Invasion of gene duplication through masking for maladaptive gene flow

Gene duplication can increase an organism's ability to mask the effect of deleterious alleles present in the population, but this is typically a small effect when the source of the genetic variation is mutation. Migration can introduce orders of magnitude more deleterious alleles per generation and may therefore be an important force acting on the structure of genomes. Using formal analytical methods, we study the invasion of haplotypes containing two copies of the resident allele, assuming that a single-locus equilibrium is already established in a continent-island model of migration. Provided that the immigrant allele can be completely masked by multiple functional gene copies, a new duplication will deterministically spread so long as duplicate haplotypes are, on average, fitter than single-copy haplotypes. When fitness depends on the number of immigrant allele copies and their masking ability then the threshold for invasion depends on the rate of immigration and the rate of recombination between the gene copies. Results from several special cases, including formation of protein dimers and Dobzhansky-Muller incompatibilities, suggest that duplications can invade in a wide range of selection regimes. We hypothesize that duplication in response to gene flow may provide an explanation for the high levels of polymorphism in gene copy number observed in natural populations.