Competitive dynamics in size-structured populations with reproductive delays

• Main Author: Garcia-Alvarado, Martin Gildardo, 1962-
• Other Authors: Cushing, James M.
• Language: en_US
• Published: The University of Arizona. 1998
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/10150/282668

In this work we study the dynamics of populations whose individuals are divided into two size categories (juveniles and adults) and are competing through the exploitation of a single nutrient resource. First we study the case of a single species population. The modeling approach we use results in a partial integro-differential system for the population density and the nutrient level. In view of the lack of techniques to obtain an explicit solution, we derive a system of time varying delay differential equations for the resource level and certain population density related functionals. We study the existence and stability of steady state solutions in terms of the inherent net reproductive number and conclude that if individuals are capable of, at least, replacing themselves (by reproduction) the population equilibrates at a positive level; otherwise, the population suffers extinction. Numerical simulations seem to indicate that it is not possible to destabilize positive equilibrium solutions. The case of several species interaction is treated from the resident/invader point of view. The first observation is that it is not possible for two or more species to coexist in equilibrium. A species that can successfully exist alone at a certain resource level is called the resident species. If another species, the invader, with inherent net reproductive number less than one enters the competition, then the invader goes extinct. Otherwise the resident extincts and the invader survives at equilibrium.