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, trade-offs 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 specie...