Predicting the topography of fitness landscapes from the structure of genotype-phenotype maps.

Ruggedness-the prevalence of fitness peaks-and navigability-the existence of fitness-increasing paths to a target-are key factors affecting evolution on fitness landscapes. Here, we analyze these properties in landscapes that inherit biophysically grounded genotype-phenotype (GP) maps. By assuming a random phenotype-fitness assignment as a baseline, the structure of the GP maps is included without imposing further fitness correlations. We show analytically that the expected ruggedness can be predicted from two quantities: the sizes of neutral components (NCs)-mutationally connected genotype sets with the same phenotype-and their evolvabilities, defined as the number of distinct phenotypes among the NC's mutational neighbors. Other features-such as robustness-influence ruggedness only indirectly via correlations with evolvability. Numerical results across diverse GP maps confirm that NC size and evolvability alone suffice to predict both the mean prevalence and heights of peaks. These calculations also provide new insights: Under random phenotype-fitness assignment, peaks arising from high-evolvability NCs have higher expected fitness than those from low-evolvability NCs. Thus, when evolvability correlates positively with NC size, the formation of large low-fitness peaks is impeded. We further derive an approximate scaling law for the minimal average evolvability required for navigability. Our framework applies broadly across GP maps, providing general insight into when and why fitness landscapes are expected to be rugged or navigable.