Evolutionary Stable Strategies and Trade-Offs in Generalized Beverton and Holt Growth Models

A generalized Beverton–Holt model is considered in which a parameterγcharacterizes the onset of density dependence. An evolutionary stable strategy analysis of this parameter, reported in Getz (1996), is developed further here, using invasion exponents and the strategy dynamics of Vincentet al.(1993). The parameterγis also allowed to be density dependent, and it is shown that the most successful strategies of this type are those for whichγis large for low densities and close to its minimum for high densities. A biological interpretation is given in the context of mobile females depositing their relatively sessile young on patches of resource, namely, females should overdisperse their young on resources when adult densities are high and underdisperse them when these densities are low. Finally the per capita growth rate parameter is also allowed to depend onγ. It is shown that this dependence provides a mechanism by which periodic or chaotic attractor dynamics could evolve towards equilibrium attractor dynamics.