Inverted topologies in sequential fitness landscapes enable evolutionary control

Adaptive populations rarely evolve in a static environment. Therefore, understanding and ultimately controlling the evolution of a population requires consideration of fluctuating selective pressures. The fitness landscape metaphor has long been used as a tool for representing the selective pressures a given environment imposes on a population. Much work has already been done to understand the dynamics of evolution on a single fitness landscape. More recently, evolution on fluctuating or sequentially applied landscapes has come to the fore of evolutionary biology. As more empirical landscapes are described, metrics for describing salient features of paired landscapes will have uses for understanding likely evolutionary dynamics. Currently, Pearson correlation coefficient and collateral sensitivity likelihoods are used to quantify topological relatedness or dissimilarity of a pair of landscapes. Here, we introduce the edge flip fraction, a new metric for comparing landscapes, which quantifies changes in the directionality of evolution between pairs of fitness landscapes. We demonstrate that the edge flip fraction captures topological differences that traditional metrics may overlook. By applying this metric to both empirical and synthetic fitness landscapes, we show that it partially predicts the collateral sensitivity likelihoods and can inform the optimality of drug sequences. We show that optimal drug sequences that keep populations within lower fitness regions require shifts in evolutionary directions, which are quantified by the edge flip fraction. Edge flip fraction complements existing measures and may help researchers understand how populations evolve under changing environmental conditions.