The interaction of inbreeding depression and environmental stochasticity in the risk of extinction of small populations.

Current population genetic and population dynamic models are inappropriate to judge the risk of extinction of small populations due to the combined effects of inbreeding, genetic drift, demographic stochasticity, and environmental stochasticity. Instead, a model based on the aggregated fates of individuals is advocated. The unequal distribution of resources over individuals is an essential part of this model. The model allows the incorporation of the mutation-selection dynamics of alleles leading to inbreeding effects and to fixation of slightly deleterious mutations as a result of genetic drift. The slightly deleterious mutations lower the conversion of resources into offspring. Whereas lethal alleles are rapidly eliminated by selection in small populations, the selection against mild deleterious effects depends strongly on effective population size and on the social system, that is, on the division of resources among individuals. The model allows for the study of rates at which processes occur while far away from equilibrium, which is crucial in understanding the extinction risks of threatened populations. One example of the latter is illustrated in simulations in which small populations become extinct between approximately 100 and 200 generations after they became small populations, due to a gradual accumulation of mildly deleterious mutations.