Estimating Allele Age and Selection Coefficient from Time-Serial Data

Malaspinas, Anna-Sapfo; Malaspinas, Orestis; Evans, Steven N.; Slatkin, Montgomery

doi:10.1534/genetics.112.140939

Cited by 151 publications

(317 citation statements)

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“…In principle, it seems that dynamic data should provide researchers with more power to detect and quantify selective forces while avoiding the assumptions of stationarity that are required for many inference techniques based on static samples (Sawyer and Hartl 1992;Boyko et al 2008;Desai and Plotkin 2008). Nonetheless, the behavior and power of inference techniques based on time series data have not been thoroughly investigated.There is a well-developed literature on inferring population sizes from genetic time-series data, assuming neutrality (Pollak 1983;Waples 1989;Williamson and Slatkin 1999;Wang 2001), and a rapidly growing literature on inferring natural selection from such time series (Bollback et al 2008;Illingworth and Mustonen 2011;Illingworth et al 2012;Malaspinas et al 2012;Mathieson and McVean 2013). However, even the simplest case-the dynamics of two alternative alleles at a single genetic locus independent of all other loci-presents a number of statistical challenges that have not been resolved.…”

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“…There is a well-developed literature on inferring population sizes from genetic time-series data, assuming neutrality (Pollak 1983;Waples 1989;Williamson and Slatkin 1999;Wang 2001), and a rapidly growing literature on inferring natural selection from such time series (Bollback et al 2008;Illingworth and Mustonen 2011;Illingworth et al 2012;Malaspinas et al 2012;Mathieson and McVean 2013). However, even the simplest case-the dynamics of two alternative alleles at a single genetic locus independent of all other loci-presents a number of statistical challenges that have not been resolved.…”

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Identifying Signatures of Selection in Genetic Time Series

2014

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Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time. Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding problem with increasing relevance to modern data sets. Even in the idealized situation when the sampled locus is independent of all other loci, this problem is difficult to solve, especially when the size of the population from which the samples are drawn is unknown. A standard x 2 -based likelihood-ratio test was previously proposed to address this problem. Here we show that the x 2 -test of selection substantially underestimates the probability of type I error, leading to more false positives than indicated by its P-value, especially at stringent P-values. We introduce two methods to correct this bias. The empirical likelihood-ratio test (ELRT) rejects neutrality when the likelihoodratio statistic falls in the tail of the empirical distribution obtained under the most likely neutral population size. The frequency increment test (FIT) rejects neutrality if the distribution of normalized allele-frequency increments exhibits a mean that deviates significantly from zero. We characterize the statistical power of these two tests for selection, and we apply them to three experimental data sets. We demonstrate that both ELRT and FIT have power to detect selection in practical parameter regimes, such as those encountered in microbial evolution experiments. Our analysis applies to a single diallelic locus, assumed independent of all other loci, which is most relevant to full-genome selection scans in sexual organisms, and also to evolution experiments in asexual organisms as long as clonal interference is weak. Different techniques will be required to detect selection in time series of cosegregating linked loci. P OPULATION geneticists typically seek to understand the forces responsible for patterns observed in contemporaneous samples of genetic data, such as the nucleotide differences fixed between species, polymorphisms within populations, and the structure of linkage disequilibrium. Recently, however, there has been a rapid increase in the availability of dynamic data, where the frequencies of segregating alleles in an evolving population are monitored through time, both in laboratory experiments (Hegreness et al. 2006;Bollback and Huelsenbeck 2007;Barrick et al. 2009;Lang et al. 2011;Orozco-terWengel et al. 2012;Lang et al. 2013) and in natural populations (Barrett et al. 2008;Reid et al. 2011;Denef and Banfield 2012;Winters et al. 2012;Daniels et al. 2013;Maldarelli et al. 2013; Pennings et al. 2013). One important question is whether the changes in allele frequencies observed in such data are the result of natural selection or are simply consequences of genetic drift or sampling noise. In principle, it seems that dynamic data should provide researchers with more power to detect and quantify selective forces while avoiding the assumptions of stationarity that are required...

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Identifying Signatures of Selection in Genetic Time Series

2014

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“…The mutation in GYS1 might thus have undergone selection in the past, but the relaxed constraints prevailing today, including a limited population size, might ultimately lead to the disappearance of this allele in this breed (McCoy et al 2014). It is noteworthy that in such cases of fluctuating selection, ancient DNA can help recover full time series of allele frequencies (Ludwig et al 2015) and better characterize the dynamics of underlying selective regimes (Malaspinas et al 2012;Schraiber et al 2016).…”

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The Evolutionary Origin and Genetic Makeup of Domestic Horses

et al. 2016

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The horse was domesticated only 5.5 KYA, thousands of years after dogs, cattle, pigs, sheep, and goats. The horse nonetheless represents the domestic animal that most impacted human history; providing us with rapid transportation, which has considerably changed the speed and magnitude of the circulation of goods and people, as well as their cultures and diseases. By revolutionizing warfare and agriculture, horses also deeply influenced the politico-economic trajectory of human societies. Reciprocally, human activities have circled back on the recent evolution of the horse, by creating hundreds of domestic breeds through selective programs, while leading all wild populations to near extinction. Despite being tightly associated with humans, several aspects in the evolution of the domestic horse remain controversial. Here, we review recent advances in comparative genomics and paleogenomics that helped advance our understanding of the genetic foundation of domestic horses.

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“…They chose to use a uniform prior on the initial frequency; however, in truth the initial allele frequency is dictated by the fact that the allele at some point arose as a new mutation. Using this information, Malaspinas et al (2012) developed a method that also infers allele age. They also extended the selection model of Bollback et al (2008) (2014) is ideally suited to experimental evolution studies because they work in a strong selection, weak drift limit that is common in evolving microbial populations.…”

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“…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.…”

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Bayesian Inference of Natural Selection from Allele Frequency Time Series

2016

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The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We developed a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in nonequilibrium populations. We introduce a novel path augmentation approach, in which we use Markov chain Monte Carlo to integrate over the space of allele frequency trajectories consistent with the observed data. Using simulations, we show that this approach has good power to estimate selection coefficients and allele age. Moreover, when applying our approach to data on horse coat color, we find that ignoring a relevant demographic history can significantly bias the results of inference. Our approach is made available in a C++ software package.KEYWORDS Bayesian inference; diffusion theory; natural selection; path augmentation T HE ability to obtain high-quality genetic data from ancient samples is revolutionizing the way that we understand the evolutionary history of populations. One of the most powerful applications of ancient DNA (aDNA) is to study the action of natural selection. While methods making use of only modern DNA sequences have successfully identified loci evolving subject to natural selection (Nielsen et al. 2005;Voight et al. 2006;Pickrell et al. 2009), they are inherently limited because they look indirectly for selection, finding its signature in nearby neutral variation. In contrast, by sequencing ancient individuals, it is possible to directly track the change in allele frequency that is characteristic of the action of natural selection. This approach has been exploited recently, using whole-genome data to identify candidate loci under selection in European humans (Mathieson et al. 2015).To infer the action of natural selection rigorously, several methods have been developed to explicitly fit a population genetic model to a time series of allele frequencies obtained via aDNA. Initially, Bollback et al. (2008) extended an approach devised by Williamson and Slatkin (1999) to estimate the population-scaled selection coefficient, a ¼ 2N e s; along with the effective size, N e : To incorporate natural selection, Bollback et al. (2008) used the continuous diffusion approximation to the discrete Wright-Fisher model. This required them to use numerical techniques to solve the partial differential equation (PDE) associated with transition densities of the diffusion approximation to calculate the probabilities of the population allele frequencies at each time point. Ludwig et al. (2009) obtained an aDNA time series from six coatcolor-related loci in horses and applied the method of Bollback et al. (2008) to find that two of the...

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Estimating Allele Age and Selection Coefficient from Time-Serial Data

Cited by 151 publications

References 28 publications

Identifying Signatures of Selection in Genetic Time Series

Identifying Signatures of Selection in Genetic Time Series

The Evolutionary Origin and Genetic Makeup of Domestic Horses

Bayesian Inference of Natural Selection from Allele Frequency Time Series

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