Fig 1.
Panel (A) shows the population cycles in habitat 1 (color coded blue) and habitat 2 (red), including formation of social groups and playing the public goods game, resulting in the production of dispersing offspring, some of which go to the dispersal pool in their birth habitat and some go the pool in the other habitat. New social groups are then formed from the pool in each habitat. (B) The expected payoff Eq (2) for mutant trait z′ in habitat 1 (blue) and habitat 2 (red) in the limit of no between-habitat dispersal. The resident traits in habitats 1 and 2 are z1 and z2 (blue and red vertical lines). The gray curve shows mutant payoff when there is random dispersal, with the same two resident traits. (C) Illustration of group formation for two groups in habitat 1 with N1 = 3. First founding group members are randomly drawn from the dispersal pool, followed by asexual reproduction forming N1 offspring, each of which is a copy of a randomly selected parent in the founding group. (D) For a rare mutant (darker blue), founding groups with mutants will predominantly contain a single mutant. The offspring groups can contain from 0 to N1 mutants, and in expectation contain one mutant.
Fig 2.
Evolutionary equilibrium dimorphisms.
The equilibrium dimorphisms z1 and z2, color coded blue and red, are plotted as functions of the rate of recombination ρ between cue and modifier loci. The two habitats differ in the size of social groups, with N1 = 20 and N2 = 2, resulting in lower relatedness in habitat 1 (r1 = 0.05) than in habitat 2 (r2 = 0.5). Three examples are shown, labeled with the rate of migration between habitats: m12 = m21 = m = 0.01, 0.05, 0.10. The total population size is the same in both habitats, and the parameters for the public goods game are also the same: W1 = W2 = 0.5, b1 = b2 = 3.0, c1 = c2 = 1.5. The gray horizontal line shows the equilibrium of gradual evolution in a monomorphic population, which does not depend on m or ρ. The dark gray points (with error bars) at ρ = 0.0 and ρ = 0.5, shifted slightly left and right for visibility, show mean and standard deviation of the average phenotype over 10 replicate individual-based evolutionary simulations. In these simulations, ag in Eq (5) was encoded by a single locus whereas a0 was kept at a fixed value (see S1 Text for further explanation).
Fig 3.
Trait evolution plots for dimorphisms.
In each example, the shaded region shows where a dimorphism z1, z2 can be maintained, the arrows indicate the direction and magnitude of the selection gradient Eq (7), and the dots show evolutionarily equilibrium dimorphisms. The examples differ in between-habitat migration rate m12 = m21 = m and rate of recombination ρ. (A) m = 0.05, ρ = 0.001; (B) m = 0.05, ρ = 0.5; (C) m = 0.10, ρ = 0.001; (D) m = 0.10, ρ = 0.5. Other parameters: N1 = 20 and N2 = 2, W1 = W2 = 0.5, b1 = b2 = 3.0, c1 = c2 = 1.5.
Fig 4.
Results from individual-based simulations, illustrating consequences of genetic conflict.
(A) Same as the simulations in Fig 2 except that a0, in addition to ag, in Eq (5) is determined by a single locus. The blue and red points (with error bars) show the deviating outcome for m = 0.10, ρ = 0.5, which is a consequence of genetic conflict between the cue locus and the locus encoding ag: ag became close to zero, but a0 became polymorphic, and the polymorphism at the original cue locus collapsed. The outcome is further illustrated in (B), showing a kernel-smoothed distribution of phenotypes in a typical simulation. The blue and red vertical lines show the prediction from Fig 3C, where ρ = 0, and the blue and red dashed lines the prediction from Fig 3D, where ρ = 0.5. The outcome where an unlinked modifier (a0) takes over the polymorphism depends on the genetic architecture, as illustrated in (B), (C) and (D). In (C) the modifiers a0 and ag in Eq (5) are each determined by several loci with small additive effects, and the loci contributing to a0 all became polymorphic. In (D) there is a more complex architecture for a0, with additive effects that in turn can be modified with an adjustable threshold limiting the amount of gene expression, and this threshold became polymorphic (see text and S1 Text for further explanation).
Fig 5.
Illustration of the information contained in genetic cues.
Panel (A) shows the conditional probability of being in habitat 1 (with r1 = 0.05) for an individual possessing cue allele x1 (blue curves, q11) versus cue allele x2 (red curves, q12). The probability is given as a function of the recombination rate ρ between cue and modifier loci. The three cases are from Fig 2, with different rates of between-habitat migration m12 = m21 = m = 0.01, 0.05, 0.10. The blue lines in panels (B) to (D) show logistic regressions of habitat 1 on the liability a0+ag x in eq (5), for the individual-based simulations in Fig 4B to 4D (with m = 0.10 and ρ = 0.5). The distributions of this liability are shown in gray, and the vertical blue and red lines indicate ‘typical’ low and high values (mean ± sd for (C) and (D)). See S1 Text for further explanation.