Ecological Archives E096-006-A1

Oded Berger-Tal, Keren Embar, Burt P. Kotler, 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 wiindicates the AICc weight of a given model among the whole set of models fitted.

Model

np

AICc

ΔAICc

wi

#Gerbils  + EvTr + ID + #Ger X EvTr

4

650.954

0.000

0.998

EvTr + ID + #Ger X EvTr

3

663.356

12.402

0.002

#Gerbils  + EvTr + ID

3

671.065

20.111

0.000

#Gerbils  + ID + #Ger X EvTr

3

680.230

29.276

0.000

EvTr + ID

2

683.804

32.850

0.000

ID +

#Ger X EvTr

2

692.968

42.014

0.000

#Gerbils  + ID

2

701.505

50.551

0.000

ID

1

714.528

63.574

0.000

#Gerbils  + EvTr

2

722.685

71.731

0.000

EvTr

1

725.018

74.064

0.000

#Gerbils 

1

725.862

74.908

0.000

#Gerbils  + EvTr + #Ger X EvTr

3

727.447

76.493

0.000

EvTr + #Ger X EvTr

2

729.568

78.614

0.000

#Gerbils  + #Ger X EvTr

2

729.983

79.023

0.000

#Ger X EvTr

1

731.569

80.615

0.000

 

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 wiindicates the AICc weight of a given model among the whole set of models fitted.

Model

np

AICc

ΔAICc

wi

#Gerbils  + EvTr + ID + #Ger X EvTr

4

406.584

0.000

0.909

EvTr + ID + #Ger X EvTr

3

411.532

4.948

0.077

#Gerbils  + EvTr + ID

3

414.973

8.389

0.014

EvTr + ID

2

420.257

13.673

0.001

#Gerbils  + ID + #Ger X EvTr

3

426.014

19.430

0.000

ID +

#Ger X EvTr

2

431.299

24.715

0.000

#Gerbils  + ID

2

435.130

28.546

0.000

ID

1

440.698

34.114

0.000

#Gerbils  + EvTr

2

441.361

34.777

0.000

EvTr

1

442.343

35.759

0.000

#Gerbils  + EvTr + #Ger X EvTr

3

444.935

38.351

0.000

EvTr + #Ger X EvTr

2

445.780

39.196

0.000

#Gerbils 

1

446.456

39.872

0.000

#Gerbils  + #Ger X EvTr

2

449.599

43.015

0.000

#Ger X EvTr

1

449.968

43.384

0.000

 

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 wiindicates the AICc weight of a given model among the whole set of models fitted.

Model

np

AICc

ΔAICc

wi

#Gerbils  + EvTr + ID

3

195.228

0.000

0.485

EvTr + ID

2

196.725

1.496

0.229

#Gerbils  + EvTr + ID + #Ger X EvTr

4

198.332

3.104

0.103

#Gerbils  + EvTr

2

198.689

3.460

0.086

EvTr + ID + #Ger X EvTr

3

199.492

4.264

0.057

#Gerbils  + EvTr + #Ger X EvTr

3

202.229

7.000

0.015

EvTr

1

203.829

8.601

0.007

#Gerbils 

1

204.175

8.947

0.006

#Gerbils  + ID

2

204.413

9.184

0.005

#Gerbils  + ID + #Ger X EvTr

3

205.983

10.755

0.002

ID

1

206.193

10.964

0.002

#Gerbils  + #Ger X EvTr

2

206.613

11.385

0.002

EvTr + #Ger X EvTr

2

207.419

12.190

0.001

ID +

#Ger X EvTr

2

207.479

12.251

0.001

#Ger X EvTr

1

210.523

15.294

0.000

 

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 wiindicates the AICc weight of a given model among the whole set of models fitted.

Model

np

AICc

ΔAICc

wi

Rank + EvTr + ID + Rank X EvTr

4

651.223

0.000

1.000

Rank  + EvTr + ID

3

671.180

19.958

0.000

EvTr + ID + Rank X EvTr

3

671.593

20.370

0.000

Rank + ID + Rank X EvTr

3

677.808

26.585

0.000

EvTr + ID

2

692.346

41.124

0.000

ID +

Rank X EvTr

2

697.495

46.272

0.000

Rank + ID

2

698.992

47.770

0.000

Rank + EvTr

2

718.091

66.898

0.000

ID

1

719.275

68.052

0.000

Rank

1

721.162

69.939

0.000

Rank + EvTr +

Rank X EvTr

3

723.294

72.071

0.000

Rank +

Rank X EvTr

2

725.416

74.194

0.000

EvTr

1

728.116

76.893

0.000

EvTr +

Rank X EvTr

2

733.121

81.898

0.000

Rank X EvTr

1

733.660

82.438

0.000

 

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 wiindicates the AICc weight of a given model among the whole set of models fitted.

Model

np

AICc

ΔAICc

wi

Tray + ID + Tray X EvTr

3

377.113

0.000

0.262

Tray + EvTr + ID + Tray X EvTr

4

377.281

0.169

0.241

Tray + EvTr + ID

3

378.346

1.234

0.141

Tray + EvTr

2

378.619

1.506

0.123

Tray

1

379.143

2.030

0.095

Tray + ID

2

379.265

2.152

0.089

Tray + EvTr + Tray X EvTr

3

383.128

6.015

0.013

Tray +

Tray X EvTr

2

383.549

6.437

0.010

EvTr + ID + Tray X EvTr

3

384.028

6.915

0.008

ID +

Tray X EvTr

2

384.443

7.330

0.007

EvTr

1

385.277

8.164

0.004

EvTr + ID

2

386.023

8.910

0.003

ID

1

387.379

10.266

0.002

Tray X EvTr

1

390.277

13.164

0.000

EvTr + Tray X EvTr

2

390.516

13.404

0.000

 

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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