Breaking the sticks: a hierarchical change-point model

18 1. Stable isotopes are increasingly used in ecology to investigate ontogenetic shifts 19 1 ha l-0 06 27 20 0, v er si on 1 30 S ep 2 01 1 in foraging habitat (via δ13C) and in trophic level (via δ15N). These shifts are in 20 essence an individual-level phenomenon, requiring repeated measures throughout the 21 life of individuals, that is longitudinal data. Longitudinal data require in turn 22 specifying an appropriate covariance structure. Here we present a hierarchical model 23 to jointly investigate individual ontogenetic shifts in δ13C and δ15N values. 24 2. In a Bayesian framework, we used a Cholesky decomposition for estimating a 25 moderately-sized covariance matrix, thereby directly estimating correlations between 26 parameters describing time-series of isotopic measurements. We offer guidelines on 27 how to select the covariance structure. 28 3. The approach is illustrated with a hierarchical change-point (or broken stick) model 29 applied to a data set collected on Southern Elephant Seals, Mirounga leonina. 30 Ontogenetic shifts in foraging habitat, following a juvenile and variable stage, were 31 detected and interpreted as fidelity to a foraging strategy; while ontogenetic shifts in 32 trophic level were more likely the result of complete independence from maternal 33 resources followed by a gradual increase in trophic level as seals aged. 34 4. Specifying both an appropriate covariance and mean structure enabled us to draw 35 strong inferences on the ecology of an elusive marine predator, and has wide 36 applicability for isotopic ecology provided repeated isotopic measurements are 37 available. 38