Ecological Archives E093-136-A1
Cajo J. F. ter Braak, Anouk Cormont, and Stéphane Dray. 2012. Improved testing of species traits–environment relationships in the fourth corner problem. Ecology 93:1525–1526. http://dx.doi.org/10.1890/12-0126.1
Appendix A (Table A1). Results of the simulation study for the two-step and sequential approaches. Rejection rates of H0 (tested against the alternative hypothesis that both R and Q are linked to L) at the 5% significance level. In scenario 1, R and Q are linked to L (in scenario 1N, a normal noise is added to reduce the intensity of the link). In scenario 2, only R is linked to L. In scenario 3, only Q is linked to L. In scenario 4, both R and Q are not linked to L. µtol is the average species tolerance (see Dray and Legendre (2008) for details).
μtol |
No. sites |
No. species |
Rejection rate for scenario | |||||||||
Two-step approach | Sequential approach | |||||||||||
1 | 1N | 2 | 3 | 4 | 1 | 1N | 2 | 3 | 4 | |||
10 | 30 | 30 | 1.000 | 0.802 | 0.232 | 0.217 | 0.130 | 1.000 | 0.480 | 0.058 | 0.046 | 0.012 |
10 | 30 | 50 | 1.000 | 0.915 | 0.220 | 0.240 | 0.123 | 1.000 | 0.670 | 0.038 | 0.066 | 0.011 |
10 | 30 | 100 | 1.000 | 0.992 | 0.228 | 0.237 | 0.116 | 1.000 | 0.903 | 0.039 | 0.053 | 0.005 |
10 | 50 | 30 | 1.000 | 0.916 | 0.210 | 0.215 | 0.140 | 1.000 | 0.652 | 0.052 | 0.040 | 0.014 |
10 | 50 | 50 | 1.000 | 0.976 | 0.219 | 0.213 | 0.122 | 1.000 | 0.854 | 0.059 | 0.041 | 0.008 |
10 | 50 | 100 | 1.000 | 1.000 | 0.221 | 0.236 | 0.125 | 1.000 | 0.989 | 0.052 | 0.047 | 0.014 |
10 | 100 | 30 | 1.000 | 0.989 | 0.212 | 0.246 | 0.108 | 1.000 | 0.902 | 0.040 | 0.057 | 0.007 |
10 | 100 | 50 | 1.000 | 0.999 | 0.230 | 0.212 | 0.116 | 1.000 | 0.984 | 0.058 | 0.035 | 0.006 |
10 | 100 | 100 | 1.000 | 1.000 | 0.224 | 0.229 | 0.126 | 1.000 | 1.000 | 0.049 | 0.045 | 0.016 |
30 | 30 | 30 | 1.000 | 0.938 | 0.213 | 0.204 | 0.078 | 1.000 | 0.728 | 0.040 | 0.043 | 0.004 |
30 | 30 | 50 | 1.000 | 0.996 | 0.238 | 0.237 | 0.080 | 1.000 | 0.918 | 0.061 | 0.057 | 0.005 |
30 | 30 | 100 | 1.000 | 1.000 | 0.258 | 0.243 | 0.077 | 1.000 | 0.999 | 0.064 | 0.053 | 0.005 |
30 | 50 | 30 | 1.000 | 0.988 | 0.218 | 0.192 | 0.085 | 1.000 | 0.908 | 0.044 | 0.048 | 0.006 |
30 | 50 | 50 | 1.000 | 0.999 | 0.219 | 0.215 | 0.091 | 1.000 | 0.994 | 0.058 | 0.044 | 0.003 |
30 | 50 | 100 | 1.000 | 1.000 | 0.250 | 0.232 | 0.094 | 1.000 | 1.000 | 0.068 | 0.044 | 0.006 |
30 | 100 | 30 | 1.000 | 1.000 | 0.213 | 0.199 | 0.083 | 1.000 | 0.995 | 0.048 | 0.036 | 0.005 |
30 | 100 | 50 | 1.000 | 1.000 | 0.219 | 0.238 | 0.101 | 1.000 | 1.000 | 0.054 | 0.048 | 0.003 |
30 | 100 | 100 | 1.000 | 1.000 | 0.198 | 0.230 | 0.082 | 1.000 | 1.000 | 0.050 | 0.047 | 0.004 |
60 | 30 | 30 | 1.000 | 0.781 | 0.224 | 0.217 | 0.068 | 1.000 | 0.404 | 0.043 | 0.059 | 0.003 |
60 | 30 | 50 | 1.000 | 0.897 | 0.234 | 0.213 | 0.039 | 1.000 | 0.609 | 0.055 | 0.049 | 0.001 |
60 | 30 | 100 | 1.000 | 0.989 | 0.218 | 0.218 | 0.052 | 1.000 | 0.882 | 0.041 | 0.052 | 0.005 |
60 | 50 | 30 | 1.000 | 0.891 | 0.224 | 0.235 | 0.061 | 1.000 | 0.625 | 0.044 | 0.054 | 0.002 |
60 | 50 | 50 | 1.000 | 0.958 | 0.217 | 0.219 | 0.057 | 1.000 | 0.796 | 0.049 | 0.042 | 0.003 |
60 | 50 | 100 | 1.000 | 1.000 | 0.204 | 0.209 | 0.056 | 1.000 | 0.979 | 0.044 | 0.052 | 0.003 |
60 | 100 | 30 | 1.000 | 0.974 | 0.211 | 0.250 | 0.057 | 1.000 | 0.864 | 0.048 | 0.058 | 0.002 |
60 | 100 | 50 | 1.000 | 1.000 | 0.219 | 0.237 | 0.047 | 1.000 | 0.982 | 0.041 | 0.051 | 0.003 |
60 | 100 | 100 | 1.000 | 1.000 | 0.223 | 0.212 | 0.066 | 1.000 | 0.998 | 0.050 | 0.034 | 0.002 |
Literature Cited
Dray, S., and P. Legendre. 2008. Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology 89:3400–3412.