Advertisement

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
Method

Abstract

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.

Keywords

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.

Notes

Acknowledgments

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

227_2014_2574_MOESM1_ESM.pdf (76 kb)
Supplementary material 1 (PDF 76 kb)
227_2014_2574_MOESM2_ESM.docx (96 kb)
Supplementary material 2 (DOCX 97 kb)

References

  1. Authier M, Martin C, Ponchon A, Steelandt S, Bentaleb I, Guinet C (2012) Breaking the sticks: a hierarchical change-point model for estimating ontogenetic shifts with stable isotope data. Method Ecol Evol 3:281–290CrossRefGoogle Scholar
  2. Blüthgen N, Gebauer G, Fiedler K (2003) Disentangling a rainforest food web using stable isotopes: dietary diversity in a species-rich ant community. Oecologia 137:426–435CrossRefGoogle Scholar
  3. Boecklen WJ, Christopher TY, Cook BA, James AC (2011) On the use of stable isotopes in trophic ecology. Annu Rev Ecol Evol Syst 42:411–440CrossRefGoogle Scholar
  4. Carlier A, Riera P, Amouroux JM, Bodiou JY, Grémare A (2007) Benthic trophic network in the Bay of Banyuls-sur-Mer (northwest Mediterranean, France): an assessment based on stable carbon and nitrogen isotopes analysis. Estuar Coast Shelf Sci 72:1–15CrossRefGoogle Scholar
  5. Gelman A (2005) Analysis of variance? Why it is more important than ever. Ann Stat 33:1–53CrossRefGoogle Scholar
  6. Gelman A (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1:515–534CrossRefGoogle Scholar
  7. Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  8. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2014) Bayesian data analysis. CRC Press, Boca RatonGoogle Scholar
  9. Hadfield JD (2010) MCMC methods for multi-response generalized linear mixed models: the MCMCglmm R package. J Stat Soft 33:1–22Google Scholar
  10. Healy MC (1991) Life history of Chinook salmon (Oncorhynchus tshawytscha). In: Groot C, Margolis L (eds) Pacific salmon life histories. Vancouver, UBC Press, pp 313–393Google Scholar
  11. Hobson KA, Sirois J, Gloutney ML (2000) Tracing nutrient allocation to reproduction with stable isotopes: a preliminary investigation using colonial waterbirds of Great Slave Lake. Auk 117:760–774CrossRefGoogle Scholar
  12. Hox J (2010) Multilevel analysis: techniques and applications. Routledge Academic, New YorkGoogle Scholar
  13. Jennings S, Warr KJ (2003) Environmental correlates of large-scale spatial variation in the δ15N of marine animals. Mar Biol 142:1131–1140Google Scholar
  14. Johnson PC (2014) Extension of Nakagawa & Schielzeth’s R 2 GLMM to random slopes models. Method Ecol Evol. doi: 10.1111/2041-210X.12225 Google Scholar
  15. Kéry M (2010) Introduction to WinBUGS for ecologists: a Bayesian approach to regression. ANOVA and related analyses. Academic Press, BulringtonGoogle Scholar
  16. Layman CA, Araujo M, Boucel R, Hammerschlag-Peyer CM, Harrison E, Zachary JR, Matich P, Rosenblatt AE, Vaudo JJ, Yeager LA (2012) Applying stable isotopes to examine food-web structure: an overview of analytical tools. Biol Rev 87:545–562CrossRefGoogle Scholar
  17. Leakey CDB, Attrill MJ, Jennings S, Fitzsimons MF (2008) Stable isotopes in juvenile marine fishes and their invertebrate prey from the Thames Estuary, UK, and adjacent coastal regions. Estuar Coast Shelf Sci 77:513–522CrossRefGoogle Scholar
  18. Lesage V, Hammill MO, Kovacs KM (2001) Marine mammals and the community structure of the Estuary and Gulf of St Lawrence, Canada: evidence from stable isotope analysis. Mar Ecol Prog Ser 210:203–221CrossRefGoogle Scholar
  19. Littell RC, Milliken GA, Stroup WW, Wolfinger RD (1996) SAS system for mixed models. Sas Institute Inc., CaryGoogle Scholar
  20. McConnaughey T, McRoy CP (1979) Food-web structure and the fractionation of carbon isotopes in the Bering Sea. Mar Biol 53:257–262CrossRefGoogle Scholar
  21. Nakagawa S, Schielzeth H (2013) A general and simple method for obtaining R 2 from generalized linear mixed-effects models. Method Ecol Evol 4:133–142CrossRefGoogle Scholar
  22. Olson RJ, Popp BN, Graham BS, López-Ibarra GA, Galván-Magaña F, Lennert-Cody CE, Bocanegra-Castillo N et al (2010) Food-web inferences of stable isotope spatial patterns in copepods and yellowfin tuna in the pelagic eastern Pacific Ocean. Prog Oceanogr 86:124–138CrossRefGoogle Scholar
  23. Parnell AC, Phillips DL, Bearhop S, Semmens BX, Ward EJ, Moore JW, Jackson AL, Grey J, Kelly DJ, Inger R (2013) Bayesian stable isotope mixing models. Environmetrics 24:387–399Google Scholar
  24. Peterson BJ, Fry B (1987) Stable isotopes in ecosystem studies. Annu Rev Ecol Evol Syst 18:293–320CrossRefGoogle Scholar
  25. Piñeiro G, Perelman S, Guerschman JP, Paruelo JM (2008) How to evaluate models: observed vs. predicted or predicted vs. observed? Ecol Model 216:316–322CrossRefGoogle Scholar
  26. R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.r-project.org
  27. Reum JCP, Essington TE (2013) Spatial and seasonal variation in δ15N and δ13C values in a mesopredator shark, Squalus suckleyi, revealed through multitissue analyses. Mar Biol 160:399–411CrossRefGoogle Scholar
  28. Rice CA, Duda JJ, Greene CM, Karr JR (2012) Geographic patterns of fishes and jellyfish in Puget Sound surface waters. Mar Coast Fish 4:117–128CrossRefGoogle Scholar
  29. Searle SR (1987) Linear models for unbalanced data. Wiley, New YorkGoogle Scholar
  30. Semmens BX, Ward EJ, Moore JW, Darimont CT (2009) Quantifying inter- and intra-population niche variability using hierarchical Bayesian stable isotope mixing models. PLoS One 4(7):e6187CrossRefGoogle Scholar
  31. Snijders T, Bosker R (1999) Multilevel modeling: an introduction to basic and advanced multilevel modeling. SAGE Publications Ltd, Thousand OaksGoogle Scholar
  32. Spiegelhalter DJ, Best NG, Carlin BP, Van der Linde A (2002) Bayesian measures of model complexity and fit. J R Stat Soc: Ser B (Stat Methodol) 64:583–639CrossRefGoogle Scholar
  33. Tabachnick BG, Fidell LS (2007) Using multivariate statistics, 5th edn. Pearson Education, BostonGoogle Scholar
  34. Turner TF, Collyer ML, Krabbenhoft TJ (2010) A general hypothesis-testing framework for stable isotope ratios in ecological studies. Ecology 91:2227–2233CrossRefGoogle Scholar
  35. Zeug SC, Peretti D, Winemiller KO (2009) Movement into floodplain habitats by gizzard shad (Dorosoma cepedianum) revealed by dietary and stable isotope analyses. Environ Biol Fishes 84:307–314CrossRefGoogle Scholar

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

Personalised recommendations