Time-Dependent Effective Sampling Bias in Populations with Broad Offspring Numbers

It has been increasingly recognized that natural populations exhibit broad family size distributions, either because offspring numbers are strongly variable or because range expansion processes generate jackpot events. Despite recent progress in the neutral dynamics induced by broad offspring numbers, our knowledge of their interactions with selection remains limited, except for certain special cases. Here, we establish a number of new scaling relations about the fixation probability, the extinction time and the site frequency spectrum that arise when offspring
numbers are distributed according to a power law with divergent variance. Finally, we validate the new findings within semi-pushed traveling waves, which are microscopic models that give rise to the power law of offspring numbers.