Architecture-dependent Effects of Trade-offs on Evolutionary Navigability and Epistasis

Abstract

The structure of the genotype-phenotype map plays a central role in determining how populations move through fitness landscapes, yet less is known about how this structure interacts with environmental constraints and fitness trade-offs. Here, we study evolution on a tunable multilayer genotype-phenotype map in which binary genotypes are transformed through successive feed-forward layers before being evaluated by phenotype-level fitness functions. We explicitly model the phenotype to fitness transformation in order to compare an emergent trade-off fitness with a no-trade-off control. We explore different map architecture as models of more and less complex genotype-phenotype relationships by tuning the genotype length and number of layers. We find that ruggedness and navigability have a complex, architecture-dependent relationship. Landscapes with few local maxima can still have low navigability for wide and shallow maps, and navigability is high even at mean values of ruggedness for wide and deep maps. Trade-offs increase navigability in wide and shallow maps, while their effect is muted in other architectures. The effect of trade-offs on epistasis depends on evolutionary history. While trade-offs change which mutational neighborhoods are sampled by evolution, the background degree of epistatic interactions is set by map architecture. Finally, we use our framework to investigate micro-evolution of high-fitness populations and show that temporal covariance in allele-frequency changes can arise from the internal structure of a rugged genotype-phenotype map, producing signatures that resemble short-term alternating selection.