Phylogenetic reconstruction of trait summary statistics and disparity dynamics

Authors

Didier, G.

Abstract

Summary statistics are essential tools for understanding the overall behaviour of a collection of measurements. In a phylogenetic context, however, trait measurements are generally observed only for extant taxa and, when available, fossil taxa, while the questions of interest concern the evolution of the trait through time rather than only its static properties among the observed taxa. To investigate how the empirical mean and variance of a trait evolve through time, we derive, under Brownian evolution, their conditional distributions given trait values observed at extant or fossil tips. This provides reconstructed trajectories of both summary statistics together with a direct quantification of their uncertainty. Among these two summaries, the empirical variance is of particular interest as a measure of past phenotypic disparity. To assess reconstructed disparity, we define the disparity level at any time as the probability that a value drawn from the conditional distribution of the empirical variance exceeds an independent value drawn from the corresponding unconditional Brownian distribution. As a dimensionless quantity with a common interpretation, the disparity level enables comparisons across times, clades, phylogenies, and datasets. Applications to cetacean body length reveal contrasting trajectories among major subclades and suggest that much of the disparity reconstructed for the complete clade is associated with differences among these subclades. An analysis of body mass in living and fossil mammaliaforms identifies low disparity relative to the Brownian reference through most of the Mesozoic, followed by a sustained expansion around and after the K--Pg boundary. These patterns are broadly consistent with previous analyses of the same datasets, while providing a direct reconstruction of changes in the location and spread of trait distributions through time. The methods are implemented in the R package PastMoments.

Preprint server: bioRxiv
The authors list and abstract were imported from bioRxiv on 21 Aug 2026.

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