It is difficult to imagine a biotic environment remaining unchanged for a sufficiently long time to allow significant evolutionary change. Nevertheless, our understanding of the process of genetic evolution by natural selection is founded primarily on considerations of deterministic processes in a constant environment. This discord is avoided if time-homogeneous deterministic models are considered as a description of the average evolutionary change in the population. This assertion is corroborated by results of population genetic models in which selection varies through time. Haldane and Jayakar (1963) and Gillespie (1973) showed that the condition for initial increase of a rare allele is the same in a varying environment as in a constant environment when the genotypic fitnesses are calculated as the geometric average fitness through time. Thus, the establishment of a new allele in the population is fully described by the average selection over time and the condition for protected polymorphism of the allele and its alternative is also formulated in terms of time-average genotypic fitnesses. However, directional selection in time-average fitnesses does not exclude the existence of stable polymorphism (Karlin and Liberman 1974).
Rare Allele Intrinsic Rate Hyperbolic Model Density Response Density Dependent Death Rate
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