SUMMARY: The phylogenetic signal, frequently used to identify signatures of adaptive evolution or important associations between genes and phenotypes, measures the tendency for recently diverged species to resemble each other more than distantly related species. An example of such a measure is the δ statistic, which uses Shannon entropy to measure the degree of phylogenetic signal between a categorical trait and a phylogeny. In this study, we refined this statistic to account for tree uncertainty, resulting in more accurate assessments of phylogenetic associations. In addition, we provided a more accessible and computationally efficient implementation of the δ statistic that will facilitate its use by the evolutionary community. AVAILABILITY AND IMPLEMENTATION: github.com/diogo-s-ribeiro/delta-statistic.

MOTIVATION: Determining whether a trait and phylogeny share some degree of phylogenetic signal is a flagship goal in evolutionary biology. Signatures of phylogenetic signal can assist the resolution of a broad range of evolutionary questions regarding the tempo and mode of phenotypic evolution. However, despite the considerable number of strategies to measure it, few and limited approaches exist for categorical traits. Here, we used the concept of Shannon entropy and propose the δ statistic for evaluating the degree of phylogenetic signal between a phylogeny and categorical traits. RESULTS: We validated δ as a measure of phylogenetic signal: the higher the δ-value the higher the degree of phylogenetic signal between a given tree and a trait. Based on simulated data we proposed a threshold-based classification test to pinpoint cases of phylogenetic signal. The assessment of the test's specificity and sensitivity suggested that the δ approach should only be applied to 20 or more species. We have further tested the performance of δ in scenarios of branch length and topology uncertainty, unbiased and biased trait evolution and trait saturation. Our results showed that δ may be applied in a wide range of phylogenetic contexts. Finally, we investigated our method in 14 360 mammalian gene trees and found that olfactory receptor genes are significantly associated with the mammalian activity patterns, a result that is congruent with expectations and experiments from the literature. Our application shows that δ can successfully detect molecular signatures of phenotypic evolution. We conclude that δ represents a useful measure of phylogenetic signal since many phenotypes can only be measured in categories. AVAILABILITY AND IMPLEMENTATION: https://github.com/mrborges23/delta_statistic. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In this work a modified version of AMUSE, called dAMUSE, is proposed. The main modification consists in increasing the dimension of the data vectors by joining delayed versions of the observed mixed signals. With the new data a matrix pencil is computed and its generalized eigendecomposition is performed as in AMUSE. We will show that in this case the output (or independent) signals are filtered versions of the source signals. Some numerical simulations using artificially mixed signals as well as biological data (RR and QT intervals of Electrocardiogram) are presented.