Genetic Variability Under the Seedbank Coalescent

Abstract

We analyze patterns of genetic variability of populations in the presence of a large seedbank with the help of a new coalescent structure called the seedbank coalescent. This ancestral process appears naturally as a scaling limit of the genealogy of large populations that sustain seedbanks, if the seedbank size and individual dormancy times are of the same order as those of the active population. Mutations appear as Poisson processes on the active lineages and potentially at reduced rate also on the dormant lineages. The presence of "dormant" lineages leads to qualitatively altered times to the most recent common ancestor and nonclassical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with a seedbank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seedbank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seedbank, are compared. The effect of a seedbank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seedbank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect from genetic data the presence of a large seedbank in natural populations.KEYWORDS Wright-Fisher model; seedbank coalescent; dormancy; site-frequency spectrum; distance statistics M ANY microorganisms can enter reversible dormant states of low [respectively (resp.) zero] metabolic activity, for example when faced with unfavorable environmental conditions; see, e.g., Lennon and Jones (2011) for a recent overview of this phenomenon. Such dormant forms may stay inactive for extended periods of time and thus create a seedbank that should significantly affect the interplay of evolutionary forces driving the genetic variability of the microbial population. In fact, in many ecosystems, the percentage of dormant cells compared to the total population size is substantial and sometimes even dominant (for example, $20% in human gut, 40% in marine water, and 80% in soil; cf. Lennon and Jones 2011, box 1, table a). This abundance of dormant forms, which can be short-lived as well as stay inactive for significant periods of time (decades-or century-old spores are not uncommon), thus creates a seedbank that buffers against environmental change, but potentially also against classical evolutionary forces such as genetic drift, mutation, and selection.In this article, we investigate the effect of large seedbanks (that is, comparable to the size of the active population) on the patterns of genetic variability in populations over macroscopic timescales. In particular, we extend a recently introduced mathematical ...

Fisher–Wright model with deterministic seed bank and selection

“…The conditional time to fixation of a neutral allele is slowed down by a factor B 2 ( Figure 3 (right), dotted line) compared to the absence of seed bank. These results are consistent with the backward in time coalescent model from Kaj et al [26], and differs from the strong seed bank model of Blath et al [3]. We evaluate the SFS based on our diffusion process and confirm agreement to the SFS obtained under discrete time Fisher-Wright simulations.…”

“…A second class of models assumes a strong seed bank effect, whereby the time seeds can spend in the bank is very long, that is longer than the population coalescent time [18], or the time for two lineages to coalesce can be unbounded. This latest model generates a seed bank coalescent [3], which may not come down from infinity and for which the expected site-frequency spectrum (SFS) may differ significantly from that of the Kingman coalescent [5]. In effect, the model of [26] represents a special case, also called a weak seed bank, where the time for lineages to coalesce is finite because the maximum time that seeds can spend in the bank is bounded.…”

The Fisher-Wright model with deterministic seed bank and selection

“…The conditional time to fixation of a neutral allele is slowed down by a factor B 2 ( Figure 3 (right), dotted line) compared to the absence of seed bank. These results are consistent with the backward in time coalescent model from Kaj et al [19], and differs from the strong seed bank model of Blath et al [2]. We evaluate the SFS based on our diffusion process and confirm agreement to the SFS obtained under discrete time Fisher-Wright simulations.…”

“…A second class of models assumes a strong seed bank effect, whereby the time seeds can spend in the bank is very long, that is longer than the population coalescent time [14], or the time for two lineages to coalesce can be unbounded. This latest model generates a seed bank coalescent [2], which may not come down from infinity and for which the expected site-frequency spectrum (SFS) may differ significantly from that of the Kingman coalescent [4]. In effect, the model of [19] represents a special case, also called a weak seed bank, where the time for lineages to coalesce is finite because the maximum time that seeds can spend in the bank is bounded.…”

Evolution with a seed bank: The population genetic consequences of microbial dormancy

“…While dormant individuals can die in this model, their death rate is much lower than that of active individuals. This conceptual model was first presented in an ecological context (Lennon & Jones, ) and later used for the seed bank coalescent (Blath et al., )…”