Deterministic single-locus density-dependent selection.

Density-regulated selection is considered for a single, multiallele gene locus and separated generations. Characteristics resulting from the basic assumption that the average population fitness decreases with increasing density are derived. Under this assumption, it proves to be necessary to distinguish between regions of allelic frequencies which imply limited population growth, unlimited growth, or ultimate extinction when the population stays in the respective region. Particular attention is given to the investigation of the region of limited growth and the 'carrying capacity function' theta defined on it. Relationships between theta and the average fitness (adaptive surface) in the non-density dependent model are explained. Besides stability properties of equilibrium points, more general characteristics concerning the asymptotic behavior of population trajectories are treated. In this context, the problems of sudden loss of alleles and of population extinction as a result of large fluctuations in density are discussed.