On the relevance of three genetic models for the description of genetic variance in small populations undergoing selection

The conservation of genetic variability is recognized as a necessary objective for the optimization of selection schemes, particularly when populations are small. Numerous models, differing by the genetic model they rely on, are available to better understand and predict the evolution of genetic variance in a small population undergoing selection. This paper compares three genetic models, treated either analytically or with Monte-Carlo simulations, first in order to validate the predictions provided by a 'full-finite model' for well-known phenomena (e.g. the effect of population management on genetic variability), and second, to evaluate when and how the assumptions made in the two analytical models induce the departure from the third model. The FFM is shown, first, to be in close agreement with the Gaussian theory when used with a large number of loci, the stochastic approach making it much more flexible than the two algebraic models. In the second part of the study, the infinitesimal model appears to be more robust than the semi-infinitesimal one. Major sources of discrepancy between the deterministic models and the FFM are identified, notably the hypothesis of independence between loci, and then the infinite number of loci or alleles per locus. (C) Inra/Elsevier, Paris.