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Background  Understanding the genotype-phenotype map is fundamental to our understanding of genomes. Genes do not function independently, but rather as part of networks or pathways. In the case of metabolic pathways, flux through the pathway is an important next layer of biological organization up from the individual gene or protein. Flux control in metabolic pathways, reflecting the importance of mutation to individual enzyme genes, may be evolutionarily variable due to the role of mutation-selection-drift balance. The evolutionary stability of rate limiting steps and the patterns of inter-molecular co-evolution were evaluated in a simulated pathway with a system out of equilibrium due to fluctuating selection, population size, or positive directional selection, to contrast with those under stabilizing selection.    Results  Depending upon the underlying population genetic regime, fluctuating population size was found to increase the evolutionary stability of rate limiting steps in some scenarios. This result was linked to patterns of local adaptation of the population. Further, during positive directional selection, as with more complex mutational scenarios, an increase in the observation of inter-molecular co-evolution was observed.    Conclusions  Differences in patterns of evolution when systems are in and out of equilibrium, including during positive directional selection may lead to predictable differences in observed patterns for divergent evolutionary scenarios. In particular, this result might be harnessed to detect differences between compensatory processes and directional processes at the pathway level based upon evolutionary observations in individual proteins. Detecting functional shifts in pathways reflects an important milestone in predicting when changes in genotypes result in changes in phenotypes.    Electronic supplementary material  The online version of this article (doi:10.1186/s12862-017-0962-7) contains supplementary material, which is available to authorized users.

Characterizing the roles of changing population size and selection on the evolution of flux control in metabolic pathways