Contest and scramble competition with a dynamic resource

A system of difference equations derived from a general matrix population model with a dynamically varying resource is used to study two extreme forms of intra-specific competition. Both the per capita survival probability and birth rate are dependent on an individual's hierarchical ranking in the population. It is shown that contest competition yields a larger equilibrium size than the scramble competition. Moreover, contest competition may also be more stable in the sense that the interior steady state is always locally asymptotically stable if the inherent net reproductive number is larger than 1.