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Keywords:

  • comparative method;
  • cross-validation;
  • evolutionary models;
  • graph theory;
  • Ornstein–Uhlenbeck process;
  • phylogenetic eigenvectors;
  • phylogenetic modelling;
  • phylogenetic signal;
  • statistical modelling;
  • trait values

Summary

  1. Phylogenetic signals are the legacy related to evolutionary processes shaping trait variation among species. Biologists can use these signals to tackle questions related to the evolutionary processes underlying trait evolution, estimate the ancestral state of a trait and predict unknown trait values from those of related species (i.e. ‘phylogenetic modelling’). Approaches to model phylogenetic signals rely on quantitative descriptors of the structures representing the consequences of evolution on trait differences among species.
  2. Here, we propose a novel framework to model phylogenetic signals: Phylogenetic Eigenvectors Maps (PEM). PEM are a set of eigenfunctions obtained from the structure of a phylogenetic graph, which can be a standard phylogenetic tree or a phylogenetic tree with added reticulations. These eigenfunctions depict a set of potential patterns of phenotype variation among species from the structure of the phylogenetic graph. A subset of eigenfunctions from a PEM is selected for the purpose of predicting the phenotypic values of traits for species that are represented in a tree, but for which trait data are otherwise lacking. This paper introduces a comprehensive view and the computational details of the PEM framework (with calculation examples), a simulation study to demonstrate the ability of PEM to predict trait values and four real data examples of the use of the framework.
  3. Simulation results show that PEM are robust in representing phylogenetic signal and in estimating trait values.
  4. The method also performed well when applied to the real-world data: prediction coefficients were high (0·76–0·88), and no notable model biases were found.
  5. Phylogenetic modelling using PEM is shown to be a useful methodological asset to disciplines such as ecology, ecophysiology, ecotoxicology, pharmaceutical botany, among others, which can benefit from estimating trait values that are laborious and often expensive to obtain.