APPENDICES FOR ONLINE PUBLICATION ONLY
Appendix I. Mesocosm Transplant Experiment along the C. Hart Merriam Elevation
Gradient
Figure A1. C. Hart Merriam elevation gradient map and photos of interactive precipitation and
temperature treatments. Four ecosystems along the elevation gradient are meadows in mixed
conifer forests (MC) and ponderosa pine forests (PP), grass-dominated interspaces pinyonjuniper woodlands (PJ), and high desert grassland (GL). Twenty intact plant-soil mesocosms
were transplanted to the next lower elevation as a warming treatment (that is, from mixed conifer
forest to ponderosa pine forest). The lowest elevation site (The Great Basin desert) is only used
for its warmer temperature as the warming treatment for high desert grassland mesocosms.
Twenty mesocosms from undisturbed areas next to the experimental plot were transplanted to the
original site as control groups. The mesocosms were arranged in four rows with ten mesocoms in
each row. The control and experimental mesocoms were placed in alternating rows. Pictures
overlaid on the elevation map showed the mesocoms at each site. Reduced precipitation
treatment was achieved by intercepting precipitation by two clear acrylic channels above the
mesocoms, the total area of which equals to 30% of the surface area of the mesocosm. Increased
precipitation treatment was achieved by collecting 50% of precipitation by a rain collector (50%
of the surface area of the mesocosm) and redirecting the collected precipitation to the
mesocosms. For each transplanted mesocosm (warming treatment), another rain collector was
added to compensate for the long-term precipitation difference between the original and
transplanted sites. Therefore, it is a full-factorial design of temperature (warming) and
precipitation (increased and decreased) treatments with a sample size of 6 or 7. The C. Hart
Merriam elevation gradient map is from the Merriam Powell Center for Environmental Research
of Northern Arizona University (http://www.mpcer.nau.edu/gradient/map_elevation.php).
Appendix II. Detailed Structural Equation Modeling Methods
To analyze selected interrelationships among our variables as a system, we used a structural
equation modeling approach. Structural equation modeling combines path analysis and
maximum likelihood estimation, and is useful for partitioning direct and indirect effects of one
variable on another and to compare the relative strengths of such effects. Prior to modeling, to
satisfy the assumptions of the method, we applied some data transformations. Due to positive
skew, we log transformed environmental variables and ecosystem respiration (ER). Because
daytime net ecosystem exchange (NEE) was negatively skewed, it required a reflected log
transformation.
We developed an a priori conceptual model as a starting point for our modeling (Figure A2),
including climate change treatments (precipitation and warming treatments), environmental
variables (soil moisture and soil temperature) and ecosystem C cycling (ER and daytime
NEE).The descriptions of the paths are as follows: (1) Precipitation treatments are expected to
alter soil moisture; (2) warming is expected to increase soil temperature; (3) increased soil
temperature due to warming treatment is expected to decrease soil moisture; (4) soil moisture is
expected to affect ER and daytime NEE; (5) soil temperature is expected to affect ER and
daytime NEE; and (6) ER is expected to affect daytime NEE, because NEE is the difference
between gross ecosystem photosynthesis and ER. Because the two studied years were so
different, we employed a multi-group modeling approach using the two years as groups (Grace
2006; Pugesek and others 2003). This method allows us to track changes over time in the relative
strength and sign of hypothesized pathways. A multigroup model starts with the hypothesis that
the same model structure fits both groups and that the pathways are of equal sign and magnitude
among groups (Grace 2006). Initially we tested whether the same model structure fit both groups
of data. To do so we fit our a priori model to the data corresponding to each year, separately.
When the model is fit to a dataset, maximum likelihood estimates of all path coefficients is
generated. Path coefficients describe the strength of a causal influence that one variable has on
another, and in their standardized form are directly analogous to partial correlation coefficients,
or regression weights. A goodness of fit test such as the χ2 test is employed; this test estimates
the probability that the data fit the hypothesized model structure, thus a low probability value
(commonly p < 0.05, though this is only tradition) indicates a poor fit. When justified on a priori
grounds, we applied modification indices (Jöreskog and Sörbom 1984), which are algorithmsuggested single changes to the model structure that improve fit. This step allowed us to identify
three paths in the 2008 data which we interpret as experimental artifacts: (1) there were effects of
the warming treatment on both soil moisture and daytime NEE which we interpret as effects of
transplantation because they were independent of measured soil temperature, and (2) there was a
direct effect of enhanced precipitation on daytime NEE. Including these paths in the model
allows us to partition such artifacts, so that unbiased estimates of the other paths can be made.
With these alterations, we arrived at a model structure that fit both the 2008 and 2009 data so
that we could proceed with multi-group modeling by fitting the model to the pooled 2008 and
2009 data. Because the purpose of multi-group analyses is to highlight the differences in path
coefficients among groups, usually the initial model fit is poor. The modeler then relaxes model
constraints one by one, allowing path coefficients or residual variances to take on different
values in different groups. To select which constraints to relax, we viewed a table of residuals
between the observed correlation matrix derived from the data, and that implied by the model
structure that we imposed (Grace 2006). The following parameters were relaxed to allow model
fit, in order of importance: soil temperature → ER, soil moisture variance, soil temperature →
soil water, warming → soil moisture, ER → NEE, ER variance, warming → NEE, NEE
variance, precipitation increase → NEE. We stopped relaxing constraints at the point where the
improvement in fit had a smaller effect than the loss of degrees of freedom, corresponding in our
case to a goodness of fit probability of approximately 0.10. We confirmed adequate model fit
with an additional test, the RMSEA index (Browne and Cudeck 1993). All structural equation
modeling was conducted in AMOS 18.0 (SPSS Inc., Chicago, IL, USA).
Jöreskog KG, Sörbom D. 1984. LISREL-VI user’s guide (3rd ed.). Scientific Software,
Mooresville, Indiana.
Figure A2. An a priori model showing the hypothesized causal relationships among climate
change treatments, environmental variables and ecosystem carbon cycling in this study. Climate
change treatments include precipitation treatments and warming (transplant). Dashed box
denotes a composite variable of precipitation treatments including increased and decreased
precipitation treatments. Environmental variables include soil moisture and soil temperature ,
both of which are measured variables. Ecosystem C cycling includes two measured variables
ecosystem respiration and daytime net ecosystem exchange. Arrows indicate unidirectional
causal relationship, and the numbered pathways correspond to descriptions in Appendix II.
Appendix III. Warming Treatment Effects on Soil Temperature and Moisture
Figure A3. Warming (downward transplant) treatment effects on soil temperature in growing
seasons of (a) 2008 and (b) 2009. From lowest to highest elevation, four grass-dominated
ecosystems are high desert grassland (GL), grassy interspaces in pinyon-juniper woodlands (PJ),
meadows in ponderosa pine forests (PP) and mixed conifer forests (MC). Error bars indicate
standard error. Bars labeled *** differ significantly from control groups (p < 0.001).
Figure A4. Warming (downward transplant) treatment effects on soil moisture in growing
seasons of (a) 2008 and (b) 2009. From lowest to highest elevation, four grass-dominated
ecosystems are the high desert grassland (GL), grassy interspaces in pinyon-juniper woodlands
(PJ), meadows in ponderosa pine forests (PP) and mixed conifer forests (MC). Error bars
indicate standard error. Bars labeled *** differ significantly from control groups (p < 0.001).