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.


[Back toE093-136]