Loss of fitness due to the accumulation of deleterious mutations appears to be inevitable in small, obligately asexual populations, as these are incapable of reconstituting highly fit genotypes by recombination or back mutation. The cumulative buildup of such mutations is expected to lead to an eventual reduction in population size, and this facilitates the chance accumulation of future mutations. This synergistic interaction between population size reduction and mutation accumulation leads to an extinction process known as the mutational meltdown, and provides a powerful explanation for the rarity of obligate asexuality. We give an overview of the theory of the mutational meltdown, showing how the process depends on the demographic properties of a population, the properties of mutations, and the relationship between fitness and number of mutations incurred.

Abstract. -Previous attempts to model the joint action of selection and mutation in finite populations have treated population size as being independent of the mutation load. However, the accumulation of deleterious mutations is expected to cause a gradual reduction in population size. Consequently, in small populations random genetic drift will progressively overpower selection making it easier to fix future mutations. This synergistic interaction, which we refer to as a mutational melt-down, ultimately leads to population extinction. For many conditions, the coefficient of variation of extinction time is less than 0.1, and for species that reproduce by binary fission, the expected extinction time is quite insensitive to population carrying capacity. These results are consistent with observations that many cultures of ciliated protozoans and vertebrate fibroblasts have characteristic extinction times. The model also predicts that c10nallineages are unlikely to survive more than 10 4 to 10' generations, which is consistent with existing data on parthenogenetic animals. Contrary to the usual view that Muller's ratchet does more damage when selection is weak, we show that the mean extinction time declines as mutations become more deleterious. Although very small sexual populations, such as self-fertilized lines, are subject to mutational meltdowns, recombination effectively eliminates the process when the effective population size exceeds a dozen or so. The concept ofthe effective mutation load is developed, and several procedures for estimating it are described. It is shown that this load can be reduced substantially when mutational effects are highly variable.Received June 27, 1989. Accepted January 17, 1990.All populations are doomed to eventual in small populations. On the other hand, extinction. The reasons include temporal Kimura et al. (1963) argued that the load variation in the environment, demographic due to mildly deleterious mutations is instochasticity (random variation in survi-versely proportional to population size, apvorship, birth rate, and sex ratio), and ge-proaching the selection coefficient in the abnetic problems such as inbreeding depres-sence of back-mutation. sion, the loss of adaptive variation by These results for sexual populations in random drift, and recurrent deleterious mu-drift-mutation-selection balance may be tations (Soule, 1987;Lande, 1988). This pa-contrasted with Muller's (1964) idea that a per is concemed exclusively with the latter mutational ratchet operates in asexual popproblem. Deleterious mutations impose a ulations, continually driving them to lower load on populations through the reduction and lower fitness. The idea here is that, in in the mean survivorship and/or reproduc-the absence of sex, no genotype can ever tive rates of individuals (Haldane, 1937; produce an offspring with fewer mutations Muller, 1950;Wallace, 1987). IDtimately, than its own load. In a finite population, this load should be manifested in a higher there is always a possibility that the class ...

The success of a species, its numbers, sometimes its size, etc., are determined largely by the degree of deviation of a single factor (or factors) from the ränge of Optimum of the species. Victor E. Shelford (1913, p. 303) These words, written by one of the founders of ecology at an early stage in his career, are so deeply embedded in ecological thought that they sound quite trite. Although Shelford's "law of tolerance" is still given significant coverage in some ecology texts (Odum 1971), it has largely been supplanted by the concept of the niche (Whittaker and Levin 1975), which underlies many ecological and evolutionary problems of current interest. Among investigators in evolutionary ecology and ecological genetics, there is much interest in the way in which natural selection interacts with the genome to determine a population's fitness response to different gradients of density-independent and density-dependent factors. In many areas of applied ecology, such as toxicity testing and the development of new crop varieties, a substantial proportion of research focuses on the sensitivity of different genotypes, populations, and/or species to environmental extremes.In the following, we refer to the response of a genotype's total fitness over an environmental gradient as a tolerance curve. Our definition is a special case of the norm of reaction of Woltereck (1909) and Schmalhausen (1949), which relates the phenotypic expression of a genotype to its environment. Although a genotypefocused definition necessarily introduces some analytic and empirical difficulties, it is an essential starting point in any effort to understand the mechanisms underlying a population-level response to an environmental gradient. The significance of this point was considered first by Van Valen (1965) and later by Roughgarden (1972), who drew a distinction between the within-and betweenphenotype components of niche width. The sensitivity of a population to environmental extremes is a function of both the between-individual variance in environmental optima and the within-individual breadth of adaptation.The focus of this paper is threefold. First, we wish to point out some of the * Present address: Department of Ecology, Ethology, and Evolution, University of Illinois, Shelford Vivarium, 606 East Healey Street, Champaign, Illinois 61820. Am. Nat. 1987. Vol. 129, pp. 283-303. © 1987 by The University of Chicago. 0003-0147/87/2902-0007S02.00. All rights reserved. 284THE AMERICAN NATURALIST proximate causes that interact to shape a genotype's tolerance curve and some of the difficulties in identifying them. Second, we consider how temporal and spatial Variation in the environment may influence the evolution of specific properties of the tolerance curve. Finally, we discuss a Statistical protocol for the estimation of tolerance-curve parameters. We emphasize at the outset that in order to present some of the fundamental concepts of this paper without being overly technical, we have relied on a number of mathematical assumptions, particular...

Abstract. -We extend our earlier work on the role of deleterious mutations in the extinction of obligately asexual populations. First, we develop analytical models for mutation accumulation that obviate the need for time-consuming computer simulations in certain ranges of the parameter space. When the number of mutations entering the population each generation is fairly high, the number ofmutations per individual and the mean time to extinction can be predicted using classical approaches in quantitative genetics. However, when the mutation rate is very low, a fixationprobability approach is quite effective. Second, we show that an intermediate selection coefficient (s) minimizes the time to extinction. The critical value of s can be quite low, and we discuss the evolutionary implications ofthis, showing that increased sensitivity to mutation and loss ofcapacity for DNA repair can be selectively advantageous in asexual organisms. Finally, we consider the consequences of the mutational meltdown for the extinction of mitochondrial lineages in sexual species.

Phenotypic plasticity is a key factor for the success of organisms in heterogeneous environments. Although many forms of phenotypic plasticity can be induced and retracted repeatedly, few extant models have analyzed conditions for the evolution of reversible plasticity. We present a general model of reversible plasticity to examine how plastic shifts in the mode and breadth of environmental tolerance functions (that determine relative fitness) depend on time lags in response to environmental change, the pattern of individual exposure to inducing and noninducing environments, and the quality of available information about the environment. We couched the model in terms of prey-induced responses to variable predation regimes. With longer response lags relative to the rate of environmental change, the modes of tolerance functions in both the presence or absence of predators converge on a generalist strategy that lies intermediate between the optimal functions for the two environments in the absence of response lags. Incomplete information about the level of predation risk in inducing environments causes prey to have broader tolerance functions even at the cost of reduced maximal fitness. We give a detailed analysis of how these factors and interactions among them select for joint patterns of mode and breadth plasticity.