Abstract
Linkage effects in a multi-locus population strongly influence its evolution. The models based on the traveling wave approach enable us to predict the average speed of evolution and the statistics of phylogeny. However, predicting statistically the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effects of epistasis, the interaction of gene regions contributing to phenotype, is difficult to predict theoretically and detect experimentally in sequence data. A large number of false-positive interactions arises from stochastic linkage effects and indirect interactions, which mask true epistatic interactions. Here we develop a proof-of-principle method to filter out false-positive interactions. We start by demonstrating that the averaging of haplotype frequencies over multiple independent populations is necessary but not sufficient for epistatic detection, because it still leaves high numbers of false-positive interactions. To compensate for the residual stochastic noise, we develop a three-way haplotype method isolating true interactions. The fidelity of the method is confirmed analytically and on simulated genetic sequences evolved with a known epistatic network. The method is then applied to a large sequence database of neurominidase protein of influenza A H1N1 obtained from various geographic locations to infer the epistatic network responsible for the difference between the pre-pandemic virus and the pandemic strain of 2009. These results present a simple and reliable technique to measure epistatic interactions of any sign from sequence data.
Highlights
About a century ago, it was realized that the evolution of a population is strongly affected by the fact that the fates of alleles at different loci are linked unless separated by recombination
The knowledge of topology and strength of interactions is vital for predicting the escape of viruses from drugs and immune response and their passing through fitness valleys
We start by simulating the evolution of a haploid asexual population using a Wright-Fisher process including the factors of random mutation, random genetic drift, and constant directional selection (Fig 1A) (Methods)
Summary
It was realized that the evolution of a population is strongly affected by the fact that the fates of alleles at different loci are linked unless separated by recombination. Linkage decreases the speed of adaptation and creates random associations between pairs of mutations occurring on the same branch of the ancestral tree These effects have been taken into account in early mathematical models considering two loci [6] and, more recently, in the traveling wave approach, which describes an arbitrarily large number of linked sites [7,8,9,10,11,12]. These models describe the dynamics of fitness classes and include the factors of selection, mutation, random genetic drift and recombination [13,14,15,16]. The same general approach was used to predict the statistical properties of the ancestral tree [15,16,20,21,22]
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