Appendix A. Tables with additional methods and analysis for "Effects of competition on phylogenetic signal and phenotypic plasticity in plant functional traits." including descriptions of focal species (Table A1), model selection criteria (Tables A2–A5), and a priori model for pot productivity (Table A6).
TABLE A1. Species used in the species interaction experiment to determine the degree of plasticity in species traits, such as SLA, and the potential effect of such plasticity on phylogenetic signal.
Triplet |
Focal Species |
Confamilial |
1 |
Erigeron foliosus |
Solidago californica |
1 |
Erigeron glaucus |
Solidago californica |
2 |
Fragaria chiloensis |
Potentilla anserina |
2 |
Fragaria vesca |
Potentilla anserina |
3 |
Gnaphalium purpureum |
Helenium puberulum |
3 |
Gnaphalium ramosissimum |
Helenium puberulum |
4 |
Juncus breweri |
Luzula comosa |
4 |
Juncus lesueurii |
Luzula comosa |
5 |
Rumex occidentalis |
Eriogonum latifolium |
5 |
Rumex salicifolius |
Eriogonum latifolium |
6 |
Trifolium barbigerum |
Lotus heermannii |
6 |
Trifolium macraei |
Lotus heermannii |
TABLE A2. Model selection for traits, SLA and root:shoot using AICc (Burnham and Anderson 2002) with a phylogenetic generalized least squares model with Gaussian distribution (R Statistics, Version 2.11.0). SLA was square-root transformed, root:shoot and total biomass were natural log transformed. Bold values indicate models chosen by AICc and chosen models differed from less preferred models by at least 2 DAICc. Note that the three-way interaction species × soil × interactor could never be included in models as a result of complete mortality by some species in some interactor/soil treatments; the set of models evaluated never included this three-way interaction. The Brownian motion model of evolution was used to model phylogeny for SLA (DAICc > 2, compared with Grafen, not different from OU) and the Grafen model was chosen for root:shoot ratio (DAICc > 2, compared with Brownian and OU). Because models were conducted using PGLS, we used the categorical taxonomic rank "interactor," rather than the continuous variable "phylogenetic distance to interactor," in order to avoid putting branch lengths from the phylogeny in the model twice.
Total biomass |
Species |
Soil type |
Interactor |
Species × Soil type |
Species × Interactor |
Soil × Interactor |
|
AICc |
SLA |
||||||||
*** |
*** |
*** |
*** |
|
|
** |
|
3269.915 |
|
*** |
*** |
*** |
|
|
** |
|
3310.952 |
*** |
*** |
*** |
*** |
|
|
|
|
3278.838 |
|
*** |
*** |
*** |
|
|
|
|
3321.413 |
*** |
*** |
*** |
|
|
|
|
|
3549.441 |
|
*** |
*** |
|
|
|
|
|
3610.033 |
*** |
** |
|
ns |
|
|
|
|
3714.508 |
|
*** |
|
ns |
|
|
|
|
3801.727 |
*** |
|
*** |
ns |
|
|
|
|
3732.180 |
|
|
*** |
ns |
|
|
|
|
3838.222 |
*** |
** |
|
|
|
|
|
|
3705.424 |
|
*** |
|
|
|
|
|
|
3793.302 |
*** |
|
*** |
|
|
|
|
|
3722.970 |
|
|
*** |
|
|
|
|
|
3831.268 |
Root:shoot |
||||||||
† |
*** |
*** |
* |
|
|
ns |
|
2351.504 |
|
. |
*** |
** |
|
|
** |
|
2396.836 |
† |
*** |
*** |
* |
|
|
|
|
2319.578 |
|
*** |
*** |
† |
|
|
|
|
2366.440 |
† |
*** |
*** |
|
|
|
|
|
2311.416 |
|
*** |
*** |
|
|
|
|
|
2356.137 |
† |
*** |
|
ns |
|
|
|
|
2500.033 |
|
*** |
|
ns |
|
|
|
|
2494.181 |
† |
|
*** |
* |
|
|
|
|
2357.223 |
|
|
*** |
† |
|
|
|
|
2404.496 |
† |
*** |
|
|
|
|
|
|
2488.399 |
|
*** |
|
|
|
|
|
|
2482.175 |
† |
|
*** |
|
|
|
|
|
2348.348 |
|
|
*** |
|
|
|
|
|
2393.711 |
ns |
|
|
ns |
|
|
|
|
2533.336 |
|
|
|
ns |
|
|
|
|
2528.103 |
*** P < 0.001, ** P < 0.01, * P < 0.05, † 0.10 > P > 0.05, ns P > 0.10
TABLE A3. Model selection for trait divergence, with phylogeny modeled using the Grafen model for divergence in SLA and the OU model for divergence in root:shoot ratio, as chosen by AICc. Models with phylogeny were preferred to models without phylogeny (DAICc > 2). Divergence in SLA and root:shoot ratio were natural log transformed. Species × soil type, species × interactor, and soil × interactor could not be tested in the PGLS. Models with higher order interactions that could not be tested (due to mortality or small plant size that precluded SLA measurements) are not included.
Total biomass |
Species |
Soil type |
Interactor |
|
AICc |
Divergence in SLA |
|||||
* |
*** |
ns |
** |
|
727.8457 |
|
*** |
ns |
** |
|
730.9047 |
* |
*** |
ns |
|
|
735.1393 |
|
*** |
ns |
|
|
737.0484 |
* |
*** |
|
*** |
|
719.5184 |
|
*** |
|
** |
|
723.1253 |
** |
|
ns |
*** |
|
725.3860 |
|
|
ns |
*** |
|
729.5407 |
* |
*** |
|
|
|
727.7911 |
|
*** |
|
|
|
729.8763 |
** |
|
ns |
|
|
737.4662 |
|
|
ns |
|
|
741.2024 |
** |
|
|
*** |
|
718.8169 |
|
|
|
*** |
|
722.7510 |
Divergence in root:shoot ratio |
|||||
ns |
*** |
*** |
*** |
|
612.4880 |
|
*** |
*** |
*** |
|
606.5201 |
ns |
*** |
*** |
|
|
650.3693 |
ns |
ns |
|
ns |
|
653.8381 |
|
ns |
|
ns |
|
649.2391 |
ns |
|
† |
ns |
|
666.3739 |
|
|
* |
ns |
|
661.2890 |
ns |
ns |
|
|
|
650.1598 |
|
ns |
|
|
|
645.4724 |
ns |
|
† |
|
|
662.7309 |
|
|
* |
|
|
657.6534 |
ns |
|
|
ns |
|
713.8320 |
|
|
|
ns |
|
709.0255 |
*** P < 0.001, ** P < 0.01, * P < 0.05, † 0.10 > P > 0.05, ns P > 0.10
TABLE A4. Model selection for trait divergence and plasticity to test the hypothesis that trait divergence as a result of phenotypic plasticity is potentially adaptive (Table 4). In these tests, congener, and conspecific competition treatments were treated separately in analyses to remove trait divergence owing to species' differences. The phylogeny was modeled with the Brownian, Grafen, or OU model, as chosen by AICc. The model with phylogeny was preferred to the model without phylogeny in most cases (DAICc > 2), with exceptions noted below. Models that could not be tested (e.g., due to mortality) are not included.
Species |
Divergence in trait |
Soil type |
Species × divergence |
Species × soil |
Divergence × soil |
Species × divergence × soil |
AICc |
Trait = SLA, competition = conspecific (Grafen) |
|||||||
*** |
ns |
*** |
|
|
ns |
|
354.3137 |
|
ns |
*** |
|
|
ns |
|
367.0289 |
*** |
ns |
*** |
|
|
|
|
342.5930 |
|
ns |
*** |
|
|
|
|
356.4058 |
*** |
ns |
|
|
|
|
|
353.4284 |
|
ns |
|
|
|
|
|
363.4151 |
*** |
|
*** |
|
|
|
|
338.1516 |
|
|
*** |
|
|
|
|
352.6533 |
Trait = SLA, competition = congener (OU) |
|||||||
ns |
ns |
** |
|
|
† |
|
138.1199 |
|
ns |
** |
|
|
† |
|
137.2301 |
ns |
ns |
** |
|
|
|
|
130.5612 |
|
ns |
** |
|
|
|
|
134.1935 |
ns |
ns |
|
|
|
|
|
130.4537 |
|
ns |
|
|
|
|
|
137.1074 |
ns |
|
** |
|
|
|
|
127.2657 |
|
|
** |
|
|
|
|
131.6789 |
Trait = SLA, competition = confamilial (model without phylogeny preferred) |
|||||||
ns |
ns |
ns |
ns |
ns |
ns |
ns |
118.2484 |
ns |
ns |
ns |
ns |
ns |
ns |
|
210.7398 |
ns |
ns |
ns |
ns |
ns |
|
|
107.5414 |
ns |
ns |
ns |
ns |
|
ns |
|
107.7843 |
ns |
ns |
ns |
|
ns |
ns |
|
106.5978 |
ns |
ns |
ns |
ns |
|
|
|
89.3565 |
ns |
ns |
ns |
|
ns |
|
|
89.3523 |
† |
ns |
ns |
|
|
ns |
|
89.5861 |
† |
ns |
ns |
|
|
|
|
83.4379 |
|
ns |
ns |
|
|
|
|
83.1105 |
† |
ns |
|
|
|
|
|
80.2613 |
|
ns |
|
|
|
|
|
81.4828 |
† |
|
ns |
|
|
|
|
77.7841 |
Trait = root:shoot, competition = conspecific (OU model) |
|||||||
ns |
ns |
*** |
|
|
ns |
|
268.5244 |
|
ns |
*** |
|
|
ns |
|
280.2765 |
ns |
ns |
*** |
|
|
|
|
256.4279 |
|
ns |
*** |
|
|
|
|
269.9271 |
ns |
ns |
|
|
|
|
|
270.0899 |
|
ns |
|
|
|
|
|
283.8748 |
ns |
|
*** |
|
|
|
|
249.4001 |
|
|
*** |
|
|
|
|
263.4522 |
Trait = root:shoot, competition = congener (OU) |
|||||||
ns |
ns |
** |
|
|
ns |
|
143.9204 |
|
ns |
** |
|
|
ns |
|
142.7785 |
ns |
ns |
** |
|
|
|
|
125.8187 |
|
ns |
** |
|
|
|
|
129.2172 |
ns |
ns |
|
|
|
|
|
126.9778 |
|
ns |
|
|
|
|
|
133.5080 |
ns |
|
*** |
|
|
|
|
119.3582 |
|
|
*** |
|
|
|
|
123.5406 |
Trait = root:shoot, competition = confamilial (model without phylogeny is preferred) |
|||||||
** |
* |
ns |
ns |
ns |
ns |
ns |
-63.8925 |
** |
* |
ns |
ns |
ns |
|
|
86.5864 |
** |
* |
ns |
ns |
|
ns |
|
85.7054 |
** |
* |
ns |
|
ns |
ns |
|
84.9496 |
** |
* |
ns |
ns |
|
|
|
49.7918 |
** |
* |
ns |
|
ns |
|
|
49.2313 |
** |
* |
ns |
|
|
ns |
|
48.8251 |
|
† |
ns |
|
|
ns |
|
44.3411 |
*** |
ns |
ns |
|
|
|
|
36.3463 |
|
† |
ns |
|
|
|
|
38.4459 |
*** |
ns |
|
|
|
|
|
28.6722 |
|
* |
|
|
|
|
|
33.2899 |
*** |
|
ns |
|
|
|
|
28.0294 |
|
|
ns |
|
|
|
|
36.0336 |
*** P < 0.001, ** P < 0.01, * P < 0.05, † P < 0.10, ns P > 0.10.
TABLE A5. The 10 most probable models ranked by AICc, relating standardized total biomass per pot (natural-log transformed), to fixed treatment effects, including divergence in root:shoot ratio and SLA, which were natural-log transformed for analysis. Soil × phylogenetic distance was included in model selection, but was not included amongst the top 10 models. An 'X' indicates that the effect was included in the model.
Species |
Soil |
PD |
SLA |
RS |
S × soil |
S × PD |
AICc |
Rank |
X |
X |
X |
X |
X |
X |
X |
428.7 |
1 |
X |
X |
X |
X |
X |
X |
|
432.2 |
2 |
X |
|
X |
X |
X |
|
|
434.1 |
3 |
X |
|
X |
X |
X |
|
X |
434.3 |
4 |
X |
|
|
|
X |
|
|
436.2 |
5 |
X |
X |
X |
X |
X |
|
X |
439.4 |
6 |
X |
X |
X |
X |
X |
|
|
439.7 |
7 |
X |
X |
|
|
X |
|
|
440.8 |
8 |
X |
X |
|
X |
X |
|
|
442.1 |
9 |
X |
X |
X |
|
X |
|
|
444.2 |
10 |
TABLE A6. A priori model for standardized total biomass (natural-log transformed) as a function of random effects, species, species × soil, species × phylogenetic distance, and the following fixed effects. The a priori model had an AICc of 447.9 > 2 DAICc greater than that of the best model (AICc = 428.7), presented in Table 5 (Table A5).
Source |
df |
df denom. |
F ratio |
P value |
Phylogenetic distance |
1 |
5 |
13.56 |
0.01 |
Divergence in root:shoot ratio |
1 |
255 |
10.94 |
< 0.01 |
Divergence SLA |
1 |
247 |
6.08 |
0.01 |
Soil type |
3 |
11 |
0.23 |
0.88 |
Phylogenetic distance × soil type |
3 |
90 |
2.96 |
0.04 |
Model adjusted R² = 0.44.
LITERATURE CITED
Blomberg, S. P., T. Garland, and A. R. Ives. 2003. Testing for phylogenetic signal in comparative data: Behavioral traits are more labile. Evolution 57:717–745.
Burnham, K. P., and D. Anderson. 2002. Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach. Second edition edition. Springer, New York, New York, USA.