  The fitness landscape defines the relationship between genotypes and fitness
in a given environment, and underlies fundamental quantities such as the
distribution of selection coefficient, or the magnitude and type of epistasis.
A better understanding of variation of landscape structure across species and
environments is thus necessary to understand and predict how populations will
adapt. An increasing number of experiments investigates the properties of
fitness landscapes by identifying mutations, constructing genotypes with
combinations of these mutations, and measuring the fitness of these genotypes.
Yet these empirical landscapes represent a very small sample of the vast space
of all possible genotypes, and this sample is often biased by the protocol used
to identify mutations. Here we develop a rigorous statistical framework based
on Approximate Bayesian Computation to address these concerns, and use this
flexible framework to fit a broad class of phenotypic fitness models (including
Fisher's model) to 26 empirical landscapes representing 9 diverse biological
systems. In spite of uncertainty due to the small size of most published
empirical landscapes, the inferred landscapes have similar structure in similar
biological systems. Surprisingly, goodness of fit tests reveal that this class
of phenotypic models, which has been successful so far in interpreting
experimental data, is a plausible model in only 3 out of 9 biological systems.
More precisely, although Fisher's model was able to explain several statistical
properties of the landscapes - including mean and standard deviation of
selection and epistasis coefficients -, it was often unable to explain the full
structure of fitness landscapes.
