Ecological Archives E096-006-A1

Oded Berger-Tal, Keren Embar, Burt P. Kotler, and David Saltz. 2015. Everybody loses: intraspecific competition induces tragedy of the commons in Allenby’s gerbils. Ecology 96:54–61. http://dx.doi.org/10.1890/14-0130.1

Appendix A. Model selection tables ranking the best models to explain the foraging behavior of gerbils.

Model selection tables ranking the best models to explain the foraging behavior of gerbils in an experiment testing for a tragedy of the commons between foraging gerbils (Berger-Tal et al. 2014). Model selection was based on the Akaike's Information Criterion corrected for small sample sizes (AICc), as recommended when the number of observations is low compared to number of parameters in models (Burnham and Anderson 2002).  The model with the lowest AICc is considered the most likely model and other models are ranked according to the differences between their AICc and the best model. Wi measures the relative likelihood that a given model is the best among a set of models fitted (Burnham and Anderson 2002).

Table A1. The models explaining differences in the amount of time (in seconds) spent in food patches by the gerbils in an experiment testing for a tragedy of the commons between foraging gerbils (Berger-Tal et al. 2014). For details on the experimental design, see main text. The possible parameters are: number of gerbils foraging (#Gerbils: one or two), the environmental quality treatment (EvTr: first rich period, poor period, second rich period), the identity of the gerbils (ID: a random variable nested within treatment), and the interaction between the number of gerbils and the treatment (#Ger X EvTr). np is the number of estimated parameters for each model, AICc is the Akaike Information Criterion corrected for small sample sizes, ΔAICc is the difference in AICc between the model with lowest AIC and the model considered, and w_iindicates the AICc weight of a given model among the whole set of models fitted.

Table A2. The models explaining differences in the number of visits to food patches paid by the gerbils in an experiment testing for a tragedy of the commons between foraging gerbils (Berger-Tal et al. 2014). For details on the experimental design, see main text. The possible parameters are: number of gerbils foraging (#Gerbils: one or two), the environmental quality treatment (EvTr: first rich period, poor period, second rich period), the identity of the gerbils (ID: a random variable nested within treatment), and the interaction between the number of gerbils and the treatment (#Ger X EvTr). np is the number of estimated parameters for each model, AICc is the Akaike Information Criterion corrected for small sample sizes, ΔAICc is the difference in AICc between the model with lowest AIC and the model considered, and w_iindicates the AICc weight of a given model among the whole set of models fitted.

Table A3. The models explaining differences in the amount of food harvested (in grams) by the gerbils in an experiment testing for a tragedy of the commons between foraging gerbils (Berger-Tal et al. 2014). For details on the experimental design, see main text. The possible parameters are: number of gerbils foraging (#Gerbils: one or two), the environmental quality treatment (EvTr: first rich period, poor period, second rich period), the identity of the gerbils (ID: a random variable nested within treatment), and the interaction between the number of gerbils and the treatment (#Ger X EvTr). np is the number of estimated parameters for each model, AICc is the Akaike Information Criterion corrected for small sample sizes, ΔAICc is the difference in AICc between the model with lowest AIC and the model considered, and w_iindicates the AICc weight of a given model among the whole set of models fitted.

Table A4. The models explaining differences in the time spent in the food patches between gerbils foraging alone and the dominant individuals within a foraging pair (for details on the experimental design, see main text). The possible parameters are: gerbil rank (Rank: single or dominant), the environmental quality treatment (EvTr: first rich period, poor period, second rich period), the identity of the gerbils (ID: a random variable nested within treatment), and the interaction between the rank of gerbils and the treatment (Rank X EvTr). np is the number of estimated parameters for each model, AICc is the Akaike Information Criterion corrected for small sample sizes, ΔAICc is the difference in AICc between the model with lowest AIC and the model considered, and w_iindicates the AICc weight of a given model among the whole set of models fitted.

Table A5. The models explaining differences in the number of chases recorded between two gerbils within a pair. The possible parameters are: tray number (Tray: 1-4), the environmental quality treatment (EvTr: first rich period, poor period, second rich period), the identity of the gerbils (ID: a random variable nested within treatment), and the interaction between the rank of gerbils and the treatment Tray X EvTr). np is the number of estimated parameters for each model, AICc is the Akaike Information Criterion corrected for small sample sizes, ΔAICc is the difference in AICc between the model with lowest AIC and the model considered, and w_iindicates the AICc weight of a given model among the whole set of models fitted.

Literature cited

Berger-Tal, O., K. Embar, B. P. Kotler, and D. Saltz. 2014. Everybody loses: intraspecific competition induces tragedy of the commons in Allenby's gerbils. Ecology, in press.

Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference: a practical information-theoretic approach, Second edition. Springer-Verlag, New York, New York, USA.

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