Article,
Selection-like biases emerge in population models with recurrent jackpot events
bioRxiv, (2017)
DOI: 10.1101/182519
Abstract
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 Delbrueck called "jackpot" events. Here, we show that recurrent jackpot events generate a deterministic bias favoring majority alleles, which is equivalent to an effective 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 flipside 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 overall unless genuine selection is present. The limiting allele frequency process is dual to the Bolthausen-Sznitman coalescent and has a particularly simple representation in terms of the logarithm of the mutant frequency. 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 changes and different forms of selection. The fixation of unconditionally beneficial mutations is shown to be exponentially suppressed and balancing selection can maintain diversity only if the population size is large enough. We briefly discuss analogous effects in disordered complex systems, where sampling-induced biases can be viewed as ergodicity breaking driving forces.
