The role of competition and clustering in population dynamics

A simple argument based on the distribution of individuals amongst discrete resource sites is used to show how the form of single species population models depends on the type of competition between, and the spatial clustering of, the individuals. For scramble competition between individuals, we confirm earlier demonstrations that the Ricker model is a direct consequence of a uniform random distribution of individuals across resources. By introducing spatial clustering of individuals according to a negative binomial distribution, we are able to derive the Hassell model. Furthermore, the tent map model is seen to be a consequence of scramble competition and an ideal-free distribution of individuals. To model contest competition under different degrees of spatial clustering we derive a new three-parameter model, of which the Beverton-Holt and Skellam models are special cases, where one of the parameters relates directly to the clustering distribution. Other population models, such as the quadratic model and the theta-Ricker models, cannot be derived in our framework. Taken together our derivations of population models allows us to make a more rigorous prescription for model choice when fitting to particular datasets.