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In this article, we derive statistical tools to analyze and distinguish thepatterns of genetic variability produced by classical and recent populationgenetic models related to seed banks. In particular, we are concerned withmodels described by the Kingman coalescent (K), models exhibiting so-calledweak seed banks described by a time-changed Kingman coalescent (W), models withso-called strong seed bank described by the seed bank coalescent (S) and theclassical two-island model by Wright, described by the structured coalescent(TI). As the presence of a (strong) seed bank should stratify a population, weexpect it to produce a signal roughly comparable to the presence of populationstructure.  We begin with a brief analysis of Wright's $F_{ST}$, which is a classical butcrude measure for population structure, followed by a derivation of theexpected site frequency spectrum (SFS) in the infinite sites model based on'phase-type distribution calculus' as recently discussed by Hobolth et al.(2019). Both the $F_{ST}$ and the SFS can be readily computed under variouspopulation models, they discard statistical signal. Hence we also derive exactlikelihoods for the full sampling probabilities, which can be achieved viarecursions and a Monte Carlo scheme both in the infinite alleles and theinfinite sites model. We employ a pseudo-marginal Metropolis-Hastings algorithmof Andrieu and Roberts (2009) to provide a method for simultaneous modelselection and parameter inference under the so-called infinitely-many sitesmodel, which is the most relevant in real applications.  It turns out that this full likelihood method can reliably distinguish amongthe model classes (K, W), (S) and (TI) on the basis of simulated data even frommoderate sample sizes. It is also possible to infer mutation rates, and inparticular determine whether mutation is taking place in the (strong) seedbank.

Statistical tools for seed bank detection