Total consensus under high reproductive-variance conditions

Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among parents in mass spawns. When extreme reproduction events occur, offspring from very few parents dominate the population (whereby multiple mergers, or subsets of lineages with star-like trees, arise) and thus, the loss of genetic diversity is significant. Under high reproductive-variance conditions (assuming that reproduction occurs by sampling from the Pareto distribution), this paper explores the distribution of heterozygosity across generations. The result shows that zero heterozygosity is not achieved, implying that the populations may decline without evident loss of genetic variation. It is also found that there are singularities in the heterozygosity distributions. However, in the case of high reproductive variance, the locations of the singular points subtly deviate from those of the case where reproduction occurs by Wright-Fisher sampling.