Appendix F. Results of the PCA, RDA and RDA with latents with 10 traits, the extended SEM, path coefficients and justification.
Here, we determine whether the conclusion that disturbance and nutrient availability do not act on a separate suite of traits, still holds when the model is extended with three more traits (Table F1).
To account for the fact that an increase in canopy height often leads to shift in other traits that are caused by a shift in growth form and not by height per se, we recorded whether a species had a woody stem (woody / non-woody). This simple division distinguishes mainly investments in structural biomass. In this paper we will refer to a shift towards woodiness as GF approaches one. In addition we also included seed mass of the dispergule (SM_d in mg; including the mass of the germinule) and a phenology trait flowering onset (FO in months).
TABLE F1. Extra traits used for the analysis of the extended model, the number of species involved and its literature sources. In total 346 species were present in the plots.
Trait category |
Trait (acronym) | Scale and units |
No. species |
Source |
Allometric traits |
Growth form (GF) | Ordinal (0: non-woody, 1: woody) | 346 | 1 |
Seed traits |
Seed mass with dispergule included (SM_d) |
Log 10 Continuous (mg) | 276 | 2 |
Phenology traits |
Flowering onset (FO) | Ordinal (Months, 1: Jan. – 12: Dec.) | 342 | 1 |
Sources. 1. BioBase 2003, Centraal Bureau voor de Statistiek, Voorburg/Heerlen.
2. see Douma et al. (in press)
The covariance among trait averages of species assemblages was analyzed first without explicitly defining possible underlying causes of common axes of variability between plots by submitting 156 plots × 10 traits to a principal component analysis. The results are shown in Table F2. Subsequently, we explicitly constrained the multivariate structure in traits by environmental data, but still without imposing any causal hypotheses, using a redundancy analysis (RDA; ter Braak 1987) based on 3 environmental variables (Soil C/P ratio, Soil C/N ratio, ‘time since disturbance’). The results are shown in Table F3.
TABLE F2. Results of Principal Component Analysis (PCA) of the site-trait matrix (156 sites × 10 traits). The explained variance is shown as well as the trait scores. Abbreviations of traits: Leaf nitrogen content (LNC), leaf phosphorus content (LPC), specific leaf area (SLA), seed mass of the germinule (SM_g), seed mass of the dispergule (SM_d), maximum canopy height (maxCH), Growth form (GF), relative growth rate (RGR), germination onset (GO), flowering onset (FO).
PCA 1 | PCA 2 | |
Cumulative Explained Variance |
0.55 | 0.79 |
Scores | ||
SLA | -0.46 | 1.55 |
LNC | -0.86 | 1.39 |
LPC | -0.64 | 1.69 |
RGR | 0.74 | 1.25 |
maxCH | -1.20 | -0.60 |
GF | -1.20 | -0.73 |
SM_g | -1.17 | 0.14 |
SM_d | -1.27 | -0.23 |
GO | 1.11 | 0.45 |
FO | 0.97 | -0.18 |
TABLE F3. Results of the RDA with the relevé-traits (156 sites × 10 traits) constrained by 2 environmental factors (measured TSD and measured Soil C/P and Soil C/N). The cumulative explained variance of the constrained axis, and the scores of the environmental constraints are shown.
RDA1 | RDA2 | RDA3 | |
Cumulative explained variance |
0.35 | 0.41 | 0.42 |
LogC/N | 0.176 | -0.5874 | -0.78997 |
LogC/P | 0.358 | -0.9011 | 0.24455 |
TSD | -0.9564 | -0.2889 | -0.04322 |
The model developed in this appendix differs from the way the environmental drivers affect the traits. Since exact measurements of disturbance frequency and nutrient availability at temporal and spatial scales relevant to plants are rarely directly available; i.e. they are “latent” variables, one usually has only indirect and imperfect measurements. This is particularly true for nutrient availability, which is highly dynamic in space and time. Therefore soil nutrient concentrations do not necessary reflect nutrient availability as experienced by plants in the long run (Ordoñez et al. 2010). SEM allows us to explicitly incorporate the uncertainty by introducing a latent variable (Shipley 2002), which is estimated as the common variance of the soil nutrient parameters and the traits associated with the latent variable. Based on two latents a new SEM was developed, shown in Fig. F1. Note that the latent specified in this model takes the common variance of the leaf traits and the soil C/P ratio (a model including soil C/N did not fit) and measured time since disturbance and maxCH, GF, SM_d and GO. It would be better to have to obtain multiple and independent estimates of the error associated with soil fertility and disturbance but that this is not yet possible. Alternatively, one could build more explicit measurement models of environmental drivers that include more or better indicators and test them with independent data. This is not possible with our data
The model as presented in Fig. F1 fit the data (χ2 = 47.68, df = 35, P = 0.07) The covariance matrix and the modeled covariance matrices are given in Table F4 and F5. Parameter estimates and standard errors of the model are given in Table F6. The fit increased significantly if a free covariance between LNC and SM_g was added (χ2 = 31.89, df = 34, P = 0.57). Because RGR is central to the model and we lowered the minimum amount of species needed to calculate a plot mean, we ran a control analysis which revealed that the structure of the SEM, the significance and sign of the paths remained unchanged for modeled values of RGR (see Appendix C for details).
FIG. F1. Standardized path coefficients, explained variance (in squares) and significance (between parentheses) of the final model of nutrient availability, disturbance and their related traits (χ2 = 47.68, df = 35, P = 0.07, only significant paths shown). Note that the relationship between nutrient availability and Soil C/P ratio is negative.
TABLE F1. Covariance matrix of the variables used in the model of F1.
10Log C/P | TSD | maxCH | LNC | SLA | SM_G | SM_D | LPC | RGR | GO | FO | GF | |
10Log C/P | 0.135 | |||||||||||
TSD | -0.855 | 630.625 | ||||||||||
maxCH | -0.024 | 7.365 | 0.14 | |||||||||
LNC | -0.638 | 20.15 | 0.465 | 10.379 | ||||||||
SLA | -0.451 | 20.216 | 0.096 | 6.814 | 12.042 | |||||||
SM_G | -0.042 | 6.069 | 0.12 | 0.854 | 0.413 | 0.191 | ||||||
SM_D | -0.048 | 11.959 | 0.209 | 1.063 | 0.567 | 0.249 | 0.413 | |||||
LPC | -0.102 | 1.676 | 0.037 | 1.417 | 1.257 | 0.095 | 0.108 | 0.26 | ||||
RGR | -0.001 | -0.489 | -0.007 | 0.006 | 0.018 | -0.006 | -0.012 | 0.003 | 0.001 | |||
GO | 0.005 | -1.152 | -0.021 | -0.086 | -0.032 | -0.018 | -0.033 | -0.007 | 0.001 | 0.005 | ||
FO | 0.036 | -4.624 | -0.078 | -0.593 | -0.349 | -0.104 | -0.158 | -0.087 | 0.005 | 0.014 | 0.163 | |
GF | -0.012 | 4.992 | 0.087 | 0.249 | 0.081 | 0.072 | 0.135 | 0.015 | -0.005 | -0.014 | -0.056 | 0.059 |
TABLE F5. Modeled covariance matrix of the model Fig. F1.
10Log C/P |
TSD (measured) |
maxCH | LNC | SLA | SM_G | SM_D | LPC | RGR | GO | FO | GF |
Latent Nutrient Availability |
Latent TSD |
|
10Log C/P | 0.135 | |||||||||||||
TSD (measured) |
-1.627 | 630.625 | ||||||||||||
maxCH | -0.032 | 7.320 | 0.140 | |||||||||||
LNC | -0.596 | 23.206 | 0.461 | 10.379 | ||||||||||
SLA | -0.484 | 21.227 | 0.102 | 6.798 | 11.955 | |||||||||
SM_G | -0.051 | 6.415 | 0.120 | 0.742 | 0.439 | 0.191 | ||||||||
SM_D | -0.065 | 12.251 | 0.209 | 0.930 | 0.573 | 0.250 | 0.414 | |||||||
LPC | -0.100 | 1.919 | 0.038 | 1.421 | 1.242 | 0.097 | 0.102 | 0.259 | ||||||
RGR | 0.000 | -0.484 | -0.007 | 0.009 | 0.017 | -0.006 | -0.012 | 0.004 | 0.001 | |||||
GO | 0.006 | -1.172 | -0.021 | -0.080 | -0.034 | -0.019 | -0.033 | -0.008 | 0.001 | 0.005 | ||||
FO | 0.042 | -4.509 | -0.078 | -0.600 | -0.443 | -0.103 | -0.154 | -0.085 | 0.004 | 0.014 | 0.162 | |||
GF | -0.016 | 4.976 | 0.086 | 0.238 | 0.087 | 0.072 | 0.135 | 0.015 | -0.005 | -0.014 | -0.056 | 0.058 | ||
Latent Nutrient Availability |
0.204 | -7.960 | -0.155 | -2.915 | -2.367 | -0.252 | -0.316 | -0.488 | -0.002 | 0.027 | 0.205 | -0.080 | 1.000 | |
Latent TSD |
-1.627 | 497.212 | 7.320 | 23.206 | 21.227 | 6.415 | 12.251 | 1.919 | -0.484 | -1.172 | -4.509 | 4.976 | -7.960 | 497.212 |
Mathematical specification of the model (Fig. F1):
10log Soil C/P = 0.204 × latent_NA† + 1.000 e_10log Soil C/P
TSD = 1.000 latent_TSD‡ + 1.000 e_TSD
maxCH = 3.735 × V44 + 0.018 × latent_TSD + 1.000 e_maxCH
LNC = -2.915 × latent_NA + 1.000 e_LNC
SLA = -10.585 × maxCH -2.778 × latent_NA + 0.154 × latent_TSD + 1.000 e_SLA
SM_g = 0.724 × maxCH - 0.140 × latent_NA + 1.000 e_SM_g
SM_d = 0.801 × SM_g + 0.650 × GF + 0.008 × latent_TSD + 1.000 e_SM_d
LPC = -0.323 × maxCH - 0.538 × latent_NA + 1.000 e_LPC
RGR = 0.002 × LNC + 0.003 × SLA - 0.117 × GF + 1.000 E44
GO = -0.059 × maxCH - .138 × GF + 0.007 × latent_NA + 1.000 e_GO
FO = 1.159 × maxCH - .260 × SM_g - 2.809 × GF + 0.156 × latent_NA + 0.008 × latent_TSD + 1.000 e_FO
†latent_NA is latent Nutrient Availability, ‡latent_TSD is latent Time since disturbance
Free covariances:
latent_NA - latent_TSD: -7.96
latent_NA - e_GF: 0.017
SM_g - RGR: -0.001
TABLE F6. Unstandardized path coefficients of full model (Fig. 3c main text). Standard error given in brackets, error variances with standard error in diagonal (calculated with robust estimates). Traits in rows are cause and traits in columns are effects. Correlational relationships in italics. Abbreviations of variables: Leaf nitrogen content (LNC), leaf phosphorus content (LPC), specific leaf area (SLA), seed mass of the germinule (SM_g), seed mass of the dispergule (SM_d), maximum canopy height (maxCH), Growth form (GF), relative growth rate (RGR), germination onset (GO), flowering onset (FO). Time since disturbance latent (TSD_l), Soil CP ratio (Soil CP), Time since disturbance measured (TSD_m).
Nutrient availability |
TSD_l | SoilCP | TSD_m | LNC | SLA | LPC | RGR | maxCH | GF | SM_g | SM_d | GO | FO | |
Nutrient availability |
1 | 7.960 (2.021) | -0.204 (0.027) | 2.915 (0.202) | 2.778 (0.272) | 0.538 (0.034) | -0.017 (0.005) | 0.140 (0.025) | -0.007 (0.004) | -0.156 (0.030) | ||||
TSD_l | 0.026 | 497.212 (72.414) | 1 | 0.154 (0.028) | 0.018 (0.002) | 0.003 (0.001) | 0.008 (0.003) | 0.008 (0.004) | ||||||
SoilCP | 0.094 (0.011) | |||||||||||||
TSD_m | 133.413 (23.910) | |||||||||||||
LNC | 1.880 (0.286) | 0.002 (0.001) | ||||||||||||
SLA | 3.466 (0.601) | 0.003 (0.001) | ||||||||||||
LPC | 0.009 (0.006) | |||||||||||||
RGR | 0.001 (0.000) | 3.735 (1.480) | -0.001 (0.001) | |||||||||||
maxCH | -10.581 (1.665) | -0.323 (0.062) | 0.043 (0.014) | 0.462 (0.048) | 0.724 (0.066) | -0.059 (0.030) | 1.159 (0.223) | |||||||
GF | -0.117 (0.010) | 0.003 (0.001) | 0.649 (0.237) | -0.138 (0.044) | -2.809 (0.472) | |||||||||
SM_g | 0.072 (0.008) | 0.801 (0.047) | -0.260 (0.082) | |||||||||||
SM_d | 0.031 (0.004) | |||||||||||||
GO | 0.001 (0.000) | |||||||||||||
FO | 0.071 (0.009) |
An alternative SEM that was consistent with the data (χ2= 49.93, df = 36, P = 0.06, CFI = 0.99) is nested in Fig. F1 and differed in a few aspects: the causal direction between maxCH and GF is reversed, the path from nutrient-availability to GF was removed, a free covariance between nutrient availability and maxCH was added (also possible with a path from nutrient availability to maxCH), and the path from TSD to maxCH was removed. The path from SLA to RGR was not significant anymore. Reversing the path from maxCH to SLA lead to a model that was not consistent with the data (P = 0.0003). Although the mdoel is consistent with the data, it is ecologically less likely as maxCH is not driven at all by ‘time since disturbance’. Additionally, RGR is not significantly affected by SLA. Therefore based on ecological considerations we prefer the model presented in Fig. F1.
Replacing the measured estimates by the latent estimates of nutrient availability and disturbance (Fig. F1) to a RDA, increased the explained variance of the environmental drivers to 70%, i.e. 89% of the maximally explained variation (Table F7), Fig. F2.
TABLE F7. Results of the RDA with the relevé-traits (156 sites × 10 traits) constrained by 2 environmental factors (latent TSD and latent Nutrient availability (Nu.availability)). The cumulative explained variance of the constrained axis, and the scores of the environmental constraints are shown.
RDA1 | RDA2 | |
Cumulative explained variance |
0.50 | 0.70 |
Nutrient availability |
-0.72 | 0.70 |
TSD | -0.90 | -0.44 |
FIG. F2. RDA with the relevé-traits (156 sites × 10 traits) constrained by 2 environmental factors (latent TSD and latent Nutrient availability (abbreviated by Nu.avail)). Abbreviations of traits and environmental drivers: Leaf nitrogen content (LNC), leaf phosphorus content (LPC), specific leaf area (SLA), seed mass of the germinule (SM_g), seed mass of the dispergule (SM_d), maximum canopy height (maxCH), Growth form (GF), relative growth rate (RGR), germination onset (GO), flowering onset (FO).
The relative effects of environmental drivers on traits were calculated in the same way as the model from Fig. 3 (of the manuscript). These calculations showed that nutrient availability predominantly constrained leaf traits, such as SLA, LNC and LPC and that ‘time since disturbance’predominantly affected allometric, seed traits and relative growth rate, constraining maxCH, GF, RGR, SM_g, SM_d and GO (Table F8). However, the effect of both drivers was not simply restricted to one suite of traits, but affected both suites of traits simultaneously. For example SM_g and FO were almost equally affected by nutrient availability and ‘time since disturbance’. The constraining effects of environmental drivers on traits were only in 5 out of 10 traits stronger than trait-trait constraints. Allometric traits predominantly constrained other traits, in particular seed- and phenology traits.
TABLE F8. The effect of environmental constraints (cause; columns) on the selection of individual traits (effect; rows) relative to the effect of trait-trait constraints. The total effects of the two environmental drivers and the trait-trait constraints add to one. The effect of the environmental drivers on traits is decomposed in both direct effects (DE) and indirect effects (IE; effects transmitted via other traits; Fig. F1). Traits-trait constraints were grouped into four categories: leaf traits (LNC, LPC and SLA), allometric traits (maxCH and GF), seed traits (SM_g and SM_d) and relative growth rate (RGR). Additionally, the dominant environmental driver and the dominant trait-trait constraints, as well as the explained variance of the traits.
Cause | Environmental constraint | Trait–trait constraint |
Dominant driver |
Dominant trait |
R2 sub-model 2: disturbance* |
|||||
Effect |
Nutrient availability |
Time since disturbance |
DE > IE |
Leaf traits |
Allometric traits |
Seed traits |
Relative growth rate |
|||
LNC | 1.00 | 0.00 | yes | 0.00 | 0.00 | 0.00 | 0.00 | Nutrients | ||
SLA | 0.30 | 0.01 | 0.06 | 0.49 | 0.00 | 0.13 | Nutrients | Allometric traits | ||
LPC | 0.66 | 0.13 | yes | 0.02 | 0.15 | 0.00 | 0.04 | Nutrients | Allometric traits | |
RGR | 0.10 | 0.25 | 0.12 | 0.45 | 0.00 | 0.08 | Disturbance | Allometric traits | ||
maxCH | 0.05 | 0.48 | yes | 0.07 | 0.26 | 0.00 | 0.15 | Disturbance | Allometric traits | 0.83 |
GF | 0.04 | 0.46 | 0.04 | 0.36 | 0.00 | 0.10 | Disturbance | Allometric traits | 0.96 | |
SM_g | 0.22 | 0.30 | 0.04 | 0.35 | 0.00 | 0.09 | Disturbance | Allometric traits | 0.53 | |
SM_d | 0.10 | 0.34 | 0.03 | 0.23 | 0.24 | 0.06 | Disturbance | Seed traits | 0.93 | |
GO | 0.08 | 0.34 | 0.04 | 0.45 | 0.00 | 0.09 | Disturbance | Allometric traits | 0.69 | |
FO | 0.16 | 0.10 | yes | 0.01 | 0.60 | 0.09 | 0.03 | Nutrients | Allometric traits | 0.47 |
* see Fig. F1
LITERATURE CITED
Douma, J. C., Aerts, R., Witte, J. P. M., Bekker, R. M., Kunzmann, D., Metselaar, K., and van Bodegom, P. M. (2011) A combination of functionally different plant traits provides a means to quantitatively predict a broad range of species assemblages in NW Europe. Ecography. DOI: 10.1111/j.1600-0587.2011.07068.x (in press)
Ordoñez, J. C., P. M. van Bodegom, J. P. M. Witte, R. P. Bartholomeus, J. R. van Hal, and R. Aerts. 2010. Plant strategies in relation to resource supply in mesic to wet environments: does theory mirror nature? American Naturalist 175:225–239.
Shipley, B. 2002, Cause and Correlation in Biology - a user's guide to path analysis, structural equations and causal inference. Cambridge, Cambridge University Press.
ter Braak, C. J. F. 1987. Ordination in R. H. G. Jongman, and O. F. R. van Tongeren, eds. Data analysis in community and landscape ecology. Wageningen, Pudoc.