Evolutionary model of exoenzyme production
Assuming heritable variation in the exoenzyme allocation fraction trait,φ , we use the framework of adaptive dynamics (Metz et al.1992; Geritz et al. 1998) to predict the strength and direction of selection on trait φ and the evolutionarily stable value,φ *. In this framework, evolution is modeled as a competition process between a ‘resident strategy’ (wild-type) and alternate strategies (mutants) within a set of feasible phenotypes. In a given environment (e.g. at a given temperature), an evolutionarily stable strategy (ESS) is a phenotype that when resident, no mutant can invade. The adaptive dynamics framework provides the mathematical criteria to identify ESSs and check their attractivity, i.e. that they can be reached by a sequence of small evolutionary steps, each step involving the replacement of a resident phenotype by a mutant phenotype. Here the set of feasible phenotypes is the range (φ min, φ max) at a given temperature, for which the non-trivial ecosystem equilibrium exists (see Box 1). The derivation of the selection gradient and evolutionarily stable trait value, φ *, as a function of temperature T , is presented in Box 2.