Necessary and Sufficient Conditions for Evolutionary Suicide

Abstract

Evolutionary suicide is an evolutionary process where a viable population adapts in such a way that it can no longer persist. It has already been found that a discontinuous transition to extinction is a necessary condition for suicide. Here we present necessary and sufficient conditions, concerning the bifurcation point, for suicide to occur. Evolutionary suicide has been found in structured metapopulation models. Here we show that suicide can occur also in unstructured population models. Moreover, a structured model does not guarantee the possibility of suicide: we show that suicide cannot occur in age-structured population models of the Gurtin-MacCamy type. The point is that the mutant's fitness must explicitly depend not only on the environmental interaction variable, but also on the resident strategy.

Surprising evolutionary predictions from enhanced ecological realism

“…Therefore, adaptive evolution in this system can never cause evolutionary suicide by driving x toward the critical trait value x c . Similar conclusions were reached by Gyllenberg and Parvinen (2001) and by Webb (2003).…”

“…In the context of a model of dispersal evolution in metapopulations, Gyllenberg et al (2002) proved that discontinuous transitions to extinction, implying catastrophic bifurcations, are a prerequisite for evolutionary suicide. This finding applies more generally: wherever a population goes to extinction through a continuous transition, it cannot undergo evolutionary suicide (Gyllenberg and Parvinen, 2001). This is easily shown for cases in which a population's density N and adaptive trait x are both one-dimensional (Dieckmann and Ferrie`re, 2004).…”

“…Also a model developed by Gyllenberg and Parvinen (2001) was based on asymmetric competition and the incorporation of an Allee effect. Their model is similar to the previous one, except for three features: fecundity b(x) was assumed to be peaked at an intermediate value of body size x, a trait-and density-independent mortality d was considered, and the allee effect reduced fecundity by the factor NðxÞ=½1 þ NðxÞ .…”

Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

“…As illustrated also by Parvinen (2011, his Figs. 3a and 4b), for large values of the dispersal rate m and the catastrophe rate µ, the boundary of viability may become evolutionarily attracting with respect to the cooperation strategy, and thus evolutionary suicide (Ferrière, 2000;Gyllenberg and Parvinen, 2001;Gyllenberg et al, 2002;Webb, 2003;Parvinen, 2005;Rankin and López-Sepulcre, 2005) may take place. However, as we observe from Figure 2cde, near this boundary there can be selection for decreased dispersal, which means that this boundary is evolutionarily repelling with respect to the dispersal component.…”

Remarks on branching-extinction evolutionary cycles

“…Then, assuming that body size of adult individuals and cannibalism are positively correlated (as it is often the case (Fox, 1975;Polis, 1981Polis, , 1988)), we show that during the dimorphic evolutionary phase the two sub-populations evolve into a weakly cannibalistic dwarf population and a highly cannibalistic giant population, until the giant population undergoes an evolutionary extinction. The key point of our result is that the giant population density does not vanish gradually at evolutionary timescale, but rather collapses suddenly (Gyllenberg and Parvinen, 2001). Such a discontinuous extinction event reverses the selection pressure on the dwarf population, which then begins to enhance its cannibalistic attitude.…”