Evolutionary dynamics of redundant regulatory control

Many complex regulatory processes concern tracking a constant or variable set point. Examples include temperature homeostasis, rhythmic oscillation, and the concentration of key metabolites and enzymes. Control over homeostatic or tracking phenotypes often depends on multiple, overlapping regulatory systems. In this paper, I develop a theory for the evolutionary dynamics of redundant regulatory control architecture. Prior theories analyzed the evolution of redundant control architectures by the balance between improved performance for additional redundant control weighed against the decay by germline mutation that arises in characters with overlapping function. By contrast, I argue that germline mutation is likely to be a very weak balancing force in evolutionary dynamics. Instead, I analyze the evolutionary dynamics of redundant control by a balance between the benefits of reduced tracking error and the costs of building and running the multiple control systems. In one particular mathematical model that highlights key features of evolutionary dynamics, additional redundant control reduces tracking error multiplicatively but contributes to costs additively. In that model, the performance landscape has multiple peaks of the same height, one peak for each level of redundancy and the associated optimal investment per control structure. The multipeak landscape imposes evolutionary stasis, in which control systems resist invasion by increased or decreased levels of redundancy. However, fluctuating environments likely favor a rise in redundancy over time. With greater redundancy, investment per individual control structure declines, causing a decay in the performance of each individual dimension of control. I conclude that the costs of control structures may influence regulatory architecture.