Robustness revisited: On the neutral evolution of centrality and localization.

This study investigates the intricate interplay among neutral landscape structure, mutation rate, recombination rate, and population dynamics in shaping evolutionary robustness. We provide a comprehensive framework that elucidates how different evolutionary forces interact to influence genotypic robustness and localization within haploid and diploid populations. We demonstrate that in haploid populations, high mutation rates relative to recombination typically drive the population toward regions of increased eigencentrality, a graph-theoretic measure of centrality which is correlated while not identical to mutational robustness. On the other hand, recombination increases the localization of the population to a smaller region of genotypic space, while high values of recombination relative to mutation can introduce shifts in distribution away from regions of high eigencentrality and toward attractors of the recombination dynamics. Diploid dynamics further complicate these interactions, showing reduced alignment with eigencentrality under both high mutation and recombination rates, with the exception of structured diploid landscapes where dynamics are still aligned with increasing eigencentrality. Our findings underscore the nuanced dependencies of evolutionary outcomes on both local and global landscape structures as well as evolutionary parameters.