Appendix A. Parameter estimates and two-unit support intervals for the most parsimonious models for each of the 14 target tree species.
The tables below report the parameter estimates and two-unit support intervals for the most parsimonious models (i.e., lowest AICcorr in Table 2) for each of the 14 target tree species. Species are identified with acronyms consisting of the first two letters of the genus and the specific epithet. See Table 1 of the manuscript for full names.
TABLE A1. Number of observations (n), goodness of fit (R2), error variance proportionality (1 from Eq. 8), and potential diameter growth (PDG, in mm/yr). Parameters C and D control the shape of the function describing response of a target tree to variation in NCI (Eq. 6).
Species |
n |
R2 |
1 |
PDG |
C |
D |
ABBA |
429 |
0.253 |
0.667 |
4.876 |
21.163 |
|
0.657 - 0.677 |
4.826 - 4.926 |
20.663 - 21.663 |
||||
ACRU |
930 |
0.125 |
0.919 |
4.138 |
116.846 |
|
0.909 - 0.929 |
4.088 - 4.188 |
113.340 - 118.014 |
||||
ACSA |
751 |
0.214 |
0.807 |
5.227 |
1.943 |
|
0.797 - 0.837 |
5.175 - 5.384 |
1.443 - 2.443 |
||||
BEAL |
333 |
0.148 |
0.770 |
14.788 |
529.473 |
|
0.750 - 0.780 |
14.640 - 14.936 |
518.884 - 534.768 |
||||
BELE |
55 |
0.268 |
0.424 |
3.340 |
1.776 |
2.495 |
0.414 - 0.434 |
3.290 - 3.390 |
1.276 - 2.276 |
2.470 - 2.500 |
|||
BEPA |
480 |
0.148 |
0.779 |
2.563 |
2.553 |
|
0.769 - 0.789 |
2.513 - 2.613 |
2.053 - 3.053 |
||||
FAGR |
350 |
0.170 |
0.617 |
4.342 |
4.774 |
|
0.607 - 0.627 |
4.292 - 4.392 |
4.274 - 5.274 |
||||
FRAM |
134 |
0.202 |
0.651 |
5.187 |
0.761 |
|
0.631 - 0.661 |
5.135 - 5.239 |
0.261 - 1.261 |
||||
PIRU |
440 |
0.195 |
0.719 |
4.168 |
1.574 |
|
0.709 - 0.729 |
4.118 - 4.218 |
1.074 - 2.074 |
||||
PIST |
501 |
0.351 |
1.287 |
11.777 |
317.498 |
|
1.248 - 1.300 |
11.659 - 11.895 |
314.323 - 320.673 |
||||
POTR |
104 |
0.232 |
0.639 |
4.925 |
492.981 |
|
0.629 - 0.659 |
4.875 - 5.075 |
458.472 - 497.911 |
||||
PRSE |
53 |
0.228 |
0.847 |
6.713 |
2.000 |
|
0.837 - 0.877 |
6.578 - 6.780 |
1.500 - 2.500 |
||||
QURU |
224 |
0.272 |
0.613 |
42.911 |
527.547 |
|
0.603 - 0.633 |
42.482 - 43.340 |
522.271 - 532.822 |
||||
TSCA |
425 |
0.284 |
0.587 |
8.128 |
171.671 |
|
0.577 - 0.617 |
8.046 - 8.209 |
166.521 - 173.388 |
TABLE A2. If the parameter is listed, then for that species the sensitivity of a target tree to competition varied as a function of target tree DBH (Eq. 7). The and parameters control the scaling of the effects of neighbor size and distance on NCI (Eq. 5). The and parameters determine the effect of target tree size on potential growth (Eq. 2).
Species |
|||||
ABBA |
-0.903 |
0.000 |
0.527 |
0.137 |
10.989 |
-0.912 - -0.894 |
0.000 - 0.002 |
0.522 - 0.559 |
0.037 - 0.237 |
10.550 - 11.099 |
|
ACRU |
-1.535 |
1.763 |
0.381 |
3.163 |
98.223 |
-1.551 - -1.520 |
1.746 - 1.816 |
0.378 - 0.397 |
3.063 - 200.000 |
97.241 - 100.000 |
|
ACSA |
1.315 |
0.506 |
43.109 |
1.141 |
|
1.302 - 1.380 |
0.486 - 0.511 |
40.954 - 43.540 |
1.091 - 1.241 |
||
BEAL |
-2.000 |
0.317 |
0.474 |
0.001 |
5.523 |
-2.000 - -1.980 |
0.313 - 0.393 |
0.469 - 0.479 |
0.001 - 0.101 |
5.467 - 5.578 |
|
BELE |
2.807 |
0.440 |
0.001 |
13.788 |
|
2.723 - 2.835 |
0.418 - 0.444 |
0.001 - 0.101 |
13.650 - 13.925 |
||
BEPA |
1.194 |
0.316 |
17.925 |
0.865 |
|
1.182 - 1.230 |
0.284 - 0.319 |
17.388 - 18.105 |
0.815 - 0.915 |
||
FAGR |
-0.491 |
0.803 |
0.363 |
20.943 |
0.820 |
-0.501 - -0.486 |
0.691 - 0.811 |
0.359 - 0.403 |
20.734 - 21.781 |
0.770 - 0.870 |
|
FRAM |
1.930 |
0.000 |
40.045 |
1.129 |
|
1.660 - 1.950 |
0.000 - 0.012 |
39.645 - 40.846 |
1.079 - 1.179 |
||
PIRU |
1.366 |
0.543 |
32.751 |
0.886 |
|
1.352 - 1.380 |
0.538 - 0.548 |
32.424 - 33.079 |
0.836 - 0.936 |
||
PIST |
-1.598 |
2.084 |
0.248 |
0.284 |
5.846 |
-1.614 - -1.582 |
2.064 - 2.126 |
0.240 - 0.250 |
0.184 - 0.384 |
5.787 - 5.904 |
|
POTR |
-2.000 |
0.731 |
0.000 |
195.263 |
97.838 |
-2.000 - -1.980 |
0.710 - 0.739 |
0.000 - 0.002 |
0.001 - 197.216 |
96.860 - 100.000 |
|
PRSE |
1.041 |
0.000 |
40.749 |
0.936 |
|
0.999 - 1.051 |
0.000 - 0.002 |
40.342 - 41.564 |
0.886 - 0.986 |
||
QURU |
-2.000 |
1.961 |
0.203 |
0.001 |
6.810 |
-2.000 - -1.980 |
1.942 - 1.981 |
0.136 - 0.205 |
0.001 - 0.101 |
6.742 - 6.878 |
|
TSCA |
-1.482 |
0.493 |
0.658 |
0.001 |
9.736 |
-1.496 - -1.467 |
0.478 - 0.498 |
0.651 - 0.678 |
0.001 - 0.101 |
9.639 - 9.833 |
TABLE A3. Parameters controlling variation in potential tree growth along the first 1 or 2 ordination axes, for species for which including site effect terms improved the model. “Axis 1 Form” and “Axis 2 Form” identify whether the function used was Gaussian (G; Eq. 3) or logistic (L; Eq. 4).
Axis 1 |
Axis 2 |
|||||
Species |
Axis 1 Form |
Axis 2 Form |
X0 |
Xb |
X0 |
Xb |
ABBA |
||||||
ACRU |
G |
G |
-2.000 |
5.849 |
2.750 |
4.383 |
-2.000 - -1.920 |
5.791 - 6.200 |
2.723 - 2.750 |
4.333 - 4.433 |
|||
ACSA |
G |
G |
-2.000 |
2.406 |
0.282 |
1.555 |
-2.000 - -1.980 |
2.356 - 2.606 |
0.215 - 0.285 |
1.505 - 1.705 |
|||
BEAL |
||||||
BELE |
||||||
BEPA |
||||||
FAGR |
L |
2.168 |
5.493 |
|||
2.146 - 2.211 |
5.438 - 5.767 |
|||||
FRAM |
G |
1.267 |
1.726 |
|||
1.255 - 1.280 |
1.676 - 1.776 |
|||||
PIRU |
G |
0.066 |
1.362 |
|||
0.064 - 0.068 |
1.312 - 1.412 |
|||||
PIST |
G |
1.081 |
1.610 |
|||
1.070 - 1.092 |
1.560 - 1.660 |
|||||
POTR |
||||||
PRSE |
||||||
QURU |
G |
L |
-1.999 |
3.443 |
2.439 |
-0.388 |
-2.000 - -1.979 |
3.393 - 3.493 |
2.415 - 2.537 |
-0.413 - -0.363 |
|||
TSCA |
G |
1.996 |
3.234 |
|||
1.976 - 2.000 |
3.134 - 3.284 |
TABLE A4. Estimated competition coefficients () using the Mixed model, for the 12 species for which that grouping of competitors was the most parsimonious. The Mixed model estimated separate competition coefficients for intraspecific competition and 3 groups of interspecific competitors (weak, intermediate, and strong competitors), grouped based on the magnitude of species-specific competition coefficients estimated in the full model. Table 3 of the manuscript gives the species-specific values of for neighbors of each target tree species used for the grouping. Neighboring species with values between 0 – 0.33 were grouped as “Weak” competitors. Species with > 0.33 and <0.67 were grouped as “Intermediate” competitors, and species with > 0.67 were grouped as “Strong” competitors.
Species |
Intraspecific competition |
Interspecific competitors |
||
Weak |
Intermediate |
Strong |
||
ABBA |
0.357 |
0.174 |
0.484 |
1.000 |
0.353 - 0.360 |
0.170 - 0.175 |
0.465 - 0.489 |
0.990 - 1.000 |
|
ACRU |
1.000 |
0.000 |
0.536 |
1.000 |
0.960 - 1.000 |
0.000 - 0.001 |
0.525 - 0.541 |
0.990 - 1.000 |
|
ACSA |
1.000 |
0.153 |
0.508 |
0.763 |
0.990 - 1.000 |
0.020 - 0.154 |
0.483 - 0.513 |
0.702 - 0.771 |
|
BEAL |
0.599 |
0.051 |
0.601 |
1.000 |
0.593 - 0.605 |
0.050 - 0.052 |
0.595 - 0.619 |
0.990 - 1.000 |
|
BELE |
1.000 |
0.000 |
0.561 |
0.000 |
0.970 - 1.000 |
0.000 - 0.001 |
0.556 - 0.578 |
0.000 - 0.000 |
|
BEPA |
0.498 |
0.000 |
0.532 |
1.000 |
0.493 - 0.503 |
0.000 - 0.001 |
0.505 - 0.537 |
0.990 - 1.000 |
|
FAGR |
0.901 |
0.568 |
0.390 |
1.000 |
0.847 - 0.910 |
0.562 - 0.574 |
0.371 - 0.394 |
0.990 - 1.000 |
|
PIST |
0.880 |
0.000 |
0.606 |
1.000 |
0.854 - 0.889 |
0.000 - 0.001 |
0.600 - 0.679 |
0.990 - 1.000 |
|
POTR |
0.667 |
0.000 |
0.369 |
1.000 |
0.660 - 0.714 |
0.000 - 0.001 |
0.355 - 0.373 |
0.940 - 1.000 |
|
PRSE |
1.000 |
0.003 |
0.471 |
0.246 |
0.920 - 1.000 |
0.003 - 0.020 |
0.466 - 0.513 |
0.000 - 1.000 |
|
QURU |
1.000 |
0.000 |
0.701 |
1.000 |
0.810 - 1.000 |
0.000 - 0.001 |
0.694 - 0.729 |
0.990 - 1.000 |
|
TSCA |
1.000 |
0.000 |
0.567 |
0.847 |
0.990 - 1.000 |
0.000 - 0.001 |
0.562 - 0.573 |
0.805 - 0.855 |