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Most population genetic theory assumes that populations adapt to an environmental change without a change in population size. However, environmental changes might be so severe that populations decline in size and, without adaptation, become extinct. This "evolutionary rescue" scenario differs from traditional models of adaptation in that rescue involves a race between adaptation and extinction. While most previous work has usually focused on models of evolutionary rescue in haploids, here we consider diploids. In many species, diploidy introduces a novel feature into adaptation: adaptive evolution might occur either on sex chromosomes or on autosomes. Previous studies of nonrescue adaptation revealed that the relative rates of adaptation on the X chromosome versus autosomes depend on the dominance of beneficial mutations, reflecting differences in effective population size and the efficacy of selection. Here, we extend these results to evolutionary rescue and find that, given equal-sized chromosomes, there is greater parameter space in which the X is more likely to contribute to adaptation than the autosomes relative to standard nonrescue models. We also discuss how subtle effects of dominance can increase the chance of evolutionary rescue in diploids when absolute heterozygote fitness is close to 1. These effects do not arise in standard nonrescue models.

Theories of adaptation typically ignore the effect of environmental change on population size. But some environmental challenges--challenges to which populations must adapt--may depress absolute fitness below 1, causing populations to decline. Under this scenario, adaptation is a race; beneficial alleles that adapt a population to the new environment must sweep to high frequency before the population becomes extinct. We derive simple, though approximate, solutions to the probability of successful adaptation (population survival) when adaptation involves new mutations, the standing genetic variation, or a mixture of the two. Our results show that adaptation to such environmental challenges can be difficult when relying on new mutations at one or a few loci, and populations will often decline to extinction.

We review both the theory and the data supporting the neo-Darwinian claim that adaptation results from the accumulation of many alleles of small effect. The theory supporting this "micromutationist" view is inconclusive. Furthermore, the evidence from genetic analysis is mixed: although some adaptations are apparently based on many genes of small effect, others clearly involve major genes. Most genetic analyses, moreover, have lacked the power to detect major genes. We conclude that, although the neo-Darwinian view of adaptation may be correct, it is not strongly supported by evidence. The introduction of molecular approaches may, however, finally allow us to resolve this question.