Incorporating environmental stochasticity within a biological population model.

ABSTRACT

The birth and death transition rates for a population are modelled as functions of both the population size and the environmental condition. An assortment of important theoretical results and techniques that can be utilized to analyze such a population's behaviour is covered. Consequently, these results and techniques are used to study two examples. Firstly, we study a population with a stable equilibrium state, whose per capita birth and death rates are linearly related to the environmental condition. (The environmental condition in turn is modelled as an Ornstein-Uhlenbeck process.) Secondly, we study a population affected by two interdependent environmental factors.