Dynamics of non-motile populations in environment with limited resources

Abstract

The dynamics of population growth in a community of limited resources is modeled using cellular automaton with each occupied cell representing a utilized unit of resource. The agents do not move from one cell to another. Results show that an equilibrium state is independent on the initial population density, sensitive only to agents' average life expectancy and maturity age. It is found that populations eventually die (become extinct) due to depletion of maturing population caused by a decrease in the readily (nearest neighbor) available resources. The model is able to explain the clinical latency observed in HIV desease and the a parent invasion and adaptation for motile genetic models. There exist a critical value of the death probability D for any given maturity age M at which the population cannot persist indicating that longer life expectancy is not necessarily advantageous. Plots of young agents against dying agents for intermediate values of F indicate competing behavior of young and old agents for available resource.