Interpreting the pervasive observation of U-shaped Site Frequency Spectra

Abstract

The standard neutral model of molecular evolution has traditionally been used as the null model for population genomics. We gathered a collection of 45 genome-wide site frequency spectra from a diverse set of species, most of which display an excess of low and high frequency variants compared to the expectation of the standard neutral model, resulting in U-shaped spectra. We show that multiple merger coalescent models often provide a better fit to these observations than the standard Kingman coalescent. Hence, in many circumstances these under-utilized models may serve as the more appropriate reference for genomic analyses. We further discuss the underlying evolutionary processes that may result in the widespread U-shape of frequency spectra.

Fig 1. Error for estimating parameters for Beta coalescents with exponential growth and allele misorientation across the parameter grid for (α, g, e).

The space between the points stems from the grid. Sample size n = 100, 50 independent loci with 100 mutations on average. 500 simulations were performed per parameter triplet.

Fig 2. Estimates of α by species.

The four top panels represent transformed ϕ-SFS (ϕ_i = iξ_i as in [54, 55]) for four species from different taxa: two vertebrates Aptenodytes patagonicus (left) and Parus major (center right) an invertebrate Physa acuta (center left), and a bacteria Escherichia coli (right). For E. coli, the uptick in the spectrum comes exclusively from the allele miss-orientation, as $\widehat{\alpha }=2$. Black dots are the observed values, grey dotted lines are the best fits under the Kingman’s coalescent model and red lines are the best fits under a Beta-coalescent model.