Can the Site-Frequency Spectrum Distinguish Exponential Population Growth from Multiple-Merger Coalescents?

Abstract

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a wellknown characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular, the weight of the right tail, are, however, affected in specific ways by the two model classes. Using an approximate likelihood method and minimum-distance statistics, our estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiplemerger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough. A normalized version of the SFS (nSFS) is also used as a summary statistic in an approximate Bayesian computation (ABC) approach. The results give further positive evidence as to the general eligibility of the SFS to distinguish between the different histories.KEYWORDS coalescent; multiple mergers; population growth; approximate maximum likelihood test; approximate Bayesian computation; sitefrequency spectrum T HE site-frequency spectrum (SFS) at a given locus is one of the most important and popular statistics based on genetic data sampled from a natural population. In combination with the postulation of the assumptions of the infinitelymany-sites mutation model (Watterson, 1975) and a suitable underlying coalescent framework, the SFS allows one to draw inferences about evolutionary parameters, such as coalescent parameters associated with multiple-merger coalescents or population-growth models.The Kingman coalescent, developed by Kingman (1982a, b,c), Hudson (1983a,b), and Tajima (1983), describing the random ancestral relations among DNA sequences drawn from natural populations, is a prominent and widely used model from which one can make predictions about genetic diversity. Many quantities of interest, such as the expected values and covariances of the SFS associated with the Kingman coalescent, are easily computed thanks to results by Fu (1995). The robustness of the Kingman coalescent is quite remarkable; indeed, a large number of genealogy models can be shown to have the Kingman coalescent or a variant thereof as their limit process (cf., e.g., Möhle 1998). A large volume of work is thus devoted to inference methods based on the Kingman coalescent [see, e.g., Donnelly and Tavaré (1995), Hudson (1990), Nordborg (2001), Hein et al. (2005), and Wakeley (2007) for reviews].However, many evolutionary histories can lead to significant deviations from the Kingman coalescent model. Such deviations can be detected using a variety of statistical tools, such as Tajima's D (Tajima 1989a), Fu and Li's D (Fu and Li 1993), and Fay and Wu 's H (Fay and Wu 2000), which are all functions of the SFS. However, they do not always allow one to identify the actual evolutionary mechanisms leading to such deviations. Developing statistical tools that allow one to dist...

Genetic Variability Under the Seedbank Coalescent

“…If one has expressions for the expected SFS under some coalescent model, one can use the normalized expected SFS in an approximate-likelihood inference (see, e.g., Eldon et al 2015). The normalized spectrum is also appealing since it is quite robust to changes in the mutation rate (Eldon et al 2015).…”

Inference of super-exponential human population growth via efficient computation of the site frequency spectrum for generalized models

“…Furthermore, the source code of the software is freely available to allow extensions to compute other summary statistics of interest (for example, the joint SFS of samples from multiple populations under It is also possible that other families of growth models may fit the pattern of human population size history. For instance, Eldon et al (2015) considered the algebraic-growth model in the form of NðTÞ ¼ T g : In reality, however, not all demographic models have numerically stable closed-form expressions for the expected time to the first coalescent event (c j ). In these cases, fast and accurate numerical integration methods, such as the Gauss-Legendre quadrature used in this work, can be applied to evaluate c j : This technique holds the promise of efficiently generating the expected value of population genetic summary statistics under arbitrary population size functions.…”

On the importance of skewed offspring distributions and background selection in virus population genetics

“…This limitation has partially been overcome by Eldon et al (2015), who proposed an approximate likelihood method along with an approximate Bayesian computation approach based on the SFS to distinguish between the MMC and exponential population growth. Although both effects are expected to result in very similar SFSs, characterized by an excess of singletons as compared with the Kingman coalescent, the bulk and tail of the SFS (that is, the higher-order frequency classes) typically differ, which can be assessed by approximate likelihood-ratio tests and approximate Bayes factors see Box 1).…”

“…Given that skewed offspring distributions and pervasive linked selection are likely important factors influencing the inference of virus population parameters, it is important to note that multiple backward and forward simulation programs have recently been developed that make the modeling of these processes feasible (Hernandez, 2008;Messer, 2013;Thornton, 2014;Eldon et al, 2015;Zhu et al, 2015). This will allow researchers to directly simulate from parameter ranges relevant for their population of interest, developing a better intuition for the importance of these processes in shaping the observed genomic diversity.…”