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, 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.

The effect of strong purifying selection on genetic diversity

“…For instance, we have seen that once an allele spreads through the fitness distribution and reaches mutation-selection balance, an effective frequency-dependent selection coefficient emerges s eff (f ), (43) This effective selection coefficient arises due to the deleterious mutations that neutral mutations are linked to, and changes with the frequency f of the mutation as high-fitness individuals within the neutral lineage drift to extinction. This is analogous to the fictitious selection coefficient, s fic (f ) = log f 1−f , that emerges in the model analyzed by Hallatschek (2017). The difference in the form of the effective selection coefficient between our results and the Hallatschek (2017) model is large when N se −λ 1, but becomes negligible as N se −λ → 1; it underlies the differences between the site frequency spectra of rapidly adapting or ratcheting .…”

“…This is analogous to the fictitious selection coefficient, s fic (f ) = log f 1−f , that emerges in the model analyzed by Hallatschek (2017). The difference in the form of the effective selection coefficient between our results and the Hallatschek (2017) model is large when N se −λ 1, but becomes negligible as N se −λ → 1; it underlies the differences between the site frequency spectra of rapidly adapting or ratcheting . CC-BY 4.0 International license peer-reviewed) is the author/funder.…”

“…Recently, Hallatschek (2017) has studied allele frequency trajectories that arise in the forward-time dual of the Bolthausen-Sznitman coalescent. Our analysis reveals many of the interesting features seen in that work.…”

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, ; Hedgecock, ; Hedgecock & Pudovkin, ; Lallias, Taris, Boudry, Bonhomme, & Lapègue, ). Such highly skewed offspring distributions have fundamental implications for how we predict and interpret fluctuations in allele frequencies (Der et al, ; Eldon & Wakeley, ; Hallatschek, ; Hedrick, ; Hoban et al, ; Schweinsberg, ). These implications include dramatic (e.g.…”