The two-tier approach for modeling the development and evolution of social behavior is extended to provide a submodel for the numerical response component of predator-prey models.
Predator-prey and consumer-resource models in ecology contain submodels for the functional response and for the numerical response of the predator (or consumer). The functional response is the rate at which an individual predator consumes food as a function of the abundance of food. The numerical response is the rate of predator births from an individual predator as a function of the abundance of food. Conventionally, the numerical response is assumed to be proportional to the functional response, with a constant of proportionality indicating the caloric conversion ratio of captured prey into predator offspring.
For solitary foragers, optimal foraging theory provides an adequate submodel to account for the functional response. The complication of density dependence from exploitative competition for resources may be incorporated into foraging models for solitary foragers by adjusting the available resource level to reflect the division of resource across the competing animals. Social foragers are considered a case requiring further model development.
Results/Conclusions
Many predators of interest and of economic and conservation importance reproduce sexually and are therefore involved in social interaction. Hence, predator births, unlike predator foraging, cannot be approached by modifiying an originally non-interactive behavioral theory for solitary individuals. The two-tier approach developed to replace sexual-selection in evolution offers a platform for developing native submodels for the numerical response function. Using both cooperative and competitive game theory for dynamics on a behavioral time scale shows how the number of offspring produced per predator results from social organizations such as monogamy and polygyny, and takes account of the toll extracted by sexual discord, if present. Using evolutionary stability analysis (ESS) in the evolutionary time scale shows what payoff matrix of reproductive possibilities is likely to be realized in various habitats.
The approach is illustrated by considering optimal harvesting policies resulting from population production functions based on these native two-tier social-behavioral submodels of numerical response.