  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.
