Many-to-many mapping: A simulation study of how the number of traits and tasks affect the evolution of form and function.

Many-to-many mapping of form-to-function posits that multiple morphological and physiological traits affect the performance of multiple tasks in an organism, and that redundancy and multitasking occur simultaneously to shape the evolution of an organism's phenotype. Many-to-many mapping is expected to be ubiquitous in nature, yet little is known about how it influences the evolution of organismal phenotype. The F-matrix is a powerful tool to study these issues because it describes how multiple traits affect multiple tasks. We undertook a simulation study using the F-matrix to test how the number of traits and the number of tasks affect trait integration and evolvability, as well as the relationships among tasks. We found that as the number of traits and/or tasks increases, the relationships between the tasks and the integration between the traits become weaker, and that the evolvability of the traits increases, all resulting in a system that is freer to evolve. We also found that as the number of traits increases, performance tradeoffs tend to become weaker, but only to a point. Our work shows that it is important to consider not only multiple traits, but also the multitude of tasks that those traits carry out when studying form-function relationships. We suggest that evolution of these relationships follows functional lines of least resistance, which are less defined in more complex systems, resulting in a mechanism for diversification.