The flipping t ‐ratio test: Phylogenetically informed assessment of the Pareto theory for phenotypic evolution

An organism cannot be fully optimized for all tasks that are needed for its survival because of the existence of intrinsic trade‐offs among those tasks. It was recently proposed that an economics‐originated theory, the Pareto theory, is a general theory explaining the rules of phenotypic evolution under such trade‐offs. To date, many phenotype datasets have been argued to fit the Pareto theory based on a statistical method named the t ‐ratio test. Here, we show that this test suffers a serious defect in that general phenotype data can be wrongly concluded to fit the Pareto theory with a very high false‐positive rate and that the claim that the Pareto theory is a general theory should definitely be considered with caution. This is because the t ‐ratio test assumes that all phenotypic traits are independent of one another, but this assumption does not hold true—different traits of organisms have usually been affected by the same phylogenetic history and are thus typically not independent. We developed the flipping t ‐ratio test to accurately test the Pareto theory by considering phylogenetic background as well as artefacts that can be induced during dimensionality reduction. Using this improved method, we confirm that the phenotype data analysed in previous studies, including the well‐known Darwin's ground finch dataset, no longer support the Pareto theory. We hope that the flipping t ‐ratio test will contribute to examining which phenotype datasets truly fit the Pareto theory and understanding how diverse phenotypes evolve in natural ecosystems.