The evolution of resource use

Abstract.

 The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the model, a dimensionless parameter α quantifies how simultaneous consumption of both resources influences consumer growth; α<0 corresponds to hemi-essential resources, 0<α<1 corresponds to complementary resources, α=1 corresponds to perfectly substitutable resources, and α>1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to five conclusions. First, when α≤1, there is a unique singular strategy x ^* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when α=1, the singular strategy x ^* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and displace populations playing any other strategy. Third, when α>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution amplifies this specialization. Fourth, when α is slightly larger than one (i.e. the resources are slightly antagonistic), there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations specializing on different resources. Fifth, when α>>1, there is only one singular strategy and it is convergent unstable and evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately only one resource is exploited.