Fundamental restriction on epistasis detection and fitness valleys in virus evolution

Probabilistic prognosis of virus evolution, vital for the design of effective vaccines and antiviral drugs, requires the knowledge of adaptive landscape including epistatic interactions. Although epistatic interactions can, in principle, be inferred from abundant sequencing data, fundamental limitations on their detection imposed by genetic linkage between evolving sites obscure their signature and require averaging over many independent populations. We probe the limits of detection based on pairwise correlations conditioned on the state of a third site on synthetic sequences evolved in a Monte Carlo algorithm with known epistatic pairs. Results demonstrate that the detection error decreases with the number of independent populations and increases with the sequence length. The accuracy is enhanced by moderate recombination and is maximal, when epistasis magnitude approaches the point of full compensation. The method is applied to several thousands of sequences of SARS-CoV-2 sampled in three different ways. Results obtained under equal sampling from world regions imply the existence of fitness valleys connecting groups of viral variants.