Evolutionary paths to lateralization of complex brain functions

At large, most animal brains present two mirror-symmetric sides; but closer inspection reveals a range of asymmetries (in shape and function), that seem more salient in more cognitively complex species. Sustaining symmetric, redundant neural circuitry has associated metabolic costs, but it might aid in implementing computations within noisy environments or with faulty pieces. It has been suggested that the complexity of a computational task might play a role in breaking bilaterally symmetric circuits into fully lateralized ones; yet a rigorous, mathematically grounded theory of how this mechanism might work is missing. Here we provide such a mathematical framework, starting with the simplest assumptions, but extending our results to a comprehensive range of biologically and computationally relevant scenarios. We show mathematically that only fully lateralized or bilateral solutions are relevant within our framework (dismissing configurations in which circuits are only partially engaged). We provide maps that show when each of these configurations is preferred depending on costs, contributed fitness, circuit reliability, and task complexity. We discuss evolutionary paths leading from bilateral to lateralized configurations and other possible outcomes. The implications of these results for evolution, development, and rehabilitation of damaged or aged brains is discussed. Our work constitutes a limit case that should constrain and underlie similar mappings when other aspects (aside task complexity and circuit reliability) are considered.