From Mutant Invasions to Adaptive Dynamics Sample Clauses

From Mutant Invasions to Adaptive Dynamics. Interactions between individuals are bound to change the environments these individuals live in. The phenotypic composition of an evolving population therefore affects its ecological environment, and this environment in turn determines the population dynamics of the individuals involved. It is this setting of resident phenotypes into which mutant phenotypes must succeed to invade for long-term evolution to proceed. Whether or not such an event may occur can be decided by adaptive dynamics’ invasion functions: if the initial exponential growth rate of a small mutant population in an established resident population (a rate which one obtains as a Lyapunov exponent) is positive, the mutant phenotype has a chance to replace the former resident phenotype (Xxxx et al. 1992; Xxxx et al. 1994; Xxxxxx`re and Xxxxx 1995). Once the invasion function of the evolving system is known, pairwise invasibility plots can be constructed (xxx Xxxxxxxxx and xx Xxxx 1986; Xxxxxx 1989; Xxxx et al. 1996). In the simplest case mutant and resident phenotypes are distinguished by a single metric character or quantitative trait. When plotting the sign of the invasion function for each of the possible combinations of mutant and resident phenotypes, the shape of a zero contour line becomes visible, see Figure 1. This line separates regions of potential invasion success from those of invasion failure and its shape carries important information about the evolutionary process (Xxxx et al. 1996). In particular, possible end-points of the process are located at those resident phenotypes where a zero contour line and the 45 degree line intersect. In characterizing such potential end-points, also called singular points, classical evolu- tionary game theory emphasizes a single, fundamental dichotomy: either the resident phenotype is an evolutionarily stable strategy (ESS) or it is not. In the former case no mutant phenotype has a chance to invade into the resident population. In con- trast, adaptive dynamics theory uses an extended classification scheme in which four different questions are tackled simultaneously.