Open Access
December 2012 Phenotypic evolution studied by layered stochastic differential equations
Trond Reitan, Tore Schweder, Jorijntje Henderiks
Ann. Appl. Stat. 6(4): 1531-1551 (December 2012). DOI: 10.1214/12-AOAS559


Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure. The data consists of size measurements of fossilized calcite platelets (coccoliths) that cover the living cell, found in deep-sea sediment cores from six sites in the world oceans and dated to irregular points in time. To accommodate biological theory of populations tracking their fitness optima, and to allow potentially interpretable correlations in time and space, the model framework allows for an upper layer of partially observed site-specific population means, a layer of site-specific theoretical fitness optima and a bottom layer representing environmental and ecological processes. While the modeled process has many components, it is Gaussian and analytically tractable. A total of 710 model specifications within this framework are compared and inference is drawn with respect to model structure, evolutionary speed and the effect of global temperature.


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Trond Reitan. Tore Schweder. Jorijntje Henderiks. "Phenotypic evolution studied by layered stochastic differential equations." Ann. Appl. Stat. 6 (4) 1531 - 1551, December 2012.


Published: December 2012
First available in Project Euclid: 27 December 2012

zbMATH: 1263.92036
MathSciNet: MR3058674
Digital Object Identifier: 10.1214/12-AOAS559

Keywords: Causal model , coccolith , fossil data , latent processes , Ornstein–Uhlenbeck process , time series

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.6 • No. 4 • December 2012
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