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.