How large is large: estimating ecologically meaningful isotopic differences in observational studies of wild animals Matthieu Authier 1,2 *, Anne-Cécile Dragon 1,3 , Yves Cherel 1 and Christophe Guinet 1 1 Centre d’Études Biologiques de Chizé, UPR 1934 du CNRS, 79 360, Villiers-en-Bois, France 2 Centre d’Écologie Fonctionnelle et Évolutive, UMR 5175 du CNRS, 1919 Route de Mende, 34 293 Montpellier Cedex 5, France 3 LOCEAN, UPMC, 4 Place Jussieu, 75 252 Paris Cedex 05, France RATIONALE: In ecological studies of wildlife movements and foraging, bio-logging and isotopic data are routinely collected and increasingly analyzed in tandem. Such analyses have two shortcomings: (1) small sample size linked with the number of telemetric tags that can be deployed, and (2) the observational nature of isotopic gradients. Wildlife ecologists are thus put in a statistical conundrum known as the small n, large p problem. METHODS: Using shrinkage regression, which directly addresses the issue of accurately estimating effects from sparse data, we studied what counts as a biologically meaningful isotopic difference (a prerequisite to delineate isoscapes) in the southern elephant seal (Mirounga leonina), a large and elusive marine predator. RESULTS: Seals foraging in Antarctic waters had a lower carbon isotopic value (by  2%) than seals foraging either in the interfrontal zone or on the Kerguelen Plateau. The latter two foraging strategies were indistinguishable on the sole basis of d 13 C values with our data. CONCLUSIONS: Shrinkage regression is a conservative statistical technique that has wide applicability in isotopic ecology to help separate robust biological signals from noise. Copyright © 2012 John Wiley & Sons, Ltd. A popular application of stable isotopes in ecology is as natural ’tags’ to study the movement of animals between habitats. [1,2] The rationale for this approach follows from the premise that "in equilibrium situations, animal tissues reflect the isotopic structure of local food webs". [3] In other words, the foraging behaviour of consumers is investigated indirectly by taking advantage of naturally occurring differences in stable isotope composition between ecosystems. However, this reliance on natural gradients also means that stable isotopic data collected from wild animals are more observational than experimental. [4] Reviews on the use of stable isotopes in wildlife ecology have stressed some vexing problems linked to observational data, for example the accurate estimation of discrimination factors. [5,6] Because stable isotopes provide indirect evidence, their analysis requires both substantial biological knowledge and an adequate statistical analysis to account for relevant sources of variations. Hobson et al. [3] stated three major conditions for an accurate interpretation of wildlife move- ments: (1) animals must move between isotopically distinct food webs, (2) bias between the stable isotopic values of prey and consumer are accounted for (that is, discrimi- nation factors are accurately known), and (3) the isotopic turnover of the sampled tissue is known. When experi- ments cannot be performed under controlled conditions, requirements (2) and (3) may be quite difficult to meet for wildlife ecologists, more so when studying rare or cryptic or endangered species; the kind of situation where the use of stable isotopes is especially attractive. Even the first requirement of Hobson et al. [3] may be challen- ging. While for terrestrial ecosystems geographical regions with known differences in isotopic composition, or isoscapes, have been mapped (e.g. [7,8] ), there are comparatively fewer data to compile such maps for marine ecosystems. [2,9–11] Ecological knowledge of marine organisms has, however, greatly increased with the use of stable isotopes. [12] In practice, marine biologists may have to estimate the isotopic signature of oceanic basins, fractionation factors or tissue turnover rates from limited data given the difficulties associated with sampling the world’s oceans. Sampling preys in the marine environment may also be challenging for deep-diving predators. In general, we can expect the stable isotope values of animal tissues to be affected by many sources of variations, each of small magnitude and of different signs. The expected trend of the sum of all these variations is hard to predict, and there is no strong a priori reason that it should be exactly zero, although its magnitude may be small. All the aforementioned difficulties may put marine biologists into a situation where data (n) are scarce, yet many parameters (p) have to be accurately estimated: a small n, large p setting. Our aim is to illustrate with an example on a large marine predator, the southern elephant seal (Mirounga leonina), how to conduct inferences with stable isotopes in a small n, large p situation. We want to bring forward to a greater audience some statistical tools that may help wildlife ecologists to meet the first and, to a lesser extent, the third requirements of Hobson et al.: [3] how to estimate isoscapes * Correspondence to: M. Authier, Centre d’ Écologie Fonctionnelle et Évolutive, UMR 5175, du CNRS 1919 Route de Mende, 34 293 Montpellier Cedex 5, France. E-mail: authierm@gmail.com Copyright © 2012 John Wiley & Sons, Ltd. Rapid Commun. Mass Spectrom. 2012, 26, 2657–2664 Research Article Received: 4 July 2012 Revised: 30 August 2012 Accepted: 31 August 2012 Published online in Wiley Online Library Rapid Commun. Mass Spectrom. 2012, 26, 2657–2664 (wileyonlinelibrary.com) DOI: 10.1002/rcm.6389 2657