Theoretical models of the effect of population bottlenecks on genetic variation assume that individuals are removed at random from the population. We investigated this assumption in a naturally regulated, unstable population of Soay sheep (Ovis aries). During rapid population declines or `crashes', individuals were not removed at random with respect to genotype: we found associations between individual survival and certain genotypes at five polymorphic protein or microsatellite DNA loci (Ada, Got, Tf, MAF18 and OPACAP). Some loci appeared to show simple associations with survival whereas others had more complex interactions with crash year or age: all displayed different patterns of association between the sexes. Simple overdominance was not a general feature of our data; it seems likely that fluctuating selection, countervailing selection in different fitness components or frequency-dependent selection may explain the pattern and complexity of the associations shown at different loci. Our study cannot distinguish between selection acting at these loci or at other, closely linked loci. However, our empirical study implies that the molecular genetic outcome of population bottlenecks in natural populations does not always follow theoretical expectations based on the random removal of genotypes. Bottlenecks in which individuals are removed at random are distinct from bottlenecks in which there is scope for selection via non-random survival of individuals.