Lifetime and reproduction of a marked individual in a two-species competition process

Abstract

The interest is in a stochastic model for the competition of two species, which was first introduced by Reuter [18] and Iglehart [11], and then analyzed by Ridler-Rowe [19]. The model is related to the two-species autonomous competitive model (Zeeman [24]), where individuals compete either directly or indirectly for a limited food supply and, consequently, birth and death rates depend on the population size of one or both of the species. The aim is to complement the treatment of the model we started in [8,9] by focusing here on probabilistic descriptors that are inherently linked to an individual: its residual lifetime and the number of direct descendants. We present an approximating model based on the maximum size distribution, and we discuss on various models defined in terms of the underlying killing and reproductive strategies. Numerical examples are presented to show the effects of the killing and reproductive strategies on the behavior of an individual, and how the impact of these strategies on the descriptors vanishes in highly competitive ecosystems.