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 ...

Mutation accumulation and the extinction of small populations

The fixation of new deleterious mutations is analyzed for a randomly mating population of constant size with no environmental or demographic stochasticity. Mildly deleterious mutations are far more important in causing loss of fitness and eventual extinction than are lethal and semilethal mutations in populations with effective sizes, Ne , larger than a few individuals. If all mildly deleterious mutations have the same selection coefficient, s against heterozygotes and 2s against homozygotes, the mean time to extinction, t¯, is asymptotically proportional to e4Nes/Ne for 4Ne s > 1. Nearly neutral mutations pose the greatest risk of extinction for stable populations, because the magnitude of selection coefficient that minimizes t¯ is about ŝ = 0.4/Ne . The influence of variance in selection coefficients among mutations is analyzed assuming a gamma distribution of s, with mean s¯ and variance σs2. The mean time to extinction increases with variance in selection coefficients if s¯ is near ŝ, but can decrease greatly if s¯ is much larger than ŝ. For a given coefficient of variation of s, c=σs/s¯, the mean time to extinction is asymptotically proportional to Ne1+1/c2 for 4Nes¯>1. When s is exponentially distributed, (c = 1) t¯ is asymptotically proportional to Ne2. These results in conjunction with data on the rate and magnitude of mildly deleterious mutations in Drosophila melanogaster indicate that even moderately large populations, with effective sizes on the order of Ne = 103 , may incur a substantial risk of extinction from the fixation of new mutations.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1558-5646.1994.tb02188.x

Risk of population extinction from fixation of new deleterious mutations.

Mildly deleterious mutation has been invoked as a leading explanation for a diverse array of observations in evolutionary genetics and molecular evolution and is thought to be a significant risk of extinction for small populations. However, much of the empirical evidence for the deleterious-mutation process derives from studies of Drosophila melanogaster, some of which have been called into question. We review a broad array of data that collectively support the hypothesis that deleterious mutations arise in flies at rate of about one per individual per generation, with the average mutation decreasing fitness by about only 2% in the heterozygous state. Empirical evidence from microbes, plants, and several other animal species provide further support for the idea that most mutations have only mildly deleterious effects on fitness, and several other species appear to have genomic mutation rates that are of the order of magnitude observed in Drosophila. However, there is mounting evidence that some organisms have genomic deleterious mutation rates that are substantially lower than one per individual per generation. These lower rates may be at least partially reconciled with the Drosophila data by taking into consideration the number of germline cell divisions per generation. To fully resolve the existing controversy over the properties of spontaneous mutations, a number of issues need to be clarified. These include the form of the distribution of mutational effects and the extent to which this is modified by the environmental and genetic background and the contribution of basic biological features such as generation length and genome size to interspecific differences in the genomic mutation rate. Once such information is available, it should be possible to make a refined statement about the long-term impact of mutation on the genetic integrity of human populations subject to relaxed selection resulting from modern medical procedures.

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Perspective: spontaneous deleterious mutation

Although it is widely acknowledged that the gradual accumulation of mildly deleterious mutations is an important source of extinction for asexual populations, it is generally assumed that this process is of little relevance to sexual species. Here we present results, based on computer simulations and supported by analytical approximations, that indicate that mutation accumulation in small, random-mating monoecious populations can lead to mean extinction times less than a few hundred to a few thousand generations. Unlike the situation in obligate asexuals in which the mean time to extinction (te ) increases more slowly than linearly with the population carrying capacity (K), te increases approximately exponentially with K in outcrossing sexual populations. The mean time to extinction for obligately selfing populations is shown to be equivalent to that for asexual populations of the same size, but with half the mutation rate and twice the mutational effect; this suggests that obligate selfing, like obligate asexuality, is inviable as a long-term reproductive strategy. Under all mating systems, the mean time to extinction increases relatively slowly with the logarithm of fecundity, and mutations with intermediate effects (similar to those observed empirically) cause the greatest risk of extinction. Because our analyses ignore sources of demographic and environmental stochasticity, which have synergistic effects that exacerbate the accumulation of deleterious mutations, our results should yield liberal upper bounds to the mean time to extinction caused by mutational degradation. Thus, deleterious mutation accumulation cannot be ruled out generally as a significant source of extinction vulnerability in small sexual populations or as a selective force influencing mating-system evolution.

Mutational meltdowns in sexual populations

A Quantitative-Genetic Perspective on Conservation Issues

Starting from a completely homozygous population of Drosophila melanogaster, two groups of 100 inbred lines each were established and maintained for 46 generations, by a single brother-sister mating and two double first cousin matings, respectively. Sternopleural bristle number, wing length and wing width were simultaneously scored in all lines every 4-5 generations. The means of four lines in each group departed significantly from the overall mean and, in each case, this was attributed to a single mutation of relatively large effect on at least one trait (0.3-1.4 environmental standard deviations in absolute value). Further analyses revealed widespread pleiotropy, similar gene action of a given mutation for all traits affected, and predominant additive action. No apparent association was found between the magnitudes of mutational effects on the traits and fitness. However, all recessive mutations were deleterious. The distribution of mutant effects was asymmetrical (positive for bristles and negative for wing measurements). Moreover, these distributions had a high variance and may be leptokurtic, due to the presence of major genes. Estimates of the ratio of new mutational variance to environmental variance ranged within (0.7-3.4) x 10(-3), those for wing measurements being generally larger. In agreement with theory, the rate of between-line differentiation was independent of population size.

https://www.genetics.org/content/genetics/132/3/771.full.pdf

C López-Fanjul

Papers

The distribution of spontaneous mutations on quantitative traits and fitness in Drosophila melanogaster.