Mixed effects: A unifying framework for statistical modelling in fisheries biology

ICES Journal of Marine Science

Volumn 72, Issue 5, 2015, Pages 1245-1256

  Thorson, James T ^a   Minto, Cóilín ^b  

^a NORTHWEST FISHERIES SCIENCE CENTER   (United States)

^b Atlantic Technological University   (Ireland)

Author keywords

Gaussian random field; hierarchical; individual level variability; integration; latent variable; measurement error; mixed effects model; random effects; spatial variation; state space

Indexed keywords

ERROR ANALYSIS; GAUSSIAN METHOD; HABITAT USE; HIERARCHICAL SYSTEM; PHENOTYPE; POPULATION DENSITY; SPATIAL VARIATION;

EID: 84930797489     PISSN: 10543139     EISSN: 10959289     Source Type: Journal    
DOI: 10.1093/icesjms/fsu213     Document Type: Review

References (97)

1. Aitkin, M., Francis, B., Hinde, J., and Darnell, R. 2009. Statistical Modelling in R. Oxford University Press, Oxford, UK.
2. Akaike, H. 1974. New look at statistical-model identification. IEEE Transactions on Automatic Control, AC19: 716-723.
3. Andersen, K. H., and Beyer, J. E. 2006. Asymptotic size determines species abundance in the marine size spectrum. The American Naturalist, 168: 54-61.
4. Berg, C. W. 2012. Theta logistic population model writeup. National Center for Ecological Analysis and Synthesis, Santa Barbara, CA.
5. Berliner, L. M. 1996. Hierarchical Bayesian time series models. In Maximum Entropy and Bayesian Methods, pp. 15-22. Ed. by K. M. Hanson, and R. N. Silver. Springer, Santa Fe, New Mexico.
6. Beverton, R., and Holt, S. 1959. A review of the lifespans and mortality rates of fish in nature, and their relation to growth and other physiological characteristics. In Ciba Foundation Symposium-The Lifespan of Animals (Colloquia on Ageing), pp. 142-177. Ed. by G. E. W. Wolstenholme, and M. O'Conner. J and A Churchill Ltd., London.
7. Black, A. J., andMcKane, A. J. 2012. Stochastic formulation of ecological models and their applications. Trends in Ecology & Evolution, 27: 337-345.
8. Bolker, B. M., Gardner, B., Maunder, M., Berg, C. W., Brooks, M., Comita, L., Crone, E., et al. 2013. Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS. Methods in Ecology and Evolution, 4: 501-512.
9. Breslow, N. E., and Clayton, D. G. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88: 9-25.
10. Carpenter, S.R. 2002. Ecological futures: Building an ecology of the long now. Ecology, 83: 2069-2083.
11. Charnov, E. L., Gislason, H., and Pope, J. G. 2013. Evolutionary assembly rules for fish life histories. Fish and Fisheries, 14: 213-224.
12. Clark, C.W., and Mangel, M. 2000. Dynamic State Variable Models in Ecology: Methods and Applications. Oxford University Press, New York.
13. Clark, J. S., and Gelfand, A. E. 2006. A future for models and data in environmental science. Trends in Ecology & Evolution, 21: 375-380.
14. Conover, D. O., andMunch, S. B. 2002. Sustaining fisheries yields over evolutionary time scales. Science, 297: 94-96.
15. Cressie, N., Calder, C. A., Clark, J. S., Hoef, J. M. V., and Wikle, C. K. 2009. Accounting for uncertainty in ecological analysis: The strengths and limitations of hierarchical statistical modeling. Ecological Applications, 19: 553-570.
16. Cressie, N., andWikle, C. K. 2011. Statistics for Spatio-Temporal Data. JohnWiley & Sons, Hoboken, NJ.
17. Dail, D., and Madsen, L. 2011. Models for estimating abundance from repeated counts of an open metapopulation. Biometrics, 67: 577-587.
18. Debes, P. V., Fraser, D. J., McBride, M. C., and Hutchings, J. A. 2013a. Multigenerational hybridisation and its consequences for maternal effects in Atlantic salmon. Heredity, 111: 238-247.
19. Debes, P. V., McBride, M. C., Fraser, D. J., and Hutchings, J. A. 2013b. Data from: Multigenerational hybridisation and its consequences for maternal effects in Atlantic salmon. Dryad. http://dx.doi.org/ 10.5061/dryad.9cs2v (last accessed 17 November 2014).
20. De Valpine, P. 2009. Shared challenges and common ground for Bayesian and classical analysis of hierarchical statistical models. Ecological Applications, 19: 584-588.
21. Falconer, D. S., Mackay, T. F., and Frankham, R. 1996. Introduction to quantitative genetics (4th edn). Trends in Genetics, 12: 280.
22. Gay, D. M. 1996. More AD of nonlinear AMPL models: Computing Hessian information and exploiting partial separability. In Computational Differentiation: Applications, Techniques, and Tools, pp. 173-184. Ed. by M. Berz, C. Bischof, G. F. Corliss, and A. Griewank. SIAM, Philadelphia, PA.
23. Gelman, A. 2005. Analysis of variance-Why it is more important than ever. The Annals of Statistics, 33: 1-53.
24. Gelman, A., and Hill, J. 2007. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge, UK.
25. Gudmundsson, G., and Gunnlaugsson, T. 2012. Selection and estimation of sequential catch-at-age models. Canadian Journal of Fisheries and Aquatic Sciences, 69: 1760-1772.
26. Hadfield, J. D. 2010. MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R package. Journal of Statistical Software, 33: 1-22.
27. Haran, M. 2011. Gaussian random field models for spatial data. In Handbook of Markov Chain Monte Carlo. Ed. by S. Brooks, A. Gelman, G. Jones, and X-L. Meng. CRC Press, Boca Raton, FL.
28. Henderson, C. R.,Kempthorne,O., Searle, S. R., andVon Krosigk, C. M. 1959. The estimation of environmental and genetic trends from records subject to culling. Biometrics, 15: 192-218.
29. Hilborn, R. 2002. The dark side of reference points. Bulletin of Marine Science, 70: 403-408.
30. Hilborn, R., and Liermann, M. 1998. Standing on the shoulders of giants: Learning from experience in fisheries. Reviews in Fish Biology and Fisheries, 8: 273-283.
31. Hilborn, R., and Walters, C. J. 1992. Quantitative Fisheries Stock Assessment-Choice, Dynamics and Uncertainty. Springer, Norwell, MA.
32. Illian, J. B., Sørbye, S. H., and Rue,H. 2012.Atoolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA). The Annals of Applied Statistics, 6: 1499-1530.
33. Johnson, D. S., London, J. M., Lea, M-A., and Durban, J. W. 2008. Continuous-time correlated random walk model for animal telemetry data. Ecology, 89: 1208-1215.
34. Jonsen, I.D., Flemming, J. M., andMyers, R. A. 2005. Robust state-space modeling of animal movement data. Ecology, 86: 2874-2880.
35. Jorgensen, C., Enberg, K., Dunlop, E. S., Arlinghaus, R., Boukal, D. S., Brander, K., Ernande, B., et al. 2007. Managing evolving fish stocks. Science, 318: 1247-1248.
36. Kéry, M., and Schaub, M. 2012. Bayesian Population Analysis Using WinBUGS: A Hierarchical Perspective. Academic Press, Waltham, MA.
37. Knape, J. 2008. Estimability of density dependence in models of time series data. Ecology, 89: 2994-3000.
38. Law, R. 1991.Onthe quantitative genetics of correlated characters under directional selection in age-structured populations. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 331: 213-223.
39. Leibold, M. A., Holt, R. D., and Holyoak, M. 2005. Adaptive and coadaptive dynamics in metacommunities. In Metacommunities: Spatial Dynamics and Ecological Communities. Ed. by M. Holyoak, M. A. Leibold, and R. D. Holt. University of Chicago Press, Chicago, IL.
40. Lele, S. R., and Dennis, B. 2009. Bayesian methods for hierarchical models: Are ecologists making a Faustian bargain. Ecological Applications, 19: 581-584.
41. Levin, S. A., and Pacala, S. W. 1997. Theories of simplification and scaling of spatially distributed processes. In Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, pp. 271-296. Ed. by D. Tilman, and P. Kereiva. Princeton University Press, Princeton, NJ.
42. Lindgren, F. 2012. Continuous domain spatial models in R-INLA. The ISBA Bulletin, 19: 14-20.
43. Lindgren, F., Rue, H., and Lindström, J. 2011. An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73: 423-498.
44. MacKenzie, D. I., Nichols, J.D., Royle, J. A., Pollock, K. H., Bailey, L. L., and Hines, J. E. 2005. Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence. Academic Press, Burlington, MA. 344 pp.
45. Mäntyniemi, S.,Uusitalo, L., Peltonen,H.,Haapasaari, P., andKuikka, S. 2013. Integrated, age-structured, length-based stock assessment model with uncertain process variances, structural uncertainty, and environmental covariates: Case of Central Baltic herring. Canadian Journal of Fisheries and Aquatic Sciences, 70: 1317-1326.
46. Meyer, R., and Millar, R. B. 1999. BUGS in Bayesian stock assessments. Canadian Journal of Fisheries and Aquatic Sciences, 56: 1078-1087.
47. Millar,R. B., and Anderson, M. J. 2004.Remedies for pseudoreplication. Fisheries Research, 70: 397-407.
48. Millar, R. B., and Meyer, R. 2000. Bayesian state-space modeling of age-structured data: Fitting a model is just the beginning. Canadian Journal of Fisheries and Aquatic Sciences, 57: 43-50.
49. Minto, C., Mills Flemming, J., Britten, G. L., Worm, B., and Rose, K. 2014. Productivity dynamics of Atlantic cod. Canadian Journal of Fisheries and Aquatic Sciences, 71: 203-216.
50. Morgan, M. J., Perez-Rodriguez, A., Saborido-Rey, F., and Marshall, C.T. 2011. Does increased information about reproductive potential result in better prediction of recruitment? Canadian Journal of Fisheries and Aquatic Sciences, 68: 1361-1368.
51. Myers, R. A. 1998. When do environment-recruitment correlations work? Reviews in Fish Biology and Fisheries, 8: 285-305.
52. Myers, R. A., and Cadigan, N. G. 1993. Density-dependent juvenile mortality in marine demersal fish. Canadian Journal of Fisheries and Aquatic Sciences, 50: 1576-1590.
53. Nielsen, A., and Berg, C.W. 2014. Estimation of time-varying selectivity in stock assessments using state-space models. Fisheries Research, 158: 96-101.
54. Ono, K., Punt, A. E., and Rivot, E. 2012.Model performance analysis for Bayesian biomass dynamics models using bias, precision and reliability metrics. Fisheries Research, 125-126: 173-183.
55. Osenberg, C. W., Sarnelle, O., Cooper, S. D., and Holt, R. D. 1999. Resolving ecological questions through meta-analysis: Goals, metrics, and models. Ecology, 80: 1105-1117.
56. Pauly,D. 2010. Gasping Fish and Panting Squids: Oxygen, Temperature and the Growth ofWater-Breathing Animals. International Ecology Institute, Oldendorf/Luhe, Germany.
57. Pedersen, M.W., Berg, C.W., Thygesen,U. H., Nielsen, A., and Madsen, H. 2011. Estimation methods for nonlinear state-space models in ecology. Ecological Modelling, 222: 1394-1400.
58. Pella, J. J. 1993. Utility of structural time series models and the Kalman filter for predicting consequences of fishery actions. In Proceedings of the International Symposium on Management Strategies for Exploited Fish Populations. Ed. by G. Kruse. Alaska Sea Grant College Program Report, pp. 571-593.
59. Peterman, R. M., Pyper, B. J., and Grout, J. A. 2000. Comparison of parameter estimation methods for detecting climate-induced changes in productivity of Pacific salmon (Oncorhynchus spp.). Canadian Journal of Fisheries and Aquatic Sciences, 57: 181-191.
60. Petris, G., Campagnoli,P., andPetrone, S. 2009. Dynamic LinearModels with R. Springer, New York.
61. Pinheiro, J., and Bates,D. 2009. Mixed-Effects Models in S and S-PLUS. Springer, New York, NY.
62. Plummer,M. 2003. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003). Vienna, Austria.
63. Punt, A. E. 2003. Extending production models to include process error in the population dynamics. Canadian Journal of Fisheries and Aquatic Sciences, 60: 1217-1228.
64. Punt, A. E. 2008.Refocusing stock assessment in support of policy evaluation. In Fisheries for Global Welfare and Environment, pp. 139-152. Ed. by K. Tsukamoto, T. Kawamura, T. Takeuchi, T. D. Beard, and M. J. Kaiser. TerraPub, Tokyo.
65. Quinn,T. J.,and Deriso, R. B. 1999. Quantitative Fish Dynamics. Oxford University Press, Oxford, UK.
66. R Core Development Team. 2012. R: A Language and Environment for Statistical Computing. Vienna, Austria. http://www.R-project.org/ (last accessed 17 November 2014).
67. Royle, J. A. 2004. N-mixture models for estimating population size from spatially replicated counts. Biometrics, 60: 108-115.
68. Royle, J. A., and Dorazio, R. M. 2008. Hierarchical Modeling and Inference in Ecology: The Analysis of Data from Populations, Metapopulations and Communities. Academic Press, London.
69. Royle, J. A., andWikle, C. K. 2005. Efficient statistical mapping of avian count data. Environmental and Ecological Statistics, 12: 225-243.
70. Rue, H., Martino, S., and Chopin, N. 2009. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71: 319-392.
71. Rue, H., Martino, S., Lindgren, F., Simpson, D., and Riebler, A. 2013. INLA: Functions which allow to perform full Bayesian analysis of latent Gaussian models using Integrated Nested Laplace Approximaxion. http://www.r-inla.org/ (last accessed 17 November 2014).
72. Schaefer,M. B. 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bulletin Inter-American Tropical Tuna Commission, 1: 27-56.
73. Schnute, J. T. 1991. The importance of noise in fish population models. Fisheries Research, 11: 197-223.
74. Searle, S. R., Casella, G., and McCulloch, C. E. 1992. Variance Components. JohnWiley & Sons, Hoboken, NJ. 536 pp.
75. Shelton, A. O.,Munch, S. B., Keith, D., and Mangel, M. 2012. Maternal age, fecundity, egg quality, and recruitment: Linking stock structure to recruitment using an age-structured Ricker model. Canadian Journal of Fisheries and Aquatic Sciences, 69: 1631-1641.
76. Shelton, A.O., Satterthwaite,W. H., Beakes,M. P.,Munch, S. B., Sogard, S. M., and Mangel, M. 2013. Separating intrinsic and environmental contributions to growth and their population consequences. The American Naturalist, 181: 799-814.
77. Shelton, A. O., Thorson, J. T.,Ward, E. J., and Feist, B. E. 2014. Spatial semiparametric models improve estimates of species abundance and distribution. Canadian Journal of Fisheries and Aquatic Sciences, 71: 1655-1666.
78. Skaug, H., and Fournier,D. 2006. Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models. Computational Statistics & Data Analysis, 51: 699-709.
79. Smallegange, I. M., and Coulson, T. 2012. Towards a general, population-level understanding of eco-evolutionary change. Trends in Ecology & Evolution, 28: 143-148.
80. Stewart, I. J., Hicks, A. C., Taylor, I. G., Thorson, J. T., Wetzel, C., and Kupschus, S. 2013. A comparison of stock assessment uncertainty estimates using maximum likelihood and Bayesian methods implemented with the same model framework. Fisheries Research, 142: 37-46.
81. Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, M., and Munch, S. 2012. Detecting causality in complex ecosystems. Science, 338: 496-500.
82. Su, Y-S., and Yajima, M. 2012. R2jags: A Package for Running jags from R. http://CRAN.R-project.org/package=R2jags (last accessed 17 November 2014).
83. Su, Z., Peterman, R. M., and Haeseker, S. L. 2004. Spatial hierarchical Bayesian models for stock-recruitment analysis of pink salmon (Oncorhynchus gorbuscha). Canadian Journal of Fisheries and Aquatic Sciences, 61: 2471-2486.
84. Swain, D. P., and Foote, C. J. 1999. Stocks and chameleons: The use of phenotypic variation in stock identification. Fisheries Research, 43: 113-128.
85. Taylor, I. G., andMethot, R.D. 2013. Hiding or dead?Acomputationally efficient model of selective fisheries mortality. Fisheries Research, 142: 75-85.
86. Thorson, J.T., Cope, J., Kleisner, K., Shelton, A., Samhouri, J.,andWard, E. in press-a. Giants' shoulders 15 years later: Lessons, challenges, and guidelines in fisheries meta-analysis. Fish and Fisheries, DOI: 10.1111/faf.12061.
87. Thorson, J. T., Jensen,O. P., and Zipkin, E. F. 2014a. How variable is recruitment for exploited marine fishes? A hierarchical model for testing life history theory. Canadian Journal of Fisheries and Aquatic Sciences, 71: 973-983.
88. Thorson, J. T., Scheuerell, M. D., Buhle, E. R., and Copeland, T. 2014b. Spatial variation buffers temporal fluctuations in early juvenile survival for an endangered Pacific salmon. Journal of Animal Ecology, 83: 157-167.
89. Thorson, J. T., Skaug, H., Kristensen, K., Shelton, A. O., Ward, E. J., Harms, J., and Benante, J. in press-b. The importance of spatial models for estimating the strength of density dependence. Ecology. http://dx.doi.org/10.1890/14-0739.1 (last accessed 17 November 2014).
90. Thorson, J. T., Stewart, I. J., and Punt, A. E. 2012. Development and application of an agent-basedmodel to evaluatemethods for estimating relative abundance indices for shoaling fish such as Pacific rockfish (Sebastes spp.). ICES Journal ofMarine Science, 69: 635-647.
91. Thorson, J. T., Zhou, S., Punt, A. E., and Smith, T. D. M. 2013. A stepwise-selected spline approximation to time-varying parameters, with application to occupancy modelling. Methods in Ecology and Evolution, 4: 123-132.
92. Tobler,W. R. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography, 46: 234-240.
93. Van Wijk, S. J., Taylor, M. I., Creer, S., Dreyer, C., Rodrigues, F. M., Ramnarine, I.W., van Oosterhout, C., et al. 2013. Experimental harvesting of fish populations drives genetically based shifts in body size and maturation. Frontiers in Ecology and the Environment, 11: 181-187.
94. Wagner, T., Hayes, D. B., and Bremigan, M. T. 2006. Accounting for multilevel data structures in fisheries data using mixed models. Fisheries, 31: 180-187.
95. Wilson, A. J., Reale, D., Clements, M. N., Morrissey,M. M., Postma, E., Walling, C. A., Kruuk, L. E., et al. 2010. An ecologist's guide to the animal model. Journal of Animal Ecology, 79: 13-26.
96. Wu, G., Holan, S. H., and Wikle, C. K. 2013. Hierarchical Bayesian spatio-temporal Conway-Maxwell Poisson models with dynamic dispersion. Journal of Agricultural, Biological, and Environmental Statistics, 18: 1-22.
97. Zuur, A. F., Tuck, I. D., and Bailey, N. 2003. Dynamic factor analysis to estimatecommontrends in fisheries time series. Canadian Journal of Fisheries and Aquatic Sciences, 60: 542-552.