To investigate the consequences of hybridization between species, we studied three replicate hybrid populations that formed naturally between two swordtail fish species, estimating their fine-scale genetic map and inferring ancestry along the genomes of 690 individuals. In all three populations, ancestry from the "minor" parental species is more common in regions of high recombination and where there is linkage to fewer putative targets of selection. The same patterns are apparent in a reanalysis of human and archaic admixture. These results support models in which ancestry from the minor parental species is more likely to persist when rapidly uncoupled from alleles that are deleterious in hybrids. Our analyses further indicate that selection on swordtail hybrids stems predominantly from deleterious combinations of epistatically interacting alleles.