Gene genealogies in diploid populations evolving according to sweepstakes reproduction

Recruitment dynamics, or the distribution of the number of offspring among individuals, is central for understanding ecology and evolution. Sweepstakes reproduction (when the offspring number distribution has a heavy right-tail) may characterize the recruitment dynamics of highly fecund natural populations.} Sweepstakes reproduction can induce jumps in type frequencies, and multiple mergers in gene genealogies of sampled gene copies. Here, we consider gene genealogies in diploid panmictic populations evolving in a random environment. The heavy-tailed offspring number distribution is generated by mechanisms not involving natural selection, such as in chance matching of broadcast spawning with favourable environmental conditions. Our model of sweepstakes reproduction extends the one considered by Schweinsberg (2003) by applying an upper bound to the number of potential offspring of any given parent pair. Depending on the stated bound, the gene genealogies are in the domain of attraction of the Kingman coalescent, or specific familes of continuous-time Beta- or Poisson-Dirichlet simultaneous multiple-merger coalescents. The gene genealogies in a large population are viewed on a timescale proportional to at least N/ log (N) generations; N is proportional to the population size (when constant). Incorporating deterministic population size changes leads to time-changed coalescents; the time-change is independent of the skewness of the offspring-number distribution. Using simulations, we show that gene genealogies in finite populations are not well approximated by the coalescent trees. Simulation results also indicate that quenched (conditioned on the population ancestry) and annealed gene genealogies in finite populations are not in good agreement whenever the skewness of the offspring number distribution is increased.