Many-to-Many Mapping of Phenotype to Performance: An Extension of the F-Matrix for Studying Functional Complexity

Performance capacity influences ecology, behavior and fitness, and is determined by the underlying phenotype. The phenotype-performance relationship can influence the evolutionary trajectory of an organism. Several types of phenotype-performance relationships have been described, including one-to-one relationships between a single phenotypic trait and performance measure, tradeoffs and facilitations between a phenotypic trait and multiple performance measures, and redundancies between multiple phenotypic traits and a single performance measure. The F-matrix is an intraspecific matrix of measures of statistical association between phenotype and performance that is used to quantify these relationships. We extend the F-matrix in two ways. First, we use the F-matrix to describe how the different phenotype-performance relationships occur simultaneously and interact in functional systems, a phenomenon we call many-to-many mapping. Second, we develop methods to compare F-matrices among species and compare phenotype-performance relationships at microevolutionary and macroevolutionary levels. We demonstrate the expanded F-matrix approach with a dataset of eight phrynosomatine lizard species, including six phenotypic traits and two measures of locomotor performance. Our results suggest that all types of relationships occur in this system and that phenotypic traits involved in trade-offs are more functionally constrained and tend evolve slower interspecifically than those involved in facilitations or one-to-one relationships.