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.