Inferring fitness landscapes by regression produces biased estimates of epistasis

Abstract: The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is to sample as many genotypes as possible, measure their fitnesses, and fit a statistical model of the landscape that includes additive and pairwise interactive effects between loci. Here we elucidate the pitfalls of using such regressions, by studying artificial but mathematically convenient fitness landscapes. We identify two sources of bias inherent in these regression procedures that each tends to under-estimate high fitnesses and over-estimate low fitnesses. We characterize these biases for random sampling of genotypes, as well as for samples drawn from a population under selection in the Wright-Fisher model of evolutionary dynamics. We show that common measures of epistasis, such as the number of monotonically increasing paths between ancestral and derived genotypes, the prevalence of sign epistasis, and the number of local fitness maxima, are distorted in the inferred landscape. As a result, the inferred landscape will provide systematically biased predictions for the dynamics of adaptation. We identify the same biases in a computational RNA-folding landscape, as well as in regulatory sequence binding data, treated with the same fitting procedure. Finally, we present a method that may ameliorate these biases in some cases.