Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Intraspecific competition models considering two resources
Nora Stahnke

Last modified: 2014-03-28


The development of single-species population dynamics under intraspecific competition for two resources is considered in this work. The dependency of reproduction on multiple resources and thereby the competition for these is biologically more instructive than the one resource case.
For the analysis of intraspecific competition for two resources, this study defines a general (discrete) stochastic model. Depending on the used competition type, different stochastic models were generated. Corresponding deterministic models are derived and compared to their stochastic counterparts.

A site-based framework combined with an individual-based model forms the basis of the presented models. For competition, the extreme cases of scramble and contest, as well as a combination of both, were included into the models. Different temporal courses of events such as simultaneous competition or successive competition were studied. 
The considered life cycle of individuals consists of three states - adults, offspring and juveniles - where competition occurs in the latter state together with a certain probability of survival, which is added in the stochastic models. At the adult state, reproduction takes place and the expected number of offspring is a fixed value or is given by a binomial distribution. In the simplest case, the offspring is distributed uniformly over the resource sites.

The implementation of the models and the simulation runs were performed with the statistical language R. In the limit of sufficiently large number of resource sites, the use of the Poisson approximation results in deterministic models similar to the Ricker model. This is the deterministic prototype of scramble competition in the case of one resource, and the Skellam model had been shown in previous investigations to be the deterministic analogue to contest competition.
When contest competition is applied to both resources, simulations indicate a behaviour significantly different from the Skellam model. In most cases, simulations are more similar to the Ricker model. This indicates the importance of modelling competition regarding more than one resource.