Müllerian mimicry: an examination of Fisher's theory of gradual evolutionary change

Abstract

In 1927, Fisher suggested that Müllerian mimicry evolution could be gradual and driven by predator generalization. A competing possibility is the so-called two-step hypothesis, entailing that Müllerian mimicry evolves through major mutational leaps of a less-protected species towards a better-protected, which sets the stage for coevolutionary fine-tuning of mimicry. At present, this hypothesis seems to be more widely accepted than Fisher's suggestion. We conducted individual-based simulations of communities with predators and two prey types to assess the possibility of Fisher's process leading to a common prey appearance. We found that Fisher's process worked for initially relatively similar appearances. Moreover, by introducing a predator spectrum consisting of several predator types with different ranges of generalization, we found that gradual evolution towards mimicry occurred also for large initial differences in prey appearance. We suggest that Fisher's process together with a predator spectrum is a realistic alternative to the two-step hypothesis and, furthermore, it has fewer problems with purifying selection. We also examined the factors influencing gradual evolution towards mimicry and found that not only the relative benefits from mimicry but also the mutational schemes of the prey types matter.

Figure 1

Mutant survival in a situation with two resident prey types, with trait values x_a and x_b. The curves give the probability of survival over a season for a single mutant individual with trait value x. The difference in survival between the two prey types is caused by unequal protection from population sizes (N_a=1000, N_b=5000). (a) The trait values of the two resident types are relatively close together (x_a=3.5 and x_b=6.5). Predator generalization (σ=1.0) causes the survival peaks around the resident types to be slightly shifted towards each other. (b) When the resident trait values are further apart (x_a=2.0 and x_b=8.0), the peak shift is very small, leading to very weak selection for gradual change. A saltational mutation from x_a to the neighbourhood of x_b could however invade, corresponding to advergence of type a towards type b. (c) With a spectrum of predators, some of which generalize more broadly (for half of the predators we used σ=1.0 and for the other half σ=3.0), there is noticeable peak shift also with initial trait values that are further apart (x_a=2.0, x_b=8.0).

Figure 2

Invasion fitness for the three situations illustrated in figure 1. (a) When resident traits are fairly close to each other (x_a=3.5 and x_b=6.5), mutants of type a in the interval 3.50–3.62 can invade, while mutants of type b can invade in the narrower interval 6.45–6.50. Mutants of type a have a maximum invasion fitness of 2.1×10⁻³ at x=3.56, while mutants of type b have a smaller maximum invasion fitness of 0.2×10⁻³, located at x=6.48, closer to their resident trait value. (b) When resident traits are further apart (x_a=2.0 and x_b=8.0), the intervals where mutants are selected for become very narrow and the positive values of invasion fitness are quite small. (c) A spectrum of predators dramatically increases the widths of the intervals with positive invasion fitness, as well as the maximum values.

Figure 3

Gradual evolution of prey appearances for the situations illustrated in figures 1 and 2. The trajectories of x_a and x_b are average trait values as a function of time for the two prey populations. (a) Fisher's process is possible for x_a and x_b sufficiently close in trait space. (b) When the distance between initial traits increases, selection is insufficient to initiate evolution towards mimicry. (c) When a spectrum of predators is used (50% of each type), evolution leads to mimicry also for the initial trait values used in b. (d) Mimicry also evolves when a smaller part of the predators (15%) generalize more broadly. Note that the scale of the x-axis in (a) differs from those in (b), (c) and (d).

Figure 4

Degree of advergence as a function of relative population size. The population size of type a was kept constant at 1000 individuals while the population size of type b was varied. Every point is an average of the degree of advergence of 30 simulations. The curves correspond to different distributions of mutational increments. For all three distributions, the degree of advergence is greater for larger population size differences. The degree of advergence at a given population size difference decreases with decreasing range of mutational size distributions. Using a predator spectrum (dashed lines) further decreases the degree of advergence, in particular for the distribution with σ_m=0.5.