Ecological Archives A014-031-A1

Katharina E. Fabricius and Glenn De'ath. 2004. Identifying ecological change and its causes: a case study on coral reefs. Ecological Applications 14:1448–1465.

Appendix A. Simulation results to determine analysis methods for small data sets.

Table A1. Results of 1000 simulations of model selection used to identify the optimum method of analysis of the small (N = 12) and larger (N = 50) data sets relating biological properties to ecological gradients and regional differences.

Sample size (N)

Selected model

PTest

AIC

AICc

BIC

P-AIC

P-AICc

P-BIC

 

1

52

147

45

106

0.26

0.08

0.22

 

2

130

347

225

344

0.34

0.30

0.36

12

3

742

454

632

492

0.33

0.50

0.34

 

4

70

52

97

78

0.07

0.12

0.08

 

5

6

0

1

0

0.00

0.00

0.00

 

1

38

150

109

36

0.34

0.28

0.16

 

2

725

748

771

786

0.54

0.55

0.61

50

3

237

102

120

178

0.12

0.17

0.23

 

4

0

0

0

0

0.00

0.00

0.00

 

5

0

0

0

0

0.00

0.00

0.00

   Notes: Five linear regression models, namely (1) different gradient effects (slopes) within each region and region effects (intercepts), (2) same slope for both regions, but different intercepts (region effects) (3) single gradient common to both regions, (4) no gradient effect but regional effects, and (5) no gradient or regional effects. The data were generated by the model 2 (region and gradient effects; bold letters) with the ratio of systematic-to-error variance typical of the observed data. Columns 3–6 show the frequency that each of the five models was selected by backward elimination (P > 0.05), AIC, AICc and BIC. Columns 7–9 show posterior probabilities for each of the five models averaged over the 1000 simulations based on AIC, AICc and BIC.



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