Selection-Like Biases Emerge in Population Models with Recurrent Jackpot Events

Evolutionary dynamics driven out of equilibrium by growth, expansion, or adaptation often generate a characteristically skewed distribution of descendant numbers: the earliest, the most advanced, or the fittest ancestors have exceptionally large number of descendants, which Luria and Delbrück called "jackpot" events. Here, I show that recurrent jackpot events generate a deterministic median bias favoring majority alleles, which is akin to positive frequency-dependent selection (proportional to the log ratio of the frequencies of mutant and wild-type alleles). This fictitious selection force results from the fact that majority alleles tend to sample deeper into the tail of the descendant distribution. The flip side of this sampling effect is the rare occurrence of large frequency hikes in favor of minority alleles, which ensures that the allele frequency dynamics remains neutral in expectation, unless genuine selection is present. The resulting picture of a selection-like bias compensated by rare big jumps allows for an intuitive understanding of allele frequency trajectories and enables the exact calculation of transition densities for a range of important scenarios, including population-size variations and different forms of natural selection. As a general signature of evolution by rare events, fictitious selection hampers the establishment of new beneficial mutations, counteracts balancing selection, and confounds methods to infer selection from data over limited timescales.