Mutation Accumulation and the Extinction of Small Populations

-Although extensive work has been done on the relationship between population size and the risk of extinction due to demographic and environmental stochasticity, the role of genetic deterioration in the extinction process is poorly understood. We develop a general theoretical approach for evaluating the risk of small populations to extinction via the accumulation of mildly deleterious mutations, and we support this with extensive computer simulations. Unlike previous attempts to model the genetic consequences of small population size, our approach is genetically explicit and fully accounts for the mutations inherited by a founder population as well as those introduced by subsequent mutation. Application of empirical estimates of the properties of spontaneous deleterious mutations leads to the conclusion that populations with effective sizes smaller than 100 (and actual sizes smaller than 1,000) are highly vulnerable to extinction via a mutational meltdown on timescales of approximately 100 generations. We point out a number of reasons why this is likely to be an overly optimistic view. Thus, from a purely genetic perspective, current management policies that provide formal protection to species only after they have dwindled to 100-1,000 individuals are inadequate. A doubling of the deleterious mutation rate, as can result from the release of mutagenic pollutants by human activity, is expected to reduce the longevity of a population by about 50%. As some investigators have previously suggested, the genetic load of a population can be readily purged by intentional inbreeding. However, this effect is at best transient, as intentional inbreeding can only enhance the probability of fixation of deleterious alleles, and those alleles that are purged are rapidly replaced with new mutations. There has never been any question that the vulnerability of a population to extinction increases with decreasing population size (Ludwig 1976; Leigh 1981; Shaffer 1981 ; Ginzburg et al. 1982; Goodman 1987; Burgman et al. 1992; Lande 1993; Foley 1994). This is true whether the dominant risk is demographic stochasticity (random variation in birth and mortality rates and gender among individuals), temporal variation in critical environmental factors, or genetic problems (inbreeding depression, mutation accumulation, and loss of adaptive variation). Less clear is how rapidly the risk of extinction declines with increasing population size and the degree to which this relationship is nonlinear. Determination of the scaling between extinction probability and population size is of practical importance since it can help reveal whether a threshold population size exists below * E-mail: [email protected]. Am. Nat. 1995 , Vol. 146, pp. 489-518 C 1995 by The Univers~tyof Chicago. rights reserved. 490 THE AMERICAN NATURALIST which there is a rapid increase in vulnerability to extinction. Such information can be of considerable value in the design of breeding and maintenance programs for small captive populations of endangered species, exotic breeds, and inbred lines. For factors such as demographic and environmental stochasticity, the relationship between expected time to extinction and mean population size can depend rather specifically on the life-history features of the population and on the temporal patterns of environmental variation to which it is exposed. However, for certain genetic problems, general statements may be possible since the basic Mendelian mechanisms of gene transmission are essentially constant across species (Lynch and Lande 1993; Lynch et al. 1993; Lande 1994; Biirger and Lynch 1995; Lynch et al. 1995). This article is concerned with the consequences of the accumulation of unconditionally deleterious genes for the viability of sexual populations. Our primary focus will be on relatively small populations-those with effective sizes on the order of a few hundred individuals or less, which is a rough approximation of the population size to which species have typically declined by the time they are listed as threatened or endangered under the U.S. Endangered Species Act (Wilcove et al. 1993). In addition to evaluating the degree to which the risk of extinction scales with population size and fecundity, we consider the consequences of an increase in the genomic mutation rate that might result, for example, from an increase in exposure to mutagens promoted by human activities.