Unbalanced selection: the challenge of maintaining a social polymorphism when a supergene is selfish

Abstract

Supergenes often have multiple phenotypic effects, including unexpected detrimental ones, because recombination suppression maintains associations among co-adapted alleles but also allows the accumulation of recessive deleterious mutations and selfish genetic elements. Yet, supergenes often persist over long evolutionary periods. How are such polymorphisms maintained in the face of selection, drive and drift? We present a population genetic model that investigates the conditions necessary for a stable polymorphic equilibrium when one of the supergene haplotypes is a selfish genetic element. The model fits the characteristics of the Alpine silver ant, Formica selysi, in which a large supergene underlies colony social organization, and one haplotype distorts Mendelian transmission by killing progeny that did not inherit it. The model shows that such maternal-effect killing strongly limits the maintenance of social polymorphism. Under random mating, transmission ratio distortion prevents rare single-queen colonies from invading populations of multiple-queen colonies, regardless of the fitness of each genotype. A stable polymorphic equilibrium can, however, be reached when high rates of assortative mating are combined with large fitness differences among supergene genotypes. The model reveals that the persistence of the social polymorphism is non-trivial and expected to occur only under restrictive conditions that deserve further empirical investigation. This article is part of the theme issue 'Genomic architecture of supergenes: causes and evolutionary consequences'.

Keywords: ants; genetic polymorphism; heterozygote advantage; invasion analysis; selfish genetic element; social organization.

Figure 1.

Social and genetic system of F. selysi. (a) Mature monogynous colonies contain a single MM queen mated with M males. The queen produces M males (haploid, from unfertilized eggs), as well as MM queens and MM workers (diploid, from fertilized eggs). The offspring (males and queens) fly out of the colony for mating, and queens establish colonies independently. (b) Mature polygynous colonies contain multiple MP or PP queens mated with M or P males. The offspring (queens and males) also fly out of the colony for mating. MP and PP queens (and possibly MM queens mated to P males) may establish colonies independently, or, for polygynous queens, with the help of workers from their natal colony (dashed line). The P haplotype acts as a maternal-effect killer, so that all offspring of MP queens that do not inherit the P haplotype die during development. As a result, M males and MM females are never produced by polygynous colonies. (Online version in colour.)

Figure 2.

Stream plots show the dynamics of F. selysi queens when individuals in monogynous colonies are most fit. The fixation of monogynous colonies (blue) is then stable to the spread of the P haplotype (condition (3.1) does not hold because MM queens and M males are sufficiently fit). (a) When heterozygous females are low enough in fitness, the system evolves towards the fixation of either MM females (blue) or PP females (red) $(V_{MP|ij\times k}^{\mathrm{female}}=1/5)$. (b) When heterozygous females are intermediate in fitness, the system can evolve towards the fixation of either MM females (blue) or a polymorphism with both MP and PP polygynous queens (marked by an $\times$) ($V_{MP|ij\times k}^{\mathrm{female}}=3/5$). The open circle marks an unstable equilibrium point. Other parameters: $V_{MM|MP\times M}^{\mathrm{female}}=V_{M|MP}^{\mathrm{male}}=0$ (complete maternal-effect killing), $V_{MM|MM\times M}^{\mathrm{female}}=1$ and otherwise $V_{a|ij}^{\mathrm{male}}=V_{ab|ij\times k}^{\mathrm{female}}=1/5$. (Online version in colour.)

Figure 3.

Stream plots show the dynamics of F. selysi queens when individuals in monogynous colonies are not more fit than individuals in polygynous colonies. The fixation of monogynous colonies (blue) is then unstable (condition (3.1) holds). (a) There are no fitness differences except those caused by maternal-effect killing, in which case PP-fixed is the only stable equilibrium (red). (b) There is heterozygous advantage, such that condition (3.3) holds, and MP/PP with only polygynous colonies is the only stable equilibrium (marked by an $\times$ on plot; $V_{MP|ij\times k}^{\mathrm{female}}=3/5$). No internal equilibrium point exists in these cases. Other parameters: $V_{MM|MP\times M}^{\mathrm{female}}=V_{M|MP}^{\mathrm{male}}=0$ (complete maternal-effect killing) and otherwise $V_{a|ij}^{\mathrm{male}}=V_{ab|ij\times k}^{\mathrm{female}}=1/5$. (Online version in colour.)

Figure 4.

Stream plot showing the dynamics of F. selysi queens with sexual selection such that queens exhibit fixed-relative mating preferences [27]. Here, we illustrate a case when populations composed of only monogynous colonies or only polygynous colonies are both stable (condition (3.1) holds). The open circles mark unstable equilibrium points and the x's mark stable equilibrium points. Parameters: $f_{MM\times M}/f_{MM\times P}=96\hspace{0.17em}$ (an extremely strong preference), $f_{MP\times P}/f_{MP\times M}=f_{PP\times P}/f_{PP\times M}=1.47,\hspace{0.17em}{V}_{MM|ij\times k}^{\mathrm{female}}=0.46$, $V_{MP|ij\times k}^{\mathrm{female}}=0.69$, $V_{PP|ij\times k}^{\mathrm{female}}=0.33$, $V_{MM|MP\times M}^{\mathrm{female}}=V_{M|MP}^{\mathrm{male}}=0$ (complete maternal-effect killing) and $V_{a|ij}^{\mathrm{male}}=1$ (males have the same viability). (Online version in colour.)

Figure 5.

The maintenance of social polymorphism is possible with assortative mating by social form, here illustrated with complete assortative mating in monogynous queens and partial assortative mating in polygynous queens. Here, MM queens only mate with M males $(m_M=1)$. (a) The range of assortative mating in polygynous colonies $(m_P)$ and the viability of monogynous queens $(V_{MM|MM\times M}^{\mathrm{female}})$ for which a stable social polymorphism persists when $V_{MP|ij\times k}^{\mathrm{female}}=1$ and $V_{PP|PP\times P}^{\mathrm{female}}=0.3$. Grey dots, both a social polymorphism and M-fixed equilibria are stable; red dots, only the social polymorphism is stable. (b) and (c) Stream plots for the parameter sets indicated in (a) ((b) at $x_1$, (c) at $x_2$). Open circles mark unstable equilibrium points, while ${\times }_1$ and ${\times }_2$ indicate stable internal equilibrium points. Other parameters: $V_{MM|MP\times M}^{\mathrm{female}}=V_{M|MP}^{\mathrm{male}}=0$ (maternal-effect killing) and otherwise $V_{a|ij}^{\mathrm{male}}=V_{ab|ij\times k}^{\mathrm{female}}=1$.

Figure 6.

Partial assortative mating by both social forms allows for the maintenance of social polymorphism. (a) The range of assortative mating by social form in monogynous colonies $(m_M)$ and the viability of monogynous queens $(V_{MM|MM\times M}^{\mathrm{female}})$ for which a social polymorphism persists. Above the dashed line corresponds to directional selection favouring the M haplotype in females, while below the dashed line, there is heterozygous advantage. Grey dots, both a social polymorphism and M-fixed equilibria are stable; red dots, only the social polymorphism is stable. (b) The stream plot for a parameter set (marked by an X in (a)) that permits a stable internal equilibrium denoted by an X in (b) $(m_M=0.54,\hspace{0.17em}{V}_{MM|MM\times M}^{\mathrm{female}}=0.52)$. Open circles mark unstable equilibrium points. Other parameters are as in figure 5 except $V_{MP|ij\times k}^{\mathrm{female}}=0.5,\hspace{0.17em}{V}_{PP|ij\times k}^{\mathrm{female}}=0.2$ and $m_P=0.5$.