Analysis of statistical correlations between properties of adaptive walks in fitness landscapes

The fitness landscape metaphor has been central in our way of thinking about adaptation.
In this scenario, adaptive walks are an idealized dynamics that mimics the uphill movement of an evolving population towards a fitness peak of the landscape.
Recent works in experimental evolution have demonstrated that the constraints imposed by epistasis are responsible for reducing the number of accessible mutational pathways towards fitness peaks.
Here we exhaustively analyze the statistical properties of adaptive walks for two empirical fitness landscapes and for theoretical NK landscapes.
Some general scenario can be drawn from our simulation study.
Regardless the dynamics, we observe that the shortest paths are more regularly used.
Although the accessibility of a given fitness peak is reasonably correlated to the number of monotonic pathways towards it, the two quantities are not exactly proportional.
A negative correlation predictability and mean path divergence is established, and so with the decrease of the number of effective mutational pathways ensues
the convergence of the attraction basin of fitness peaks.
On the other hand, other features are not conserved among fitness landscapes, such as the relationship between accessibility and predictability.