The large amount and high quality of genomic data available today enable, in principle, accurate inference of evolutionary histories of observed populations. The Wright-Fisher model is one of the most widely used models for this purpose. It describes the stochastic behavior in time of allele frequencies and the influence of evolutionary pressures, such as mutation and selection. Despite its simple mathematical formulation, exact results for the distribution of allele frequency (DAF) as a function of time are not available in closed analytical form. Existing approximations build on the computationally intensive diffusion limit or rely on matching moments of the DAF. One of the moment-based approximations relies on the beta distribution, which can accurately describe the DAF when the allele frequency is not close to the boundaries (0 and 1). Nonetheless, under a Wright-Fisher model, the probability of being on the boundary can be positive, corresponding to the allele being either lost or fixed. Here we introduce the beta with spikes, an extension of the beta approximation that explicitly models the loss and fixation probabilities as two spikes at the boundaries. We show that the addition of spikes greatly improves the quality of the approximation. We additionally illustrate, using both simulated and real data, how the beta with spikes can be used for inference of divergence times between populations with comparable performance to an existing state-of-the-art method.KEYWORDS Wright-Fisher; beta; pure genetic drift; linear evolutionary pressures; divergence times A DVANCES in sequencing technologies have revolutionized the collection of genomic data, increasing both the volume and quality of available sequenced individuals from a large variety of populations and species (Romiguier et al. 2014;Gudbjartsson et al. 2015). These data, which may involve up to millions of single-nucleotide polymorphisms (SNPs), contain information about the evolutionary history of the observed populations. There has been a great focus in the recent years on inferring such histories, and to this end, one of the most widely used models is the Wright-Fisher model (Gautier et al. 2010; SirĂ©n et al. 2011; Malaspinas et al. 2012; Pickrell and Pritchard 2012; SteinrĂŒcken et al. 2014; Terhorst et al. 2015).The Wright-Fisher model characterizes the evolution of a randomly mating population of finite size in discrete nonoverlapping generations. The model describes the stochastic behavior in time of the number of copies (frequency) of alleles at a locus. The frequency is influenced by a series of factors, such as random genetic drift, mutations, migrations, selection, and changes in population size. When inferring the evolutionary history of a population, the effects of the different factors have to be untangled. Mutation, migration, and selection affect the allele frequency in a deterministic manner (Ewens 2004). We collectively refer to these as evolutionary pressures. The frequency also varies from one generation to the next as a resul...