Content uploaded by Sean Michaletz
Author content
All content in this area was uploaded by Sean Michaletz on Dec 06, 2017
Content may be subject to copyright.
Supplementary Information
Drivers of terrestrial plant production across broad geographic gradients
Sean T. Michaletz, Andrew J. Kerkhoff and Brian J. Enquist
Corresponding author: Sean T. Michaletz (michaletz@email.arizona.edu)
Contents
1. Figure S1 Chi-square Q-Q plot illustrating structural equation model variables departure
from multivariate normality.
2. Appendix S1 Piecewise structural equation modelling of relationships between growing
season length, average annual temperature, mean annual precipitation, and global net primary
production.
a. Table S1 Piecewise structural equation models exploring drivers of net primary
production across global climate gradients, with pathways from growing season
length to average annual temperature and mean annual precipitation as proposed by
Chu et al. (2016).
b. Table S2 Piecewise structural equation models exploring drivers of net primary
production across global climate gradients, based on Chu et al. (2016) Model C but
with revised pathways from average annual temperature and mean annual
precipitation to growing season length.
c. Figure S2 Piecewise structural equation models exploring drivers of net primary
production across global climate gradients, with pathways from growing season
length to average annual temperature and mean annual precipitation as proposed by
Chu et al. (2016).
d. Figure S2 Piecewise structural equation models exploring drivers of net primary
production across global climate gradients, with pathways from growing season
length to average annual temperature and mean annual precipitation as proposed by
Chu et al. (2016).
e. Figure S3 Piecewise structural equation models exploring drivers of net primary
production across global climate gradients, based on Chu et al. (2016) Model C but
with revised pathways from average annual temperature and mean annual
precipitation to growing season length.
3. References
1. Figure S1 Chi-square Q-Q plot illustrating structural equation model variables departure
from multivariate normality.
Figure S1 Chi-square Q-Q plot illustrating structural equation model variables departure from
multivariate normality. Multivariate non-normality was also shown by Mardia’s test (Pskew = 9.05
x 10-19, Pkurtosis = 6.36 x 10-3), Henze-Zirkler test (P = 0), and Royston’s test (P = 9.64 x 10-17).
Statistical tests were conducted using the package MVN (Korkmaz et al., 2014) in the statistical
software R (R Development Core Team, 2011).
2. Appendix S1 Piecewise structural equation modelling of relationships between growing
season length, average annual temperature, mean annual precipitation, and global net primary
production.
Here we use piecewise structural equation modelling to explore relationships between
growing season length (lgs), average annual temperature, mean annual precipitation, and net
primary production (NPP). These results are generally consistent with those in the main text for
growing season temperature and precipitation (Fig. 3, Table 1), and further support the
hypothesis that climate has a primarily indirect influence on monthly net primary production
(NPP/lgs).
As in the main text, we use a subset of the original data (n = 138) for which NPP was not
calculated from stand biomass and plant age (Michaletz et al., 2016). These analyses use
piecewise SEM (Grace et al., 2012; Lefcheck, 2015) with AIC model selection (Shipley, 2013).
Piecewise SEM is more appropriate than traditional SEM for small datasets that contain non-
independent observations of multivariate non-normally distributed variables, as in this dataset
(Fig. S1).
We conducted two separate analyses. First, we began with Chu et al.’s Model C, which was
fit to data including average annual temperature and mean annual precipitation (Fig. S2a and
Table S1). Since their model excluded age, we tested for independence of age using d-separation
(Shipley, 2013; Lefcheck, 2015). The fitted model (AICc = 188) did not represent the data well
(P = 0), and significant paths were found from average annual temperature to mean annual
precipitation (P = 0.00), from age to biomass (P = 0.00), and from age to annual NPP (P = 0.00;
Fig. S2 and Table S1).
These missing paths were incorporated into the model (Fig. S2b), which vastly improved
model fit (AICc = 54, P = 0.14; Table S1). Importantly, however, this model was not favored
over the main text Model 2 that considers growing season climate variables and lacks paths
between growing season length and climate variables (AICc = 29; Fig. 3b, Table 1).
We then removed growing season length as a predictor and used it to calculate monthly NPP
as the response variable (Fig. S2c). Although this model (AICc = 33, P = 0.50; Table S1) was
preferred over Model S2b for NPP (Fig. S2b; Table S1), it was not preferred over its analog
Model 3 that uses growing season climate variables (Fig. 3c; Table 1). Importantly, however, this
fitted model shows that average annual temperature and mean annual precipitation have a
primarily indirect (not direct) influence on monthly NPP.
Second, we revised Chu et al.’s Model C (Fig. S2a) to reverse the pathways from average
annual temperature and mean annual precipitation to growing season length (Fig. S3a and Table
S2). These pathways are more appropriate than those in Chu et al.’s Model C, because growing
season length is an outcome of (and is calculated from) climate variables (Michaletz et al.,
2014). Since the Chu et al. Model C excluded age, we tested for independence of age using d-
separation (Shipley, 2013; Lefcheck, 2015). The fitted model (AICc = 157) was preferred over
Chu et al.’s Model C (AICc = 188, Table S1), which reflects the inclusion of causal pathways
from climate variables to growing season length. However, this model did not represent the data
well (P = 0), and significant paths were found from average annual temperature to mean annual
precipitation (P = 0.00), from age to biomass (P = 0.00), and from age to annual NPP (P = 0.00;
Fig. S2 and Table S1).
These missing paths were incorporated into the model (Fig. S3b), which vastly improved
model fit (AICc = 43, P = 0.12; Table S2). However, as above, this model was not favored over
the main text Model 2 that considers growing season climate variables and lacks paths between
growing season length and climate variables (AICc = 29; Fig. 3b, Table 1).
We again removed growing season length as a predictor and used it to calculate monthly
NPP as the response variable (Fig. S3c). Although this model (AICc = 24, P = 1; Table S2) was
preferred over Model S3b for annual NPP (Fig. S3b; Table S1), it was not preferred over its
analog Model 3 that uses growing season climate variables (Fig. 3c; Table 1). Importantly,
however, this fitted Model S3b suggests there are no direct causal pathways from annual climate
variables to monthly NPP.
Although both sets of results are consistent with those reported in the main text, models
containing growing season climate variables (Fig. 3, Table 1) are preferred over the models
containing mean annual climate variables that are reported here (Figs. S2-S3, Tables S1-S2).
This is an expected result since growing season climate influences plant temperature and water
status that drive production during periods when plants are physiologically active. Further,
growing season climate variables appear to have a stronger direct influence on monthly NPP
(Model 3, Table 1), while annual climate variables appear to have a primarily indirect influence
on monthly NPP (Models S3 and S6, Tables S1-S2). These results reflect the importance of
growing season climate variables on rates of plant physiology, metabolism, and net primary
production, and illustrate why growing season (not annual) data should be used in future
analyses.
Table S1 Piecewise structural equation models exploring drivers of net primary production across global climate gradients, with 1
pathways from growing season length to average annual temperature and mean annual precipitation as proposed by Chu et al. (2016). 2
Data are from 138 woody plant communities for which NPP was estimated independently of biomass and age (cf. Michaletz et al., 3
2016). AICc is Akaike’s information criterion and ΔAICc is the difference in AICc relative to Model S3 estimated from Shipley’s d-4
separation test (Shipley, 2013). To conform with theory in Michaletz et al. (2014), all variables were loge-transformed except for the 5
average annual temperature, which was expressed as <1/kT>a, where k is the Boltzmann constant (8.617 x 10-5 eV K-1) and T is 6
temperature (K). na = not applicable. 7
Standardized effect size: total effect, direct effect, indirect effect.
Model
C (df, P)
AICc
ΔAICc
Total
stand biomass
Age
Growing season
length
Growing season
temperature
Growing season
precipitation
Model S1
(Chu Model C)
149 (10, 0)
188
155
0.35, 0.35, na
na, na, na
0.46, 0.07, 0.39
-0.42, -0.38, -0.04
0.18, 0.10, 0.08
Model S2
7 (4, 0.14) 54 21 0.65, 0.65, na 0.02, -0.43, 0.45 0.57, 0.00, 0.57 -0.41, -0.47, 0.06 0.28, -0.04, 0.32
Model S3 1 (2, 0.50) 33 0 0.72, 0.72, na 0.06, -0.43, 0.49 na, na, na 0.11, 0.07, 0.04 0.16, -0.02, 0.18
8
Table S2 Piecewise structural equation models exploring drivers of net primary production across global climate gradients, based on 9
Chu et al. (2016) Model C but with revised pathways from average annual temperature and mean annual precipitation to growing 10
season length. Data are from 138 woody plant communities for which NPP was estimated independently of biomass and age (cf. 11
Michaletz et al., 2016). AICc is Akaike’s information criterion and ΔAICc is the difference in AICc relative to Model S6 estimated 12
from Shipley’s d-separation test (Shipley, 2013). To conform with theory in Michaletz et al. (2014), all variables were loge-13
transformed except for the average annual temperature, which was expressed as <1/kT>a, where k is the Boltzmann constant (8.617 x 14
10-5 eV K-1) and T is temperature (K). na = not applicable. 15
Standardized effect size: total effect, direct effect, indirect effect.
Model
C (df, P)
AICc
ΔAICc
Total
stand biomass
Age
Growing season
length
Growing season
temperature
Growing season
precipitation
Model S4
(revised Chu Model C)
124 (6, 0)
157
133
0.35, 0.35, na
na, na, na
0.02, 0.07, -0.05
-0.39, -0.38, -0.02
0.10, 0.10, 0.00
Model S5
4 (2, 0.12) 43 19 0.65, 0.65, na 0.02, -0.43, 0.45 0.02, 0.00, 0.02 -0.49, -0.47, -0.02 -0.04, -0.04, 0.00
Model S6 0 (0, 1) 24 0 0.72, 0.72, na 0.06, -0.43, 0.49 na, na, na 0.11, 0.07, 0.04 0.23, -0.02, 0.24
16
Figure S2
Figure S2 Piecewise structural equation models exploring drivers of net primary production
(NPP) across global climate gradients, with pathways from growing season length to average
(a)
(b)
(c)
annual temperature and mean annual precipitation as proposed by Chu et al. (2016) Model C.
Data are from 138 woody plant communities for which NPP was estimated independently of
biomass and age (cf. Michaletz et al., 2016). Shipley’s test of d-separation (Shipley, 2013)
revealed significant missing paths from mean annual precipitation to average annual temperature,
age to biomass, and age to NPP in Chu et al.’s Model C (AICc = 188, P = 0; panel a). Inclusion
of these pathways vastly improved model fit (AICc = 54, P = 0.14; panel b). Model fit was
further improved when growing season length was removed as predictor variable and used to
calculate monthly NPP as the response variable (AICc = 33, P = 0.50; panel c). To conform with
theory in Michaletz et al. (2014), all variables were loge-transformed except for the average
growing season temperature <1/kT>gs, where k is the Boltzmann constant (8.617 x 10-5 eV K-1)
and T is temperature (K). Boxes represent measured variables and arrows represent
unidirectional relationships between variables. Black arrows represent positive relationships, red
arrows represent negative relationships, and grey arrows represent non-significant paths at α =
0.05. Arrow thickness has been scaled according to standardized effect sizes, which are also
reported as path coefficients.
Figure S3
Figure S3 Piecewise structural equation models exploring drivers of net primary production
(NPP) across global climate gradients, based on Chu et al. (2016) Model C but with revised
(a)
(b)
(c)
pathways from average annual temperature and mean annual precipitation to growing season
length. Data are from 138 woody plant communities for which NPP was estimated independently
of biomass and age (cf. Michaletz et al., 2016). Shipley’s test of d-separation (Shipley, 2013)
revealed significant missing paths from age to biomass and age to NPP in the revised version of
Model C from Figure 7 in Chu et al. (2016) (AICc = 157, P = 0; panel a). Inclusion of these
pathways vastly improved model fit (AICc = 43, P = 0.12; panel b). Model fit was further
improved when growing season length was removed as predictor variable and used to calculate
monthly net primary production as the response variable (AICc = 24, P = 1; panel c). To
conform with theory in Michaletz et al. (2014), all variables were loge-transformed except for the
average growing season temperature <1/kT>gs, where k is the Boltzmann constant (8.617 x 10-5
eV K-1) and T is temperature (K). Boxes represent measured variables and arrows represent
unidirectional relationships between variables. Black arrows represent positive relationships, red
arrows represent negative relationships, and grey arrows represent non-significant paths at α =
0.05. Arrow thickness has been scaled according to standardized effect sizes, which are also
reported as path coefficients.
3. References
Chu, C., Bartlett, M., Wang, Y., He, F., Weiner, J., Chave, J. & Sack, L. (2016) Does climate
directly influence NPP globally? Global Change Biology, 22, 12-24.
Grace, J.B., Schoolmaster, D.R., Guntenspergen, G.R., Little, A.M., Mitchell, B.R., Miller, K.M.
& Schweiger, E.W. (2012) Guidelines for a graph-theoretic implementation of structural
equation modeling. Ecosphere, 3, 1-44.
Korkmaz, S., Goksuluk, D. & Zararsiz, G. (2014) MVN: An R package for assessing
multivariate normality. The R Journal, 6, 151-162.
Lefcheck, J.S. (2015) piecewiseSEM: Piecewise structural equation modelling in r for ecology,
evolution, and systematics. Methods in Ecology and Evolution, n/a-n/a.
Michaletz, S.T., Cheng, D., Kerkhoff, A.J. & Enquist, B.J. (2014) Convergence of terrestrial
plant production across global climate gradients. Nature, 512, 39-43.
Michaletz, S.T., Cheng, D., Kerkhoff, A.J. & Enquist, B.J. (2016) Corrigendum: Convergence of
terrestrial plant production across global climate gradients. Nature, 537, 432.
R Development Core Team (2011) R: A Language and Environment for Statistical Computing. R
Foundation for Statistical Computing.
Shipley, B. (2013) The AIC model selection method applied to path analytic models compared
using a d-separation test. Ecology, 94, 560-564.
