A novel spectral method for inferring general diploid selection from time series genetic data

Abstract

The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of non-neutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the population allele frequency space when numerically approximating requisite integrals. Furthermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and also apply it to analyze ancient DNA data from genetic loci associated with coat coloration in horses. In contrast to previous studies, our exploration of the full fitness parameter space reveals that a heterozygote-advantage form of balancing selection may have been acting on these loci.

Bayesian Inference of Natural Selection from Allele Frequency Time Series

“…In contrast, the ASIP locus is inferred to be overdominant under a constant-size demography, but the complicated demographic history results in an inference of positive selection and a much older allele age. These results stand in contrast to those of Steinrücken et al (2014), who found that the most likely mode of evolution for both loci under a constant demographic history is one of overdominance. There are a several reasons for this discrepancy.…”

“…These results stand in contrast to those of Steinrücken et al (2014), who found that the most likely mode of evolution for both loci under a constant demographic history is one of overdominance. There are a several reasons for this discrepancy.…”

“…One key way that these methods differ from each other is in how they compute the probability of the underlying allele frequency changes. For instance, Malaspinas et al (2012) approximated the diffusion with a birth-death type Markov chain, while Steinrücken et al (2014) approximate the likelihood analytically, using a spectral representation of the diffusion discovered by Song and Steinrücken (2012). These different computational strategies are necessary because of the inherent difficulty in solving the Wright-Fisher partial differential equation.…”

“…They also extended the selection model of Bollback et al (2008) to include fully recessive fitness effects. A more general selective model was implemented by Steinrücken et al (2014), who model general diploid selection, and hence they are able to fit data where selection acts in an over-or underdominant fashion; however, Steinrücken et al (2014) assumed a model with recurrent mutation and hence could not estimate allele age. The work of Mathieson and McVean (2013) is designed for inference of metapopulations over short timescales and so it is computationally feasible for them to use a discrete time, finite population Wright-Fisher model.…”

Multi-locus analysis of genomic time series data from experimental evolution

“…The many areas where this design has been applied include demographic inference (see [1] for a recent review), recombination rate estimation [2][3][4][5][6], and detection of natural selection [7][8][9][10][11][12][13]. Recently, there has been much interest in utilizing time series genetic data-e.g., from ancient DNA [14][15][16][17][18][19][20][21], experimental evolution of a population under controlled laboratory environments [22][23][24][25][26], or direct measurements in fast evolving populations [27]-to enhance our ability to probe into evolution. In particular, understanding the genetic basis of adaptation to changes in the environment can be significantly facilitated by such temporal data.…”