Table 1.

Ability to infer the importance of competition from species' distributions models (SDMs)

Statistic derived from SDM	R 2 from linear model	Probability of ranking incorrectlya	τ	Mean estimated degrees of freedomb	σ Estimated degrees of freedom
Percent competitive exclusion
$D_{\mathrm{environment}}^2$	.007	.389	−0.22	29.41	8.153
$D_{\mathrm{improvement}}^2$	.086	.267	0.47	36.5	8.45
βcompetitor	.021	.331	−0.17	7.91	8.1
α12
$D_{\mathrm{environment}}^2$	.003	.441	−0.12	17.26	7.37
$D_{\mathrm{improvement}}^2$	.027	.504	−0.01	24.34	7.275
βcompetitor	.040	.331	−0.33	4.51	1.01

Tau refers to Kendall's tau, while estimated degrees of freedom are derived from Gaussian local‐scale additive models.

^aAs we describe in our Appendix S1, the probability of that two rankings disagree for a pair of observations is another way to represent the information in Kendall's tau.

^bThe mgcv package recommends checking dimension of the basis vector. In each case, we checked this and typically set this parameter to 4. In one case, a lower limit was set for computation 9 to speed up computation, and in another, a higher limit 100 was set.