Figure 2.
The emergence of polymorphism. (a) Average trait values in the population as a function of time (with a unit of time corresponding to an iteration of the life cycle) in a population where all traits are initially absent (at in red; bt in black; dt in grey; ht in blue; observed in a simulation in dots; see electronic supplementary material, §4 for simulation details; analytically predicted in full lines, from electronic supplementary material, equation (S9) with variance–covariance matrix G = δ2I, where I is the identity matrix and δ = 0.043 was chosen heuristically; N = 8 and m = 0.467 so that r2 = 0.125; otherwise same parameters as figure 1, middle). (b) Individual values of belligerence observed in a simulation (empty circles, each representing an individual, same parameters as (a)), as well as the observed trait population average (full line) and variance (dotted line, time on a log scale). Note that polymorphism, indicated by the bimodal distribution of empty circles, occurs before the population average has completely converged to its equilibrium in simulations due to mutations being relatively large (to speed up computation time). But as predicted, the trait variance starts to increase significantly only once the population average has stabilized. (c–f) Distribution of each trait in a simulation (calculated from time 250 000 for 100 000 time steps, same parameters as (a)).