Waltman P.E. Competition Models in Population Biology

Society for Industrial Mathematics, 1987. - 88 pages.This book uses fundamental ideas in dynamical systems to answer questions of a biologic nature, in particular, questions about the behavior of populations given a relatively few hypotheses about the nature of their growth and interaction. The principal subject treated is that of coexistence under certain parameter ranges, while asymptotic methods are used to show competitive exclusion in other parameter ranges. Finally, some problems in genetics are posed and analyzed as problems in nonlinear ordinary differential equations.Single Population Growth Models. Logistic Growth; The Simple Chemostat. Interacting Populations. The Lotka-Volterra Competition Model; Competition in the Chemostat; A Three-level Food Chain; Bifurcation from a Limit Cycle; Two Predators Competing for a Renewable Resource; Two Predators Feeding on a Prey Growing in a Chemostat. Some Deterministic Problems in Genetics. Predator Influence on the Growth of a Population with Three Genotype; A Model of Cystic Fibrosis; A Parental Selection Problem