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

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 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 populationsize 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.

Inferring Demography and Selection in Organisms Characterized by Skewed Offspring Distributions

“…Thus, the analysis of genomic data from organisms characterized by highly skewed offspring distributions-such as viruses-may be prone to serious misinference if examined with traditional WF and Kingman based approaches, even under neutrality. In particular, the neutral multiple merger events induced by the reproductive biology of these organisms may be mistaken for multiple-merger events induced by positive selection (Hallatschek 2018).…”

The multifurcating skyline plot

“…Beyond high-variance reproduction, many other phenomena can lead to multifurcations in the ancestral process of a sample, such as repeated selective sweeps (Durrett and Schweinsberg 2004), strong selective pressure (Neher and Hallatschek 2013), or oversampling (Bhaskar, Clark, and Song 2014). Using classical methods to analyze such datasets can lead to systematic biases (Hallatschek 2018; Sackman, Harris, and Jensen 2019).…”

Stochastic exits from dormancy give rise to heavy‐tailed distributions of descendants in bacterial populations

“…Previous theoretical work has demonstrated that fat‐tailed distributions of descendants with infinite variance can lead to qualitatively different population genetic dynamics (Der et al, ; Eldon & Wakeley, ; Hallatschek, ; Schweinsberg, ). While our experimentally determined distributions are fatter than log‐normal, it is unlikely that the variance diverges with population size for the particular species and conditions we examined.…”

“…However, for some animals there is high variance in reproductive success, with a minority of males fathering a large fraction of the children in each generation (Araki, Waples, Ardren, Cooper, & Blouin, 2007;Hedgecock, 1994;Hedgecock & Pudovkin, 2011;Lallias, Taris, Boudry, Bonhomme, & Lapègue, 2010). Such highly skewed offspring distributions have fundamental implications for how we predict and interpret fluctuations in allele frequencies (Der et al, 2012;Eldon & Wakeley, 2006;Hallatschek, 2018;Hedrick, 2005;Hoban et al, 2013;Schweinsberg, 2003). These implications include dramatic (e.g.…”