A Method to Derive Discrete Population Models

Abstract

We propose a derivation method to obtain discrete multi-species population models based on the assumption that the population sizes at time $$t+1$$ can be expressed as a multiple of the population sizes at time t. The multiplicative term is determined by placing the growth processes in the numerator and the decline processes in the denominator of the fitness of each population. Each resulting discrete model can be related to a continuous population model based on the same model assumptions using the relationship between discrete and continuous compounding in finance. We exploit this relationship to compare the stability for the continuous and the discrete models and argue that the corresponding continuous model analogues are more stable. We illustrate the derivation technique by providing several examples of discrete models of single and multi-species derived using this method and compare their stability properties with their continuous analogues.