  Genotypic fitness landscapes are constructed by assessing the fitness of all
possible combinations of a given number of mutations. In the last years,
several experimental fitness landscapes have been completely resolved. As
fitness landscapes are high-dimensional, their characterization relies on
simple measures of their structure, which can be used as statistics in
empirical applications. Here we propose two new sets of measures that
explicitly capture two relevant features of fitness landscapes: epistasis and
constraints. The first set contains new measures for epistasis based on the
correlation of fitness effects of mutations. They have a natural
interpretation, capture well the interaction between mutations, can be obtained
analytically for most landscape models and can therefore be used to
discriminate between different models. The second set contains measures of
evolutionary constraints based on "chains" of forced mutations along
fitness-increasing paths. Some of these measures are non-monotonic in the
amount of epistatic interactions, but have instead a maximum for intermediate
values. We further characterize the relationships of these measures to the ones
that were previous proposed (e.g. number of peaks, roughness/slope, fraction of
non-additive components, etc). Finally, we show how these measures can help
uncovering the amount and the nature of epistatic interactions in two
experimental landscapes.
