Evolution of personality differences in leadership

Abstract

When members of a group differ in their preferred course of action, coordination poses a challenge. Leadership offers one way to resolve this difficulty, but the evolution of leaders and followers is itself poorly understood. Existing discussions have frequently attributed leadership to differences in information or need among individuals. Here, however, we show that in an n-player, repeated coordination game, selection leads to evolutionary branching and diversification in intrinsic leadership among the members of a population even in the absence of any variation in state. When individuals interact in pairs, repeated branching is possible; when individuals interact in larger groups, the typical outcome is a single branching event leading to a dimorphism featuring extreme intrinsic leaders and followers. These personality types emerge and are maintained by frequency-dependent selection, because leaders gain by imposing their preferences on followers, but fail to coordinate effectively when interacting with other leaders. The fraction of intrinsic leaders in the population increases with the degree of conflict among group members, with both types common only at intermediate levels of conflict; when conflict is weak, most individuals are intrinsic followers, and groups achieve high levels of coordination by randomly converging on one individual's preferred option, whereas when conflict is strong, most individuals are intrinsic leaders, and coordination breaks down because members of a group are rarely willing to follow another.

Fig. 1.

Pairwise invisibility plots when players interact in pairs (n = 2), for three different values of k, the intensity of conflict between members of a pair (weak conflict, k = 0.25, Left; moderate conflict, k = 0.5, Center; strong conflict, k = 0.75, Right). Light shading indicates pairs of strategies λ₁ and λ₂ for which λ₂ can invade λ₁ but not vice versa, dark shading pairs of strategies for which λ₁ can invade λ₂ but not vice versa, and the unshaded region pairs of strategies each of which can invade the other, so that both can persist in a stable dimorphism. Within this last region of mutual invisibility, arrows indicate the direction of selection on the component strategies of the dimorphic coalition. Note that in each case, there is a unique singular coalition toward which a dimorphic population evolves, but that both component strategies in this coalition are unstable, leading to further branching.

Fig. 2.

Simulated branching evolution, for three different values of k, the intensity of conflict among members of a group (weak conflict, k = 0.25, Top; moderate conflict, k = 0.5, Middle; strong conflict, k = 0.75, Right), and for four different values of n, the number of individuals in a group (n = 2, 3, 5, and 10) (Left, Center Left, Center Right, and Right). Each graph shows the strategies (defined by their levels of intrinsic leadership λ) present in a simulated evolving population, with the number of elapsed time steps running from left to right (density of shading reflects the frequency of each strategy). Starting with a monomorphic population in which all individuals had an intrinsic leadership of 0.5, the simulation proceeded as described in the main text. In each discrete time step, a mutant type was introduced with probability 0.001 at an initial frequency of 0.002 (allowing no possibility of multiple mutation events in a single generation), with an intrinsic leadership value equal to that of an established type plus a normally distributed error term with mean zero and SD 0.01 (mutant leadership values lying outside the range 0–1 were discarded); established types were chosen for mutation with probabilities corresponding to their frequency in the population. Frequencies of each type changed from one time step to the next according to their fitness relative to the mean fitness of the population, as described in the main text, with types being eliminated when their frequency dropped below 0.001; following such elimination events, frequencies of the remaining types were rescaled so as to sum to 1. Output is shown every 10³ time steps from a total simulation length of 2 × 10⁶ time steps for n > 2, or of 5 × 10⁶ time steps for n = 2 (we ran simulations for longer when n = 2 because this case gave rise to multiple branching events and, thus, required longer to converge to a stable polymorphism).

Fig. 3.

Mean payoffs to leaders (λ = 0.995, dark curves) and to followers (λ = 0.005, light curves) in a group of size 10, as a function of the proportion of leaders in the group, for three different values of k, the intensity of conflict (weak conflict, k = 0.25, Left; moderate conflict, k = 0.5, Center; strong conflict, k = 0.75, Right). Values were obtained from 100 simulated interactions of 100 bouts each, with error bars giving one SD from the mean.

Fig. 4.

Typical properties of final populations from simulations similar to those illustrated in Fig. 2. We ran 10 such simulations for each possible combination of seven different levels of conflict among group members (k = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875), and four different group sizes (2, black; 3, red; 5, green; and 10, orange). To improve computational speed, we increased the mutation rate per time step to 0.01 (rather than 0.001 as in Fig. 2) and the SD of mutation size to 0.1 (rather than 0.01 as in Fig. 2), and reduced the length of each simulation to 5 × 10⁴ generations (inspection of individual simulation results indicated that this length was sufficient for convergence to stable polymorphisms). Upper Left shows the mean number of morphs present in the population at the end of the simulations, Upper Right is the mean intrinsic leadership in the population, Lower Left is the mean coordination (measured as the mean fraction of other group members that choose the same option as a randomly selected focal individual), and Lower Right is the modal number of intrinsic leaders present in the group (this graph only shows results from groups of at least three individuals, because the high degree of polymorphism in pairs does not allow one to classify individuals into just two categories of intrinsic leader and follower). For graphs that show means, error bars give one SD above and below the mean.