A probabilistic and phylogenetic principal component analysis for modelling high-dimensional trait evolution

Given the ever-increasing availability of highly detailed phenotypes, modelling trait evolution in a multivariate framework is becoming a challenging task. Current phylogenetic comparative methods often struggle with high-dimensional datasets because they suffer computational limitations and interpretability. Here, we propose a maximum likelihood-based approach called Probabilistic and Phylogenetic Principal Components Analysis (P3CA) to circumvent current limitations. This approach is based on a continuous latent variable model, whereby observed traits are explained by a smaller number of unobserved variables that evolve according to a given evolutionary model. We implement the approach under Pagels lambda model using an Expectation-Maximisation algorithm that makes it computationally efficient and allows missing values. Using simulations, we demonstrate that evolutionary parameters are accurately estimated, regardless of phylogenetic signal, the number of traits or the proportion of missing values. The reconstruction of the reduced space is more accurate than the one obtained using other dimensionality reduction approaches, such as phylogenetic and conventional PCA. Likewise, the estimated values for missing data are more accurate than those obtained using current phylogenetic data imputation approaches. We illustrate the approach on a 3D geometric morphometric dataset describing Crocodyliformes skull shapes and containing around 4% of missing data. Our P3CA method unlocks the possibility to analyse and more easily interpret the large-scale multivariate datasets generated in recent decades within a phylogenetic comparative framework.