Understanding and predicting the fitness decline of shrunk populations: inbreeding, purging, mutation, and standard selection.

The joint consequences of inbreeding, natural selection, and deleterious mutation on mean fitness after population shrinkage are of great importance in evolution and can be critical to the conservation of endangered populations. I present simple analytical equations that predict these consequences, improving and extending a previous heuristic treatment. Purge is defined as the "extra" selection induced by inbreeding, due to the "extra" fitness disadvantage (2d) of homozygotes for (partially) recessive deleterious alleles. Its effect is accounted for by using, instead of the classical inbreeding coefficient f, a purged inbreeding coefficient g that is weighed by the reduction of the frequency of deleterious alleles caused by purging. When the effective size of a large population is reduced to a smaller stable value N (with Nd ≥ 1), the purged inbreeding coefficient after t generations can be predicted as g(t) ≈ [(1 - 1/2N) g(t)(-1) + 1/2N](1 - 2d f(t)(-1)), showing how purging acts upon previously accumulated inbreeding and how its efficiency increases with N. This implies an early fitness decay, followed by some recovery. During this process, the inbreeding depression rate shifts from its ancestral value (δ) to that of the mutation-selection-drift balance corresponding to N (δ*), and standard selection cancels out the inbreeding depression ascribed to δ*. Therefore, purge and inbreeding operate only upon the remaining δ - δ*. The method is applied to the conservation strategy in which family contributions to the breeding pool are equal and is extended to make use of genealogical information. All these predictions are checked using computer simulation.