Breaking the sticks: a hierarchical change-point model for estimating ontogenetic shifts with stable isotope data

Authors

  • Matthieu Authier,

    Corresponding author
    1. Centre d’Études Biologiques de Chizé, UPR 1934 du CNRS, 79 360 Villiers-en-Bois, France
    2. École Doctorale Sciences pour l'Environnement Gay Lussac-Université de Poitiers, Poitiers, France
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  • Céline Martin,

    1. Institut des Sciences de l'Evolution, UMR 5554 du CNRS, Place E.Bataillon Bât. 22/3e/CC061, 34095 Montpellier Cedex 5, France
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  • Aurore Ponchon,

    1. Institut des Sciences de l'Evolution, UMR 5554 du CNRS, Place E.Bataillon Bât. 22/3e/CC061, 34095 Montpellier Cedex 5, France
    2. Centre d’Écologie Fonctionnelle et Évolutive, UMR 5175 du CNRS, 1919 Route de Mende, F34293 Montpellier Cedex 5, France
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  • Stephanie Steelandt,

    1. Institut des Sciences de l'Evolution, UMR 5554 du CNRS, Place E.Bataillon Bât. 22/3e/CC061, 34095 Montpellier Cedex 5, France
    2. Centre d’Études Nordiques, Université de Laval, 2405 rue de la Terrasse, Québec G1V0A6, Canada
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  • Ilham Bentaleb,

    1. Institut des Sciences de l'Evolution, UMR 5554 du CNRS, Place E.Bataillon Bât. 22/3e/CC061, 34095 Montpellier Cedex 5, France
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  • Christophe Guinet

    1. Centre d’Études Biologiques de Chizé, UPR 1934 du CNRS, 79 360 Villiers-en-Bois, France
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Correspondence author. E-mail: authier@cebc.cnrs.fr

Summary

1. Stable isotopes are increasingly used in ecology to investigate ontogenetic shifts in foraging habitat (via δ13C) and in trophic level (via δ15N). These shifts are in essence an individual-level phenomenon, requiring repeated measures throughout the life of individuals, i.e. longitudinal data. Longitudinal data require in turn specifying an appropriate covariance structure. Here we present a hierarchical model to jointly investigate individual ontogenetic shifts in δ13C and δ15N values.

2. In a Bayesian framework, we used a Cholesky decomposition for estimating a moderately-sized covariance matrix, thereby directly estimating correlations between parameters describing time-series of isotopic measurements. We offer guidelines on how to select the covariance structure.

3. The approach is illustrated with a hierarchical change-point (or broken stick) model applied to a data set collected on Southern Elephant Seals, Mirounga leonina. Ontogenetic shifts in foraging habitat, following a juvenile and variable stage, were detected and interpreted as fidelity to a foraging strategy; while ontogenetic shifts in trophic level were more likely the result of complete independence from maternal resources followed by a gradual increase in trophic level as seals aged.

4. Specifying both an appropriate covariance and mean structure enabled us to draw strong inferences on the ecology of an elusive marine predator, and has wide applicability for isotopic ecology provided repeated isotopic measurements are available.

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