Abstract
Evolutionary rescue occurs when genetic adaptation prevents extinction of a declining population. Mutation and recombination generate adaptive variation, but when their rates at adaptive loci are too low, rescue may require evolution toward higher rates of genetic change. Here, we derive and compare analytical approximations for the probability of rescue through two alternative routes: mutation-rate and recombination-rate evolution. Our model comprises two resident genotypes from which the same adaptive haplotype can arise along either route, with rescue requiring the appearance of an unlinked modifier allele that increases mutation at, or recombination between, two fitness-determining loci. We show that resident genotype composition determines the relative success of the two routes. Mutation-rate evolution yields a higher rescue probability when one resident genotype is sufficiently more common because mutation can act on either genotype whereas recombination requires both. Otherwise, the two routes yield similar rescue probabilities. Even when either route makes rescue appreciably likely, however, the modifier alleles facilitating rescue are often lost before rescue is complete. This loss is driven by multiple factors: segregation can separate the modifier from the adaptive haplotype; the fitness cost of modifier expression raises extinction risk for modifier-bearing lineages; and continued modifier-induced mutation disrupts the adaptive haplotype after it forms. The latter effect can make recombination-rate modifiers more likely to persist even when mutation-rate evolution yields a higher rescue probability. Overall, these results show that both mutation- and recombination-rate evolution can induce rescue, but successful rescue need not entail persistence of the modifier allele that facilitated it.