Skip to main content
Log in

Model selection and model averaging in behavioural ecology: the utility of the IT-AIC framework

  • Original Paper
  • Published:
Behavioral Ecology and Sociobiology Aims and scope Submit manuscript

Abstract

Behavioural ecologists often study complex systems in which multiple hypotheses could be proposed to explain observed phenomena. For some systems, simple controlled experiments can be employed to reveal part of the complexity; often, however, observational studies that incorporate a multitude of causal factors may be the only (or preferred) avenue of study. We assess the value of recently advocated approaches to inference in both contexts. Specifically, we examine the use of information theoretic (IT) model selection using Akaike’s information criterion (AIC). We find that, for simple analyses, the advantages of switching to an IT-AIC approach are likely to be slight, especially given recent emphasis on biological rather than statistical significance. By contrast, the model selection approach embodied by IT approaches offers significant advantages when applied to problems of more complex causality. Model averaging is an intuitively appealing extension to model selection. However, we were unable to demonstrate consistent improvements in prediction accuracy when using model averaging with IT-AIC; our equivocal results suggest that more research is needed on its utility. We illustrate our arguments with worked examples from behavioural experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Anderson DR, Burnham KP, Thompson WL (2000) Null hypothesis testing: problems, prevalence, and an alternative. J Wildl Manage 64:912–923

    Article  Google Scholar 

  • Bolker BM (2008) Ecological models and data in R. Princeton University Press, Princeton

    Google Scholar 

  • Buckland ST, Burnham KP, Augustin NH (1997) Model selection: an integral part of inference. Biometrics 53:603–618

    Article  Google Scholar 

  • Burnham KP, Anderson DR (2001) Kullback–Leibler information as a basis for strong inference in ecological studies. Wildlife Res 28:111–119

    Article  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York

    Google Scholar 

  • Burnham KP, Anderson DR, Huyvaert K (2010) AICc model selection in ecological and behavioral science: some background, observations, and comparisons. Behavioral Ecology & Sociobiology. doi:10.1007/s00265-010-1029-6

  • Cohen J (1994) The earth is round (P < .05). Am Psychol 49:997–1003

    Article  Google Scholar 

  • Freckleton RP (2010) Dealing with collinearity in behavioural and ecological data: model averaging and the problems of measurement error. Behavioral Ecology & Sociobiology. doi:10.1007/s00265-010-1045-6

  • Garamszegi LZ (2010) Information-theoretic approaches to statistical analysis in behavioural ecology: an introduction. Behavioral Ecology & Sociobiology. doi:10.1007/s00265-010-1028-7

  • Gurney WSC, Nisbet RM (1998) Ecological dynamics. Oxford University Press, Oxford

    Google Scholar 

  • Hegyi G, Garamszegi LZ (2010) Using information theory as a substitute for stepwise regression in ecology and behavior. Behavioral Ecology & Sociobiology (in press)

  • Heyes CM, Dawson GR (1990) A demonstration of observational-learning in rats using a bidirectional control. Q J Exp Psychol B 42:59–71

    PubMed  CAS  Google Scholar 

  • Hilborn R, Mangel M (1997) The ecological detective: confronting models with data, vol 28. Princeton University Press, Princeton

    Google Scholar 

  • Hobbs NT, Hilborn R (2006) Alternatives to statistical hypothesis testing in ecology: a guide to self teaching. Ecol Appl 16:5–19

    Article  PubMed  Google Scholar 

  • Hu B, Shao J (2008) Generalized linear model selection using R 2. J Stat Plan Inference 138:3705–3712

    Article  Google Scholar 

  • Johnson DH (1999) The insignificance of statistical significance testing. J Wildl Manage 63:763–772

    Article  Google Scholar 

  • Johnson JB, Omland KS (2004) Model selection in ecology and evolution. Trends Ecol Evol 19:101–108

    Article  PubMed  Google Scholar 

  • Krebs JR, Davies NB (1978) Behavioural ecology: an evolutionary approach. Blackwell, Oxford

    Google Scholar 

  • Lind J, Cresswell W (2005) Determining the fitness consequences of antipredation behavior. Behav Ecol 16:945–956

    Article  Google Scholar 

  • Lukacs PM, Thompson WL, Kendall WL, Gould WR, Doherty PF, Burnham KP, Anderson DR (2007) Concerns regarding a call for pluralism of information theory and hypothesis testing. J Appl Ecol 44:456–460

    Article  Google Scholar 

  • Martin TG, Wintle BA, Rhodes JR, Kuhnert PM, Field SA, Low-Choy SJ, Tyre AJ, Possingham HP (2005) Zero tolerance ecology: improving ecological inference by modelling the source of zero observations. Ecol Lett 8:1235–1246

    Article  Google Scholar 

  • Martinez-Abrain A (2007) Are there any diffferences? A non-sensical question in ecology. Acta Oecol 32:203–206

    Article  Google Scholar 

  • McCarthy MA (2007) Bayesian methods for ecology. Cambridge University Press, Cambridge

    Google Scholar 

  • Mitchell CJ, Heyes CM, Gardner MR, Dawson GR (1999) Limitations of a bidirectional control procedure for the investigation of imitation in rats: odour cues on the manipulandum. Q J Exp Psychol B 52:193–202

    Google Scholar 

  • Mundry R (2010) Issues in information theory based statistical inference—a commentary from a frequentist's perspective. Behavioral Ecology & Sociobiology. doi:10.1007/s00265-010-1040-y

  • Nakagawa S, Cuthill IC (2007) Effect size, confidence interval and statistical significance: a practical guide for biologists. Biol Rev 82:591–605

    Article  PubMed  Google Scholar 

  • Nakagawa S, Freckleton RP (2008) Missing inaction: the dangers of ignoring missing data. Trends Ecol Evol 23:592–596

    Article  PubMed  Google Scholar 

  • Nakagawa S, Freckleton RP (2010) Model averaging, missing data and multiple imputation: a case study for behavioural ecology. Behavioral Ecology & Sociobiology. doi:10.1007/s00265-010-1044-7

  • R Development Core Team (2005) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Richards SA (2005) Testing ecological theory using the information-theoretic approach: examples and cautionary results. Ecology 86:2805–2814

    Article  Google Scholar 

  • Richards SA (2008) Dealing with overdispersed count data in applied ecology. J Appl Ecol 45:218–227

    Article  Google Scholar 

  • Rogers D (1972) Random search and insect population models. J Anim Ecol 41:369–383

    Article  Google Scholar 

  • Ruxton GD, Colegrave N (2006) Experimental design for the life sciences, 2nd edn. Oxford University Press, Oxford

    Google Scholar 

  • Schielzeth H, Forstmeier W (2009) Conclusions beyond support: overconfident estimates in mixed models. Behavioral Ecology 20:416–420

    Article  PubMed  Google Scholar 

  • Stephens PA, Buskirk SW, Hayward GD, Martinez del Rio C (2005) Information theory and hypothesis testing: a call for pluralism. J Appl Ecol 42:4–12

    Article  Google Scholar 

  • Stephens PA, Buskirk SW, Hayward GD, Del Rio CM (2007a) A call for statistical pluralism answered. J Appl Ecol 44:461–463

    Article  Google Scholar 

  • Stephens PA, Buskirk SW, Martinez del Rio C (2007b) Inference in ecology and evolution. Trends Ecol Evol 22:192–197

    Article  PubMed  Google Scholar 

  • van de Pol MV, Wright J (2009) A simple method for distinguishing within- versus between-subject effects using mixed models. Anim Behav 77:753–758

    Article  Google Scholar 

  • Vander Wall SB (2000) The influence of environmental conditions on cache recovery and cache pilferage by yellow pine chipmunks (Tamias amoenus) and deer mice (Peromyscus maniculatus). Behavioral Ecology 11:544–549

    Article  Google Scholar 

  • Whittingham MJ, Stephens PA, Bradbury RB, Freckleton RP (2006) Why do we still use stepwise modelling in ecology and behaviour? J Anim Ecol 75:1182–1189

    Article  PubMed  Google Scholar 

  • Ydenberg RC, Brown JS, Stephens DW (2007) Foraging: an overview. In: Stephens DW, Brown JS, Ydenberg RC (eds) Foraging: Behavior and Ecology. University of Chicago Press, Chicago, pp 1–28

    Google Scholar 

Download references

Acknowledgements

We would like to thank Arthur Goldsmith and Rob Freckleton for helpful advice and discussions, three reviewers for their helpful comments, and Laszlo Garamszegi and Shinichi Nakagawa for inviting us to contribute to this issue. MJW was supported by a David Phillips Fellowship.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Philip A. Stephens.

Additional information

Communicated by: L. Garamszegi

This contribution is part of the Special Issue: “Model selection, multimodel inference and information-theoretic approaches in behavioural ecology” (see Garamszegi 2010).

Appendix

Appendix

A likelihood function for the functional response experiment

Recall that data consist of 50 triplets (x, i, y), where x is the initial density of seed, i = D or W (indicating dry or wet soil, respectively), and y is the number of seeds consumed. For each triplet, (x, i, y), each of the eight models provides the mean handling time and search rate, h i and s i , respectively. These two parameters can then be substituted into Eq. 2 to give the mean seed encounter rate, f. If the model assumes overdispersed data (i.e. the data are described by the NBD), then the likelihood of the model parameters, given the datum, is

$$ L\left( {{s_i},{h_i},\phi |x,y} \right) = \frac{{\Gamma (y + a)}}{{\Gamma (y + 1)\Gamma (a)}}{\left( {\frac{{b/T}}{{1 + b/T}}} \right)^a}{\left( {\frac{1}{{1 + b/T}}} \right)^y}, $$
(A.1)

where T is the duration of the experiment, ϕ is a parameter describing the amount of variation among individuals, Γ is the complete gamma function, a = f/ϕ and b = 1/ϕ. Using this formula to describe the NBD, the variance inflation factor is simply (1 + ϕ) (see Richards 2008 for details). In the limit as ϕ tends to zero, Eq. A.1 approaches the likelihood assuming a Poisson distribution. The likelihood of the model, given all the data, is the product of the likelihoods for each datum. Note that Eq. A.1 can be calculated in Microsoft Office Excel using the Gammaln function, and maximum likelihood estimates can be found using the Solver add-in; hence, a complete AIC analysis can be implemented using a spreadsheet.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Richards, S.A., Whittingham, M.J. & Stephens, P.A. Model selection and model averaging in behavioural ecology: the utility of the IT-AIC framework. Behav Ecol Sociobiol 65, 77–89 (2011). https://doi.org/10.1007/s00265-010-1035-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00265-010-1035-8

Keywords

Navigation