Density-Dependent Selection II. The Allee Effect

A density regulating mechanism is introduced which reflects the Allee effect of low numbers. Growth rates are low at low densities, increasing to a maximum as the population reaches an intermediate optimum size. Above this optimum level, further increases in density are detrimental. Analysis of simple growth equations under such a regime reveals the following features. Unlike growth rates which strictly decrease as population size increases, growth rates under this mechanism may result in two equilibrium population sizes, only one of which can be stable. Populations which fall below the lower equilibrium are doomed to extinction. Models of density-dependent selection incorporating the Allee effect are then considered. Again, extinction is possible, provided at least two of the three genotypes are adversely affected by low population sizes. The fitness of the heterozygote at low densities plays an important role. There must be overdominance in fitness at a stable interior equilibrium. However, unlike the class of decreasing fitnesses, these fitness classes may have multiple interior equilibria whose exact number depends on the exact fitness form. A maximization principle holds to varying degrees.