Module-selection balance in the evolution of modular organisms

The architecture of the genotype-phenotype-fitness map (GPFM) is a key determinant of evolutionary dynamics. One salient feature of biological GPFMs is variational modularity, where each mutation affects only a small subset of functional traits. Variational modularity may constrain the dynamics of trait evolution, but these constraints are not well understood. Here, we use several extensions of the Fishers geometric model with two functional traits to investigate these constrains. We find that on GPFMs with universal pleiotropy, populations evolve along the fitness gradient, which implies that the trait under stronger selection is optimized exponentially faster than the trait under weaker selection. In contrast, on modular GPFMs, populations approach a quasi-steady state that we term a "module-selection balance" where both traits improve at the same rate and their ratio remains constant. We demonstrate that the existence of a module-selection balance is robust with respect to the details of evolutionary dynamics and GPFMs themselves, as long as they are variationally modular. Our theory predicts that variationally modular organisms should exhibit stereotypical bi-phasic dynamics of genome evolution, especially in the strong clonal interference regime, and we find support for this prediction in metagenomic data from Lenskis long-term evolution experiment in bacterium Escherichia coli. We propose that module-selection balance is an inherent feature of variationally modular GPFMs, which imposes an important constraint on long-term trait evolution.