Occurrences of reciprocal sign epistasis in single- and multi-peaked theoretical fitness landscapes

Fitness landscapes help model the theory of adaption. We consider genetic fitness landscapes abstractly as acyclic orientations of Boolean lattices under the assumptions laid out by Crona et al. We focus on occurrences of reciprocal sign epistasis (RSE) on the faces of the lattice. We computationally study which combinations of numbers of peaks and RSE faces are possible, and we determine limits on occurrences of RSE faces in both single-peaked and multi-peaked landscapes. Our main theorem extends a theorem of Poelwijk to show that any landscape with k peaks contains at least k - 1 RSE faces.