Shallow gene genealogies have been reported in some Pacific salmon populations. Many salmon runs have been supplemented with commercial hatchery production, which may lead to the distortion of genealogies. We show that, while the genealogical tree in a naturally-reproducing population is the standard Kingman coalescent, the trees in populations supplemented by hatcheries are coalescents with multiple mergers of ancestral lineages (i.e. Λ- or Ξ-coalescents). This distortion indicates that allele-frequency changes occur in jumps, reflecting the reproductive dominance of few lineages. Our focus is to understand among-individual variation of reproductive success within salmon populations under hatchery stocking. Under high reproductive-variance conditions, we compute the distribution of heterozygosity across generations. The result shows that zero heterozygosity is not achieved, implying that salmon populations under hatchery stocking may decline without evident loss of genetic variation. We also point out that reproductive skew leads to shifting of peaks (singularities) of the heterozygosity distribution. By looking for peak shifts across many loci, one can distinguish the multiple-merger from the Kingman coalescent (which is applicable to other species as well).