Characterization of the Leslie matrix for semelparous population model

Abstract

In the ecology of animal populations, there are two types of population reproduction strategy, namely semelparous and iteroparous reproduction strategy. Semelparous population produces only once and then die, while iteroparous population does multiple reproductive cycles over the course of a lifetime as opposed to semelparous population. Studying the dynamic behavior of the semelparous population can be done using the Leslie matrix model. The Leslie matrix model is a model that describes the dynamics of growth of the female population based on the age structure. In terms of its element, the Leslie matrix is composed of the birth rate factor in the first row that is feasible to be more than or equal to zero, the survival factor in the main subdiagonal that is feasible from zero and less than one, and the other elements are set to be zero. The Leslie matrix for the semelparous population is called the Leslie semelparous matrix where there is a change in the first-row element, that is, only the last birth rate element is worth more than zero while the others are equal to zero. In this paper, we discuss the characteristic of the Leslie semelparous matrix to reveal the dynamics behavior of semelparous populations. Our results predict the important dynamics of the semelparous population, such as the appearance of cyclical population density both for total population and for each age class.