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The focus of this paper is the relationship between the dispersal rate and the conditions for invasion of a rare allele that improves performance in a marginal sink habitat at the expense of reducing fitness in the main source habitat. Classic multiple-niche population-genetic models predict that the conditions for the invasion of such an allele always become more favourable as the dispersal rate decreases. Precisely the opposite prediction was reached in demographic fitness-sensitivity studies. This study reconciles those contradictory predictions and identifies the assumptions responsible for the discrepancy. I show that whether a lower dispersal rate makes the conditions for the invasion of the allele more or less stringent depends on the magnitude of the effects of the allele. If the effect is large relative to the degree of maladaptedness of the original genotype to the marginal habitat, the conditions become less stringent with decreasing dispersal rate. The opposite is the case for mutations with very small effects. For a broad range of mutations with intermediate effects the conditions are most stringent under an intermediate dispersal rate.