over evolutionary time. To test this hypothesis, one might model whether there are situations where selection would favour linkage to a sex-determining region (SDR). Are there cases in which, given the two sterility mutations are fixed and have formed a small SDR, selection would favour the segregation of one allele with a specific sex sterility mutation more often than with the other? The hypothesis that sex chromosomes can acquire new genetic material subsequent to the transition to dioecy seems supported by phylogenetic study in Drosophila (Vicoso and Bachtrog 2015) and mammals (Cortez et al. 2014), while in other species, like ratite birds (Vicoso, Kaiser, and Bachtrog 2013), the non-recombining region of the sex chromosomes has remained small. When then does an allele that modifies recombination with the SDR invade a population?
When considering loci that modify the rate of recombination, the dynamics can be complex. Allele frequencies must be tracked at two loci between which we are interested in asking whether a recombination modifier can invade, while also tracking allele frequencies at a third locus that modifies recombination rate. The two loci of interest must be directly under selection, but this is not required for the recombination modifier. Furthermore, because the recombination rate changes according to the changes in allele frequencies, the recursion system must track the recombination rate between each of these loci. A set of equations tracking changes in allele frequency and the rate of recombination between them can have nonlinear dynamics, which are notoriously challenging and occasionally literally impossible to resolve (Boeing 2016), and therefore simplifying assumptions are often made (Lenormand 2003). First, it is often assumed that the recombination modifier is completely linked to the loci under selection. Second, it is also often assumed that the recombination modifier changes the recombination phenotype from unlinked to completely linked, rather than a range of changes in rate. These two simplifications remove the need to track the recombination rates as quantitative variables, which simplifies the equation. Using these assumptions, in 1973, Charlesworth and Charlesworth assessed the need of a linked recombination modifier to spread and showed that there are only two requirements for its invasion (B. Charlesworth and Charlesworth 1973). One requirement is a balanced polymorphism, meaning neither allele at either loci under selection should be able to fix in the population. The other requirement is linkage disequilibrium (LD), the maintenance of a correlation between the alleles at the different loci under selection.
In the case of modelling recombination modifiers linked to sex chromosomes, one of the two loci under selection is the SDR. The SDR is under balancing selection due to selection for an even sex ratio (Fisher 1930), as mentioned above. Therefore, in sex chromosome recombination models, the allele frequency at the SDR is often ignored. In terms of meeting the LD requirement, many evolutionary processes can cause correlation between alleles, including genetic linkage, population structure, and selection. Selection can act to cause correlations between alleles when there is epistasis, which is defined as an increase in the total fitness when both alleles are inherited together over that which would be expected from adding together the fitness of each allele on its own. As the SDR determines sex, alleles involved in sex-specific processes are likely to have epistatic interactions with the SDR. In the case of sex chromosomes, alleles under sex-specific selection should exhibit epistasis with the SDR, as their selection coefficient will be increased when inherited with the appropriate sterility allele. In sum, the requirements for the invasion of a linked recombination modifier on sex the chromosomes are that another locus have a balanced polymorphism and have sex-specific effects.
The first researcher to ask when a chromosome fusion would spread was M.J.D. White (M. J. White 1957). White was specifically interested in the case where autosomes fused to sex chromosomes to become themselves sex linked, a phenomenon he dubbed as the formation of a neo sex chromosome (M. J. D. White 1940). Formally, White was asking about a linked modifier of the independent assortment of chromosomes, a modifier which would lower the recombination rate below complete independence. White proposed that heterogametic-sex-specific overdominance could favour linkage to the sex chromosomes. In other words, if a locus was overdominant only in the heterogametic sex, it would be favoured by selection to link that locus to the sex determining region. Both requirements for the invasion of a recombination modifier are met: overdominance causes a balanced polymorphism and making it sex-specific causes sex-specific epistasis with the SDR. However, while possible, White’s overdominance model does not hold the explanatory power required to account for the observed variation in recombination rate between sex chromosomes of different species as overdominance is uncommon in nature (Gemmell and Slate 2006). A different source of balanced polymorphism was required to explain this variation.
In 1948, A.J. Bateman revolutionized the view of sex-specific selection in a way that massively broadened the parameter space under which polymorphism could be maintained (Bateman 1948). In Darwin’s view, sex-specific selection was a difference in the strength or in the presence/absence of selection between the sexes (Darwin 1859). In contrast, under Bateman’s new proposal, selection could act in opposite directions in each sex because males and females had different reproductive strategies (Bateman 1948). Bateman proposed that phenotypes could be favoured in one sex that were deleterious in the other sex. Indeed, Bateman’s experiments with Drosophila showed more variance in mating success in males than in females, which he proposed was best explained by opposite selection between males and females. Bateman’s proposal has since been formalized, and is described as a difference between males and females in their respective fitness optima (Parker 1979; Trivers 1972): while for males the increase in number of offspring is linearly correlated with an increase in fitness, females have a nonlinear relationship between offspring count and fitness. For females, a trade-off exists between energy spent in care versus that spend in production of more offspring such that a maximal clutch size may exist. Selection on phenotypes participating in the trade off between offspring investment and offspring count should be different between males and females. When one gene with two alleles is underlying such phenotypes, selection can maintain a stable polymorphism at that locus (Owen 1953; Kidwell et al. 1977). This form of sexual selection would later become known as ‘sexually antagonistic’ (Rice 1984, 1987). The stable maintenance of a polymorphism due to sexually antagonistic selection allowed for the invasion of dominance modifiers. In 1980, Charlesworth and Charlesworth (D. Charlesworth and Charlesworth 1980) reconsidered White’s framework of chromosomal fusions to include sexual antagonism. Sexual antagonism elegantly fills both requirements for the spread of a recombination modifier: it keeps alleles polymorphic and causes LD with the SDR through epistatic effects. Although perhaps the most intuitive explanation for the formation of neo sex chromosomes, these models require very strong sexually antagonistic selection.
The requirements for the strength of sexually antagonistic selection are less stringent when some LD already exists, as would be expected from physical linkage. In other words, the invasion of a recombination modifier is much less restricted when the locus under selection and the SDR are already on the same chromosome (Bull 1983; Rice 1987; Kirkpatrick and Guerrero 2014; Sarah P. Otto et al. 2011). This form of recombination suppression predicts that recombination loss is more likely to spread across the sex chromosomes if an SDR is established (Sarah P. Otto et al. 2011).
A recent extension to the sexual antagonism mode for the maintenance of polymorphism considers selection in the haploid phase of the lifecycle (Lenormand and Dutheil 2005; Michael F. Scott and Otto 2017; Michael Francis Scott, Osmond, and Otto 2018). Selection is expected to be more efficient on haploid expressed alleles: regardless of whether the allele is dominant of recessive in the diploid, all alleles are unmasked in the haploid stage thus removing the effect of dominance from selection and increasing selection’s efficacy. This increased efficacy of selection in the haploid may indirectly increase selection on the recombination modifier, above what would be expected for selection in the diploid phase (Michael F. Scott and Otto 2017).
Another mode for the accumulation of LD that can explain the spread of recombination modifiers is stochastic LD. This class of model is similar to those used by Otto and Barton (S. P. Otto and Barton 1997) to explain the maintenance of recombination as an adaptive strategy. This class of model assumes the recombination modifier is only loosely linked to the loci under selection. Using the assumption that traits evolve under Quasi-Linkage Equilibrium (M. Kimura 1965), Nei could explain the arrest of recombination between two sex-specific sterility mutations (Nei 1969). While Nei’s model can explain the transition from hermaphroditism to dioecy under sex-specific selection, akin to Darlington and Westergaard’s model, Nei’s model accounts for difference in the total rate of recombination between the sexes rather than the formation of sex chromosomes. In 2003, Lenormand expanded Nei’s model to consider selection on alleles with sex-specific effects, given the SDR was already established (Lenormand 2003). Sex-specific differences in total recombination rate has been reported in many species (Huxley 1928), perhaps most famous is the complete absence of cross-over in Drosophila males. I return to the topic of Stochastic linkage in the next section.
Finally, hemizygosity causes LD. The basic observation that recombination can lower LD over time has motivated the search for modes of selection that maintain alleles together. However, if there is no homologous gene copy there can be no recombination and therefore that locus is in high LD. Hemizygosity may contribute to maintaining limited crossover rates in systems where genes have been lost from the Y chromosome or when the SDR has been transposed onto one haplotype. This mode has been invoked to explain the lack of recombination across the sex determining region in polyploid Fragaria strawberries (Tennessen et al. 2018) and across the heterostyly locus in Primula vulgaris primrose (Li et al. 2016).
Selfish genetic elements can also cause the spread of recombination modifiers. In 1881, Roux conjectured a theory called Kampf der Theile im Organismus (Battle of parts in the body) (Roux 1881; Romanes 1881) in which he proposed that, as a reasonable extension of evolution by natural selection, we should expect every part of an organism to compete against every other part for survival. Haldane extended Roux’s Kampf der Theile theory to include a battle between every gene (Haldane 1933), proposing that “ the process continues until natural selection or the increased activity of other genes puts a stop to it” (Haldane, 1933, p.15). Particularly surprising is the conclusion that, despite potentially imposing substantial fitness costs upon an organism, selfish genes can be very successful. For example, Haldane noted that “competition based on such characters as embryonic or pollen tube growth rates may be expected in some cases to lead to monstrous adult forms” (Haldane, 1933, p.8). Evidence of selfish spread of genetic elements has been found in Drosophila (Wei et al. 2017; Coyne 1989), monkeyflower (Fishman and Willis 2005) and mice (Kelemen and Vicoso 2018) to name but a few. The appealing aspect of selfish genetics is that it can explain invasion of alleles that otherwise have substantial fitness costs (Dawkins 1976; Hamilton 1967; Williams 1966).
The idea that sex chromosome cytotypes evolved by selfish evolution has been considered multiple times (Ubeda, Patten, and Wild 2014; Yoshida and Kitano 2012). Indeed, because sex chromosomes are inherited in a sex-specific manner and meiotic drivers most often have sex-specific effects (Hedrick 1981; Hartl 1977), meiotic drivers are most likely to spread on the sex chromosomes. For example, selfish elements that can bias their segregation away from the polar bodies during female meiosis are most likely to spread through a population if the selfish element is inherited more often by females, and therefore linkage to the sex determining region is favoured (Yoshida and Kitano 2012; Ubeda, Patten, and Wild 2014). In this case, the recombination modifier itself is under direct selection, and therefore the status of the loci between which recombination is to be modified is only limited by how deleterious these alleles or their joint inheritance is. Sex-specific sex-linked meiotic drivers have been observed in nature several times. In Drosophila, the famous selfish element that kills Y bearing sperm, sexRatio, is sex-linked (Sturtevant and Dobzhansky 1936; Policansky and Ellison 1970; Bastide et al. 2013; Fuller et al. 2018). The many dearth of polymorphisms observed on the X chromosomes of gorillas is best explained by selective sweeps of selfish elements (Nam et al. 2015), as is the higher than expected level of LD between alleles on the X in Drosophila recens (Dyer, Charlesworth, and Jaenike 2007).
A class of selfish genetic elements known as transposable elements can induce hemizygosity by transposition, and therefore reduce recombination rate. Transposable elements (TEs), discovered in Maize by B. McClintock (McClintock 1931, 1950), are small selfish genetic elements that easily move through the genome. Transposable elements have been found to be abounding on the sex chromosomes [cit], and may occasionally bring new genes onto the sex chromosomes. For example, in Fragaria, TE vestiges surround the sex determining region, and the SDR has been observed to move to different chromosomes in closely related Fragaria species (Tennessen et al. 2018). Alternatively, TEs can have direct effects on recombination rate (as reviewed by (Kent, Uzunović, and Wright 2017)).
Recombination loss over part or all of the sex chromosomes, or even complete loss of recombination in one sex, seems to be a standard feature of species with heritable Mendelian sex determination. Various forms of selection can account for recombination loss. Although sex antagonism is the best studied, any process that can cause balanced polymorphism and sex-specific epistasis may allow for the invasion of loci that can modify rates of recombination. The following two sections build on this observation: lower rates of recombination may be the ultimate cause of Y degeneration and as that of disproportionate population differentiation on the X.
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