Marine Biology

, Volume 162, Issue 2, pp 469–478 | Cite as

Estimating continuous body size-based shifts in δ15N–δ13C space using multivariate hierarchical models

  • Jonathan C. P. ReumEmail author
  • Rachel A. Hovel
  • Correigh M. Greene


Stable isotopes (δ15N and δ13C) offer one representation of an individual’s trophic niche and are important tools for elucidating ecological patterns and testing a diversity of hypotheses. Because δ15N and δ13C values are often obtained from the same sample, they compose a bivariate response that researchers commonly analyze using multivariate statistical methods. However, stable isotope data sets often exhibit hierarchical structure whereby samples may be clustered or grouped at multiple levels either as an artifact of sampling design or due to structure inherent in the sampled population (e.g., samples from individuals grouped according to life history stages, social groups, ages, or sizes classes). Ignoring such structure can result in overly optimistic confidence intervals and heighten the risk of observing significant differences where none exist. To address these issues, we suggest researchers utilize multivariate hierarchical models, which are a simple extension of univariate hierarchical methods. The models account for potential dependencies between δ15N and δ13C values, permit valid predictions of shifts in δ15N–δ13C space related to predictor variables, provide more accurate estimates of parameter uncertainty, and improved inferences on coefficients that correspond to groups with small to moderate quantities of data. We demonstrate advantages of multivariate hierarchical models by examining size-dependent shifts in δ15N–δ13C space in outmigrating post-smolt Chinook salmon sampled from an estuarine habitat. Given the prevalence of complex structure in ecological stable isotope data sets, multivariate hierarchical models should hold considerable value to food web and stable isotope ecologists.


Stable Isotope Hierarchical Model Fork Length Chinook Salmon Slope Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Funding for JCPR was provided by a National Research Council Fellowship. RAH was funded by a University of Washington H. Mason Keeler Fellowship and a grant from Seattle Public Utilities. Stable isotope analysis was financed by a Spooner Research Grant awarded to RAH and an Intensively Monitored Watersheds grant to CMG by the Washington State Department of Ecology. J. Chamberlin, B. Ferris, M. Hunsicker, E. Howe, E. Ward, O. Shelton, and two anonymous reviewers provided valuable comments on earlier drafts of the manuscript.

Supplementary material

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Supplementary material 1 (PDF 76 kb)
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jonathan C. P. Reum
    • 1
    Email author
  • Rachel A. Hovel
    • 2
  • Correigh M. Greene
    • 3
  1. 1.Conservation Biology Division, Northwest Fisheries Science Center, National Marine Fisheries ServiceNational Oceanic and Atmospheric AdministrationSeattleUSA
  2. 2.School of Aquatic and Fishery SciencesUniversity of WashingtonSeattleUSA
  3. 3.Fish Ecology Division, Northwest Fisheries Science Center, National Marine Fisheries ServiceNational Oceanic and Atmospheric AdministrationSeattleUSA

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