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Inferring Phenotypic Trait Evolution on Large Trees With Many Incomplete Measurements

journal contribution
posted on 16.09.2020 by Gabriel Hassler, Max R. Tolkoff, William L. Allen, Lam Si Tung Ho, Philippe Lemey, Marc A. Suchard

Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the taxa to avoid spurious inference. An additional challenge arises as obtaining a full suite of measurements becomes increasingly difficult with increasing taxa. This generally necessitates data imputation or integration, and existing control techniques typically scale poorly as the number of taxa increases. We propose an inference technique that integrates out missing measurements analytically and scales linearly with the number of taxa by using a post-order traversal algorithm under a multivariate Brownian diffusion (MBD) model to characterize trait evolution. We further exploit this technique to extend the MBD model to account for sampling error or nonheritable residual variance. We test these methods to examine mammalian life history traits, prokaryotic genomic and phenotypic traits, and HIV infection traits. We find computational efficiency increases that top two orders-of-magnitude over current best practices. While we focus on the utility of this algorithm in phylogenetic comparative methods, our approach generalizes to solve long-standing challenges in computing the likelihood for matrix-normal and multivariate normal distributions with missing data at scale. Supplementary materials for this article are available online.


This work was partially supported by NIH funding: T32-GM008185 and T32-HG002536 and grants R01 AI107034 and U19 AI135995; NSERC Discovery under grant RGPIN-2018-05447 and Launch Supplement DGECR-2018-00181; the Artic Network via the Wellcome Trust under project 206298/Z/17/Z; the KU Leuven Special Research Fund (“Bijzonder Onderzoeksfonds”) under grant OT/14/115; the Research Foundation—Flanders (“Fonds voor Wetenschappelijk Onderzoek—Vlaanderen”) under grants G066215N, G0D5117N and G0B9317N; the NSF under grant DMS 1264153; the European Research Council via the European Union’s Horizon 2020 Research and Innovation Programme under grant no. 725422-ReservoirDOCS; startup funds from Dalhousie University and the Canada Research Chairs Program; and the UCLA Dissertation Year Fellowship.