Population genetics of modifiers of meiotic drive III. Equilibrium analysis of a general model for the genetic control of segregation distortion

doi:10.1016/0040-5809(76)90003-4

Theoretical Population Biology

Volume 10, Issue 1, August 1976, Pages 10-25

https://doi.org/10.1016/0040-5809(76)90003-4 Get rights and content

Abstract

Prout, Bungaard and Bryant (1973, Theor. Popul. Biol. 4, 446–465) presented the first formal treatment of a model of meiotic drive involving a modifier locus which controls the intensity of drive. They studied the equilibrium behavior in the simplest model where it is assumed that drive is maximal when not suppressed. In that case there is one polymorphic equilibrium at which there is linkage disequilibrium. The equilibrium solutions in the general model of meiotic drive proposed by Prout, et al. are given in this paper together with a stability analysis. It is shown that up to three polymorphic equilibria may exist, two of which are in linkage disequilibrium and one in linkage equilibrium. These equilibria exhibit behavior qualitatively opposite to what is widely accepted as the usual for two locus systems and which is not seem in the simple case originally treated. The polymorphic equilibria with linkage disequilibrium may be stable for loose linkage and not for tight while that with linkage equilibrium is stable in an interval of relatively tight linkage values.

References (7)

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Cited by (24)

Adaptive meiotic drive in selfing populations with heterozygote advantage
2022, Theoretical Population Biology
Citation Excerpt :
But even these cases are unstable in the long run, since an intermediate frequency of a selfish driver will select for suppressors throughout the genome, and so the existence of segregation distortion at a locus is regularly destabilized by adaptive countermeasures aimed at restoring the Mendelian order. In modeling work, the general evolutionary causes of adherence to Mendelian segregation has received sporadic attention in the theoretical population genetics literature since it was first taken up in the 1970s (Hartl, 1975; Liberman, 1976, 1990; Thomson and Feldman, 1976; Liberman and Feldman, 1980, 1982; Lloyd, 1984; Eshel, 1985; Úbeda and Haig, 2005; Brandvain and Coop, 2015; Scott and West, 2019; Madgwick and Wolf, 2021). One branch of these efforts assumes a random mating population with a focal locus subject to di-allelic variation and heterozygote advantage, in which the alleles have evolved to a stable equilibrium.
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.
Drive and sperm: The evolution and genetics of male meiotic drive
2009, Sperm Biology
Some selfish genetic elements in eukaryotic genomes have been harnessed to perform essential functions for their hosts, whereas others have gained transmission advantages at the expense of their hosts. Meiotic drive elements are particularly dramatic examples of the latter. Meiotic drive is the unequal—and thus non-Mendelian—transmission of alternative alleles or chromosomes from heterozygotes. Most drive elements achieve greater than Mendelian transmission from their carriers by excluding, impairing or killing competing alternative gametes. The best-characterized drive elements are the Segregation Distorter (SD) complex in the fruitfly Drosophila melanogaster and the t-haplotype in the Mus house mouse species. Despite being found in very distantly related species, both meiotic drive systems share genetic and chromosomal features that appear to characterize meiotic drive systems in general. For these, and all systems characterized to date, drive involves an interaction between at least two loci in which a trans-acting drive allele at one locus impairs transmission of sensitive alleles at a cis-acting target locus. In effect, the drive allele produces a toxin that incapacitates sperm bearing sensitive forms of the target. Drive chromosomes bear a driver and a drive-insensitive target, whereas non-drive chromosomes lack the driver and typically carry a drivesensitive target. This chapter reviews the genetics, molecular basis, and evolutionary history of several well-characterized drive systems, and considers the impact of drive on spermatogenesis and sperm competition, including potential evolutionary responses of organisms to drive.
Drive and sperm: The evolution and genetics of male meiotic drive
2008, Sperm Biology: An Evolutionary Perspective
Some selfish genetic elements in eukaryotic genomes have been harnessed to perform essential functions for their hosts, whereas others have gained transmission advantages at the expense of their hosts. Meiotic drive elements are particularly dramatic examples of the latter. Meiotic drive is the unequal—and thus non-Mendelian—transmission of alternative alleles or chromosomes from heterozygotes. Most drive elements achieve greater than Mendelian transmission from their carriers by excluding, impairing or killing competing alternative gametes. The best-characterized drive elements are the Segregation Distorter (SD) complex in the fruitfly Drosophila melanogaster and the t-haplotype in the Mus house mouse species. Despite being found in very distantly related species, both meiotic drive systems share genetic and chromosomal features that appear to characterize meiotic drive systems in general. For these, and all systems characterized to date, drive involves an interaction between at least two loci in which a trans-acting drive allele at one locus impairs transmission of sensitive alleles at a cis-acting target locus. In effect, the drive allele produces a toxin that incapacitates sperm bearing sensitive forms of the target. Drive chromosomes bear a driver and a drive-insensitive target, whereas non-drive chromosomes lack the driver and typically carry a drivesensitive target. This chapter reviews the genetics, molecular basis, and evolutionary history of several well-characterized drive systems, and considers the impact of drive on spermatogenesis and sperm competition, including potential evolutionary responses of organisms to drive.
Dynamic balance of segregation distortion and selection maintains normal allele sizes at the myotonic dystrophy locus
1998, Mathematical Biosciences
Myotonic dystrophy (DM), an autosomal dominant neurological disorder, is caused by CTG-repeat expansions at the DMPK locus, with affected individuals having ≥ 50 repeats of this trinucleotide. Reduced reproductive fitness of affected individuals and decreased viability of congenital DM have been noted. Expanded CTG-repeat alleles are highly unstable, predominantly yielding even higher repeat sizes. Preferential transmission of longer alleles from heterozygous mothers within the normal size range of alleles also is observed. In view of these observations, it is worth examining how DM has been maintained in human populations for hundreds of generations. We present an analysis of the dynamic properties of a model of joint effects of segregation distortion and selection (intensity of which increases with allele sizes of an individual's genotype). Our mathematical formulation and numerical analyses demonstrate that a weak segregation distortion during female meiosis, together with selection of comparable intensity (within the normal allele size range), can maintain an equilibrium distribution of allele frequencies. Genetic drift, acting in conjunction with the occasional contraction of alleles by mutation, can contribute to the balance of segregation distortion and mutation, in the sense that even weaker selection can explain the observed allele frequencies. The model is applied to CTG-repeat size distributions at the DMPK locus, observed in normal individuals from world populations.
Evolution of the segregation ratio: Modification of gene conversion and meiotic drive
1990, Theoretical Population Biology
We compare the evolutionary pressures that direct the modification of gene conversion and meiotic drive at loci subject to purifying and overdominant viability selection. Gene conversion differs from meiotic drive in that modifiers do not affect their own segregation ratios, even when linked to the viability locus. Segregation distortion generates gametic level disequilibria between alleles at the viability locus and modifiers of gene conversion and meiotic drive: enhancers of segregation distortion become positively associated with driven alleles. Suppression of gene conversion evolves if the driven allele is marginally disadvantageous (overdominant viability selection), and higher rates evolve if the driven alleles are relatively advantageous (purifying viability selection). Gametic disequilibria permit enhancers of meiotic drive that are linked to the driven locus to promote their own segregation. We attribute the failure of genetic modifiers of gene conversion and meiotic drive to maximize mean fitness to the generation of such associations.
More on recombination and selection in the modifier theory of sex-ratio distortion
1989, Theoretical Population Biology
G. Maffi and S. D. Jayakar suggested a model for the two-locus control of sex determination in the mosquito Aedes aegypti (1981, Theor. Pop. Biol.19, 19–36). This model was extended to multiple alleles and analyzed in mathematical detail by S. Lessard (1987, Theor. Pop. Biol.31, 339–358). The model supposes that males are “Mm” and females “mm” but the transmission from males is controlled by a second gene with alleles A_i. We show that in addition to the equilibrium in which mA_i in females, MA_i from males and mA_i from males all have the same frequencies, a second class of polymorphic equilibria exists and can be stable. The former class was shown by Lessard to be stable for intermediate and/or loose linkage. The new class of equilibria may be stable for tight linkage under the conditions that preclude stability of the former. We also develop the theory of linkage modification from the neighborhood of the new equilibrium. Successful modifiers of recombination may either reduce or increase the recombination fraction with the outcome depending on the linkage of the modifier to the major genes.

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^☆: Research supported in part by an 1851 Research Fellowship and a Wellcome Research Travel Grant.

^☆☆: Research supported in part by grant GB 37835 from the National Science Foundation, a grant from the U.S.-Israel Binational Research Foundation and NIH Grant USPHS 10452-11-12.

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Population genetics of modifiers of meiotic drive III. Equilibrium analysis of a general model for the genetic control of segregation distortion☆,☆☆

Abstract

Theor. Popul. Biol

Theor. Popul. Biol

Theor. Popul. Biol