On the evolutionary stability of Mendelian segregation

Abstract

We present a model of a primary locus subject to viability selection and an unlinked locus that causes sex-specific modification of the segregation ratio at the primary locus. If there is a balanced polymorphism at the primary locus, a population undergoing Mendelian segregation can be invaded by modifier alleles that cause sex-specific biases in the segregation ratio. Even though this effect is particularly strong if reciprocal heterozygotes at the primary locus have distinct viabilities, as might occur with genomic imprinting, it also applies if reciprocal heterozygotes have equal viabilities. The expected outcome of the evolution of sex-specific segregation distorters is all-and-none segregation schemes in which one allele at the primary locus undergoes complete drive in spermatogenesis and the other allele undergoes complete drive in oogenesis. All-and-none segregation results in a population in which all individuals are maximally fit heterozygotes. Unlinked modifiers that alter the segregation ratio are unable to invade such a population. These results raise questions about the reasons for the ubiquity of Mendelian segregation.

Figure 1.—

Sex-specific segregation distortion. This chart summarizes a detailed review of genetic systems in which segregation distortion in autosomes has been reported (Rhoades 1942; Cameron and Moav 1957; Loegering and Sears 1963; Maguire 1963; Rick 1966; Maan 1975; van Heermert 1977; Gropp and Winking 1981; Sandler and Golic 1985; Silver 1985; Lavery and James 1987; Agulnik et al. 1990; Sano 1990; Foster and Whitten 1991; Lyttle 1991; Pardo-Manuel de Villena et al. 2000). Each star corresponds to a particular haplotype (in italics) and its host organism. Its coordinates indicate the segregation proportion in favor of that particular haplotype in males and females. The main diagonal corresponds to sex-independent segregation distortion. This is the assumption in previous work on the evolution of Mendelian segregation. The vertical axis in k = ¹/₂ corresponds to female-limited segregation distortion while the horizontal axis in κ = ¹/₂ corresponds to male-limited segregation distortion.

Figure 2.—

Stability of Mendelian segregation. (a) Differential fitness of reciprocal heterozygotes (v₁₂ ≠ v₂₁). Mendelian segregation (MS) is susceptible to invasion by (k₊₁, κ₊₁) when this segregation scheme maps onto the shaded area. (a.1) v₂₁ > v₁₂ requires κ₊₁ > k₊₁. (a.2) v₁₂ > v₂₁ requires k₊₁ > κ₊₁. Open circles represent segregation schemes showing evolutionary genetic instability. However, all-and-none segregation (A&N) cannot be invaded by any other segregation scheme. Solid circles represent segregation schemes showing evolutionary genetic stability. (b) Identical fitness of reciprocal heterozygotes (v₁₂ = v₂₁). Invading segregation schemes are confined beneath the surface in b.1. Slices of this surface at v₁₁/v₁₂ = 5/8 (b.2) and v₁₁/v₁₂ = 0 (b.3) provide graphics with the same interpretation as the ones in a.

Figure 3.—

Genetic load in terms of fitness. The area of each square represents the genetic load corresponding to segregation scheme (k, κ). The ordering of the viability parameters considered is v₁₂ = v₂₁ > v₁₁ = v₂₂. The genetic load has two components, drive load and segregation load. With sex-independent segregation (k = κ) we consider the drive load component only. Any segregation away from Mendelian expectations increases the genetic load. With perfect compensation between drive and drag in the two sexes (k + κ = 1) we consider the segregation load component only. Any segregation away from all-and-none expectations increases the genetic load. All-and-none segregation is the only segregation scheme that gets rid off both types of load.

Figure 4.—

Evolutionary stability of segregation schemes other than Mendelian. Let v₁₁ = 1, v₁₂ = 1.5, v₂₁ = 2, v₂₂ = 0.6. For each combination of k in {0.1, 0.3, 0.5} and κ in {0.5, 0.7, 0.9} we draw a map of the genetic load (dotted squares) in the (k₊₁, κ₊₁) plane. Which combination of k and κ corresponds to each window is indicated by a number above and to the right of the graphic and is represented by a circle in the (k₊₁, κ₊₁) plane. Segregation scheme (k, κ) is susceptible to invasion by any other segregation scheme (k₊₁, κ₊₁) mapping onto the shaded area. In particular, all-and-none segregation of the type (0, 1) can invade any (k, κ) and, considering local deviations from (k, κ), the ones that can invade always reduce the genetic load.

Figure 5.—

Haplotype dynamics. We represent the change in frequency of all haplotypes after a rare modifier of segregation arises. The perpendicular distance from the bottom of the triangle to a particular point is the frequency of A₁M₁, from the left it is that of A₁M₂, and from the right it is that of A₂M₂. We use a color code to represent the frequency of A₂M₁. Vertex (1, 0, 0) corresponds to extinction of haplotypes A₂M₂ and A₁M₂; (0, 1, 0), to extinction of A₁M₁ and A₂M₂; and (0, 0, 1), to extinction of A₁M₁ and A₁M₂. Consider a population at a polymorphic short-term stable equilibrium at the main locus but fixed for allele M₁ coding for Mendelian segregation (k = κ = ¹/₂). A mutant modifier M₂ is introduced in proportion ε = 5 × 10⁻³. (a) Nonsymmetric viability of reciprocal heterozygotes. Let v₁₁ = 0.8, v₁₂ = 1.6, v₂₁ = 2, and v₂₂ = 0.8. Our results show that allele M₂ coding for segregation scheme (0, 1) in homozygotes fully replaces allele M₁. Specifically, haplotypes A₂M₂ and A₁M₂ become fixed in sperm and eggs, respectively. (b) Symmetric viability of reciprocal heterozygotes. Let v₁₁ = 0.8, v₁₂ = v₂₁ = 1.8, and v₂₂ = 0.8. Our results show that both (b.1) an allele M₂ coding for segregation scheme (0, 1) in homozygotes and (b.2) an alleleM₂ coding for segregation scheme (1, 0) in homozygotes fully replace allele M₁. While in the former case haplotypes A₂M₂ and A₁M₂ become fixed in sperm and eggs, in the latter case they become fixed in eggs and sperm, respectively. In the absence of imprinting the number of generations represented is four times larger than that in its presence. Arrows indicate the sense in which time increases.