Using the ESS Maximum Principle to Explore Root-shoot Allocation, Competition and Coexistence

Competition between plants that differ in root-shoot allocation has been modelled using consumer-resource equations where competition occurs only through the utilization of resources. Provided that such models can be put into an evolutionary game setting, we show that conditions for coexistence can be analysed using the ESS maximum principle from evolutionary game theory. We demonstrate this approach using a modified version of a consumer-resource model from Reynolds & Pacala (1993). Allocation of biomass by the consumers to root or shoot is expressed as an evolutionary strategy. Since stability conditions are defined by the ESS maximum principle, aspects of coexistence can be determined without analyses of Jacobian matrices. Using the ESS maximum principle, we confirm that coexistence between two or more species is not possible with this model. We show that this result depends on the consumer growth rate being a linear function of allocation strategy and does not depend on the form of the (nonlinear) nutrient and light availability equations. In addition, we show that species coexistence is possible if the model is modified to include a nonlinear dependence of consumer growth rate on allocation strategy. We give an example where coexistence between two species is obtained.