Time-Dependent Effective Sampling Bias in Populations with Broad Offspring Number Distributions*

It is increasingly recognized that natural populations exhibit broad family size distributions, for example, due to high fecundities and high early mortality, or due to founder effects associated with range expansion. Despite recent progress in the neutral dynamics induced by broad offspring numbers, our knowledge of interactions between broad offspring numbers and natural selection remains limited. Here, we establish several new scaling relations about the fixation probability, the extinction time, the allele-frequency fluctuations, and the site frequency spectrum, when offspring numbers are distributed according to a fat-tailed distribution with a divergent variance (1/u^α+1 with 1<α<2). We validate the new findings in a class of models of range expansions, which effectively produce broad offspring number distributions with 1<α<2.