A general model of the functional constraints on the rate and direction of phenotypic evolution is developed using Arnold’s decomposition of the multivariate breeder’s equation. The important feature of the model is the F matrix of functional performance coefficients. The structure of the F matrix constrains the rate and direction of phenotypic evolution, which constraint is independent of that determined by the G matrix. The off-diagonal elements of the F-transpose-F matrix summarize trade-offs and facilitations among performance traits. The off-diagonal elements of the F-F-transpose matrix reflect the functional correlation between two morpho-physiological (m-p) traits and an eigenanalysis of this matrix provides a novel definition of functional integration. Simulation data is used to show how the general model biases m-p trait evolution and the structure of both the G matrix and the among-species covariance matrix.