Adaptive meiotic drive in selfing populations with heterozygote advantage

The egalitarian allotment of gametes to each allele at a locus (Mendel’s law of segregation) is a near-universal phenomenon characterizing inheritance in sexual populations. As exceptions to Mendel’s law are known to occur, one can investigate why non-Mendelian segregation is not more common using modifier theory. Earlier work assuming sex-independent modifier effects in a random mating population with heterozygote advantage concluded that equal segregation is stable over long-term evolution. Subsequent investigation, however, demonstrated that the stability of the Mendelian scheme disappears when sex-specific modifier effects are allowed. Here I derive invasion conditions favoring the repeal of Mendelian law in mixed and obligate selfing populations. Oppositely-directed segregation distortion in the production of male and female gametes is selected for in the presence of overdominant fitness. The conditions are less restrictive than under panmixia in that strong selection can occur even without differential viability of reciprocal heterozygotes (i.e. in the absence of parent-of-origin effects at the overdominant fitness locus). Generalized equilibria are derived for full selfing.

Considerations such as these seem to argue that Mendelian ratios ought to be widespread 45 (in accord with observation) and evolutionarily stable. However, Úbeda and Haig (2005) 46 proved the existence of conditions in which rare modifiers are expected to invade a 47 resident population by virtue of promoting meiotic drive at unlinked autosomal loci subject 48 to fitness variation. In the present work, I demonstrate that the conditions for evolving a 49 stable phenotype of meiotic drive are even less restrictive when self-fertilization is 50 included in the model. 51 The general evolutionary causes of autosomal adherence to Mendelian segregation has 52 received sporadic attention in the theoretical population genetics literature since it was 53 first modeled in the 1970s (Hartl 1975;Liberman 1976Liberman , 1990; Thomson and Feldman 54 1976; Feldman 1980, 1982;Lloyd 1984;Eshel 1985;Úbeda and Haig 2005, 55 Brandvain and Coop 2015). One branch of these efforts assumes a random mating 56 population with a focal locus subject to di-allelic variation and heterozygote advantage, in 57 3 which the alleles have evolved to a stable equilibrium. A second locus is assumed to be 58 variable for alleles that modify the segregation ratio at the focal fitness locus. The key 59 question is: what are the conditions favoring the spread of a rare modifier? Early models 60 investigated sex-independent variables and parameters. Notable results include Liberman 61 (1976), who found that in a population fixed for a resident phenotype of Mendelian 62 segregation, rare modifiers could spread under broad conditions: any rate of 63 recombination less than one-half can result in the invasion of a drive-enhancer (i.e. a 64 modifier that imposes or increases a deviation from equal segregation) given that it is 65 sufficiently strong, with tight linkage being especially conducive to invasions. Eshel (1985) 66 showed that in the case of free recombination, the only kinds of modifiers which can invade 67 are those that reduce the intensity of drive; enhancers are uniformly selected against.

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These results recall the metaphor of Leigh (1977) who likened the genome to "a parliament 69 of genes" which enforces behavior consistent with the common good against "'cabals of a 70 few' conspiring for their 'selfish profit'" (p. 4543). Modifiers with sufficient linkage to a 71 distorting locus can form a selfish cabal, but the presumably greater number of unlinked 72 modifiers act to police outlaw behavior.

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An unsatisfying aspect of the work mentioned above is the assumption of sex-independent 74 effects. If a sex-differentiated population is assumed, and if accordingly modifiers have sex-75 specific effects on male and female segregation, then an analysis of modifier invasion 76 demonstrates that unlinked genes should evolve to subvert Mendelian ratios after all 77 (Úbeda and Haig 2005). The benefit in doing so owes to the assumption that a modifier acts 78 on a locus exhibiting heterozygote advantage. Oppositely-directed segregation schemes, in 79 which an allele has a segregation advantage in one sex but a segregation disadvantage in 80 the other sex, are selected for as a mechanism of producing a super-Mendelian proportion 81 of fit heterozygous offspring, and thus evolve to reduce the genetic load caused by the 82 production of unfit homozygous progeny (segregation load). This possibility was absent in 83 the sex-independent models. On the assumption of symmetric overdominance, in which 84 parent-of-origin effects on fitness are absent (i.e. "Aa" and "aA" genotypes have identical 85 fitnesses, where the order of the alleles distinguishes parental origin), rare modifiers of the 86 segregation scheme are selected to increase at a slow arithmetic rate. Asymmetric 87 overdominance in fitness, in which "Aa" and "aA" genotypes differ but their average fitness 88 is greater than either homozygote, is a situation which selects for the repeal of Mendelian 89 law at a speedy geometric rate. Úbeda and Haig (2005) discovered this phenomenon, which 90 I refer to as "adaptive meiotic drive" in order to contrast such cases with selfish distortions 91 of meiosis; the concept is defined here as any distortion of segregation ratios that reduces 92 the segregation load in a population, relative to the Mendelian expectation. Importantly, 93 the phenotypic state characterized by long-term stability is the rather un-Mendelian 94 scheme of "all-and-none segregation", in which ratios are maximally distorted in male and 95 female meiosis, but in opposite directions (see also Úbeda and Haig 2004).

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The importance of the sex-specific results with respect to biological phenomena is unclear 97 given that asymmetric overdominance in fitness is likely a rare class of balanced reproduction (e.g. male fertility reduction). Nevertheless, their results reveal that the 104 reasons for the ubiquity of Mendelian segregation are more obscure than is generally 105 appreciated (Úbeda 2006). 106 The impact of inbreeding on the invasion of unlinked modifiers of drive in the context of 107 heterosis has not previously been investigated, and it is reasonable to suspect that the   the genotypic proportions are given by: , which is valid for i, j = 1, 2, 3, 4 and such that ij and ji are not distinguishable. ′ is the  . 169 The stability of (̂,̂) to the introduction of infinitesimal variation at B (external stability)  Mendelian populations with partial selfing (0 < S < 1) and heterozygote advantage (0 ≤ W 181 <1) select for modifiers that impose oppositely-directed sex-specific meiotic drive of any 182 intensity: While the invasion analysis provides the conditions for the long-term spread of a rare  The lack of appreciable modifier evolution within 10 5 generations for the weakest 208 intensities of drive and selection in Fig. 1 calls for an investigation into cases where only 209 one of these processes exhibits small values, while the other process is strong. An 210 examination of cases reveals that weak segregation distortion and strong selection does 211 not guarantee timely evolution of modifiers (Fig. 2), nor does weak selection and strong 212 distortion (Fig. 3). Nevertheless, with coefficients of sufficient magnitude, cases of drive  Fig. S1).

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The invasion analysis (Result 1) and the preceding numerical results took on the 219 restrictive assumption that homozygote fitnesses were equal, and so I also present a 220 sample of numerical results where this assumption is relaxed. A difference in fitness 221 between the homozygotes (AA and aa) of course results in lower initial heterozygosity at A, 222 and a slower invasion rate of the modifier as compared to the case of equal homozygote 223 fitness (Fig. 4a,b); a shift in the frequency at the A locus occurs away from its Mendelian 224 equilibrium to a new value. In addition, if asymmetrically sex-reflected ratios (i.e. ≠ 1-

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) are investigated, a modifier polymorphism can appear (Fig. 4c-d). In some cases ( Fig.   226 4c), the mutant modifier winds up at an internal neutral equilibrium because the process of 227 modifier selection causes a frequency shift at the A locus into a fixation state; such an event 228 stops any further directional selection at the B locus. In other cases (Fig. 4d) allow for the modifier mutant to fix (Fig. 4e,f).

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External stability of all-and-none to drive suppressors in a partial selfing population 235 Úbeda and Haig (2005) reported that all-and-none segregation is stable to mutants of the heterozygotes, relative to panmictic Hardy-Weinberg proportions, even though selfing is 292 maximal (Fig. 5). Upon drive-enhancer fixation, the only modifiers which can subsequently 293 invade are those that impose even stronger oppositely-directed distortion. All-and-none 294 segregation under full selfing and stable heterozygote advantage is therefore expected to 295 persist over long-term evolution. replaced with meiotic drivers.

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Following Eshel (1985) and Úbeda and Haig (2005), here I adopt the modifier's eye view of 326 long-term evolution, rather than focusing on the short-term dynamics of meiotic drive 327 alleles per se. The modifier perspective is key, since whatever the short-term evolutionary 328 dynamics of any particular driver may be, the ultimate fate of drivers over the long-term 329 will owe to the make-up of the genetic background (Eshel 1996, Eshel andFeldman 2001).

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If the genes capable of modifying drive phenotypes overwhelmingly benefit from 331 suppressing such behavior, then any particular meiotic driver is destined for extinction on gametogenesis (Cleland 1972, Holsinger and Ellstrand 1984, Harte 1994 Additionally, there is a lack of realism associated with having a single modifier directly 370 control the production of both male and female gametes (Úbeda 2006