A consistent estimator of the evolutionary rate
Journal article, 2015

We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance sigma(2). In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2).

Tree-free phylogenetic comparative

Conditioned branching process

Branching Brownian motion


Krzysztof Bartoszek

Uppsala University

Serik Sagitov

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Journal of Theoretical Biology

0022-5193 (ISSN) 1095-8541 (eISSN)

Vol. 371 69-78

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