Evolutionary constraints in fitness landscapes

In the last years, several genotypic fitness landscapes-combinations of a small number of mutations-have been experimentally resolved. To learn about the general properties of "real" fitness landscapes, it is key to characterize these experimental landscapes via simple measures of their structure, related to evolutionary features. Some of the most relevant measures are based on the selectively acessible paths and their properties. In this paper, we present some measures of evolutionary constraints based on (i) the similarity between accessible paths and (ii) the abundance and characteristics of "chains" of obligatory mutations, that are paths going through genotypes with a single fitter neighbor. These measures have a clear evolutionary interpretation. Furthermore, we show that chains are only weakly correlated to classical measures of epistasis. In fact, some of these measures of constraint are non-monotonic in the amount of epistatic interactions, but have instead a maximum for intermediate values. Finally, we show how these measures shed light on evolutionary constraints and predictability in experimentally resolved landscapes.