Efficient inference of population size histories and locus-specific mutation rates from large-sample genomic variation data

Abstract

With the recent increase in study sample sizes in human genetics, there has been growing interest in inferring historical population demography from genomic variation data. Here, we present an efficient inference method that can scale up to very large samples, with tens or hundreds of thousands of individuals. Specifically, by utilizing analytic results on the expected frequency spectrum under the coalescent and by leveraging the technique of automatic differentiation, which allows us to compute gradients exactly, we develop a very efficient algorithm to infer piecewise-exponential models of the historical effective population size from the distribution of sample allele frequencies. Our method is orders of magnitude faster than previous demographic inference methods based on the frequency spectrum. In addition to inferring demography, our method can also accurately estimate locus-specific mutation rates. We perform extensive validation of our method on simulated data and show that it can accurately infer multiple recent epochs of rapid exponential growth, a signal that is difficult to pick up with small sample sizes. Lastly, we use our method to analyze data from recent sequencing studies, including a large-sample exome-sequencing data set of tens of thousands of individuals assayed at a few hundred genic regions.

Mutation Rate Variation is a Primary Determinant of the Distribution of Allele Frequencies in Humans

“…Small samples have the disadvantages of increased noise and limited temporal resolution of analysis. For example, in demographic inference, larger samples are essential for detecting the signal of recent rapid growth of the human population [17,64,65]. Interestingly, we found that samples much smaller than ExAC may also create an unappreciated bias, as we describe next.…”

“…For example, most demographic inference algorithms that use the SFS as a summary statistic [e.g. 6,65,77] rely on the infinite-sites model, which is evidently not a valid assumption for large samples. Adjusting demographic inference schemes to include the effects of recurrent mutations on the SFS (for examples of recent efforts towards this goal, see [78–82]) has the potential to significantly improve inference accuracy.…”

Explosive genetic evidence for explosive human population growth

“…However, the inference can be computational intractable as the number of populations and/or the number of parameters for inference become large and the desired accuracy increases, which is a general disadvantage of simulation-based methods. Bhaskar et al (2015) [18] developed a very efficient method and software ( fastNeutrino ) for inferring population size changes for a single population. The efficiency of stems from analytical computation of the SFS for a set of parameter values of a pre-defined model of population size changes, together with a fast optimization technique.…”

“…However, instead of making assumptions about the number of epochs and shape of each epoch in the history, such as exponential growth as the pre-defined model underlying other inference methods, it approximates historical population size via a non-parametric approach that fits many epochs, each of constant population size, while adding population size changing points (new epoch) until a good fit is obtained. Most recently, similar to fastNeutrino [18], we (2016) [22] developed a method (implemented in EGGS , without inference) that allows an analytical and efficient computation of the SFS for a set of parameters from more generalized models than previously possible, including population growth that is sub- or super-exponential.…”

Computing the joint distribution of the total tree length across loci in populations with variable size

“…Methods to study genetic variation, or perform inference, in populations with varying size or more complex demographic histories have been developed based on the Wright-Fisher diffusion, describing the evolution of population allele frequencies forward in time (Griffiths, 2003; Živković et al, 2015; Gutenkunst et al, 2009; Excoffier et al, 2013), or the Coalescent process, a model for the genealogical relationship in a sample of individuals (Griffiths and Tavaré, 1994; Griffiths and Marjoram, 1996; Griffiths and Tavaré, 1998; Živković and Wiehe, 2008; Bhaskar et al, 2015; Kamm et al, 2017). A powerful representation of genetic variation data that has been used in this context is the Site-Frequency-Spectrum.…”