Self-extinction through optimizing selection

Abstract

Evolutionary suicide is a process in which selection drives a viable population to extinction. So far, such selection-driven self-extinction has been demonstrated in models with frequency-dependent selection. This is not surprising, since frequency-dependent selection can disconnect individual-level and population-level interests through environmental feedback. Hence it can lead to situations akin to the tragedy of the commons, with adaptations that serve the selfish interests of individuals ultimately ruining a population. For frequency-dependent selection to play such a role, it must not be optimizing. Together, all published studies of evolutionary suicide have created the impression that evolutionary suicide is not possible with optimizing selection. Here we disprove this misconception by presenting and analyzing an example in which optimizing selection causes self-extinction. We then take this line of argument one step further by showing, in a further example, that selection-driven self-extinction can occur even under frequency-independent selection.

Keywords: Adaptive dynamics; Evolutionary suicide; Frequency-dependent selection; Life-history evolution; Tragedy of the commons.

Fig. 1

Evolutionary suicide through non-optimizing selection ($\tilde{m}=6$), panels a–c, and through optimizing selection ($\tilde{m}=0$), panels d–h (Example 1). Evolving harvesting intensities (a, d) increase over time until evolutionary suicide occurs. Other panels illustrate corresponding changes in resource densities (b, e, g) and consumer population densities (c, f, h). Whereas in the non-optimizing case (a–c) population densities monotonically decrease prior to sudden extinction, evolutionary suicide in the optimizing case (d–h) is preceded by characteristic density fluctuations (g, h). Parameters: a=18, d=1, $\tilde{d}=8$, e=0.9, and m=0.1.

Fig. 2

Evolutionary suicide through non-optimizing selection (a–c) and optimizing selection (d–g) proceed along fundamentally different routes (Example 1). A first route (a–c) leads through a local bifurcation, in which a stable equilibrium (yellow circle) collides with an unstable one (a saddle point, blue circle). Evolutionary suicide through optimizing selection requires a different route (d–g), involving a global bifurcation, in which the unstable manifold of the right saddle at (1, 0) (thick yellow curve) and the stable manifold of the left saddle at (0.125, 0) (thick blue curve) collide (thick green curve). Parameters as in Fig. 1. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 3

Evolutionary suicide through frequency-independent optimizing selection (Example 2). Evolutionary dynamics of growth rates s (a) and corresponding population sizes N (b). (c) Population-dynamical attractor and unstable equilibrium (dashed curve) as a function of the growth rate s. Parameters: k=1.