Supplementary Material
Title: Seasonality of hydraulic-redistribution by trees to grasses and changes in
water-source use that change tree-grass interactions
Running Head: Hydraulic-redistribution by trees to grasses and changes in their
water-source use
AUTHORS
Priyadarshini K V R1ab, Herbert. H. T Prins1c, Steven de Bie1d, Ignas. M. A.
Heitkönig1e, Stephan Woodborne2 , Gerrit Gort 3, Kevin Kirkman4, Fulco
Ludwig5, Todd E. Dawson6, Hans de Kroon7
AUTHOR AFFILIATIONS
1
Resource Ecology Group, Wageningen University, Wageningen, The Netherlands,
priya.kvr@gmail.com, c herbert.prins@wur.nl, dsteven.debie@gemeynt.nl ,
e
ignas.heitkonig@wur.nl
a
2
iThemba Laboratories, Private Bag 11, WITS, 2050, South Africa,
Swoodborne@tlabs.ac.za
3
Biometris, Wageningen University, The Netherlands, gerrit.gort@wur.nl
4
University of KwaZulu-Natal, Scottsville, 3209, Pietermaritzburg, South Africa,
Kirkmank@ukzn.ac.za
5
Earth system science and Climate change group, Wageningen University,
Wageningen, The Netherlands, Fulco.ludwig@wur.nl
6 Departments
of Integrative Biology and Environmental Science, Policy &
Management, University of California at Berkeley, Berkeley, CA, 94720, USA,
tdawson@berkeley.edu
7
Institute for Water and Wetland Research, Department of Experimental Plant
Ecology, Radboud University, Nijmegen, The Netherlands, h.dekroon@science.ru.nl
b
Corresponding author
1
Appendix 1
Data transformations and the linear mixed model
p
We used Box-Cox transformation functions f(OR) = (OR –1)/p for hydrogen and for
oxygen, with OR the RSAMPLE/RSTANDARD ratios, where the power ‘p’ was optimized using
PROC TRANSREG of SAS by fitting fixed effects models to the transformed odds ratio. The
power p = –10 was chosen for hydrogen, and p = –75 for oxygen. The transformation
functions for oxygen and hydrogen were small for the majority of the observations (429 out
2
of 440 δ H values were in the range –75 to 75, corresponding to the Odd Ratio (OR) values
18
0.925 to 1.075, yielding transformed values ranging from –0.12 to 0.051; the range for δ O
was –13 to 25, corresponding to OR values 0.987 to 1.040, yielding transformed values
within the range –0.019 to 0.015).
In the mixed linear model, random effects were allowed for tree pairs, trees within
pairs, and tree/grass observational units, on which repeated measurements were made. Of
these, only random effects of tree pairs were found. The residual variances were different in
some subgroups even after data transformation. Variances for tree and grass were found to be
different for the dry-wet transition, wet-dry transition and dry seasons. Measurements after
spiking were more variable than pre-spike measurements or measurements on control trees.
Decisions about this heterogeneity were made by comparisons of models using Akaike’s
Information Criterion. No repeated measurements correlation structure (like auto-regression)
was found. The test statistics for the different parts of the analysis were obtained using
CONTRAST statements within the larger overall mixed model analysis.
For oxygen, a simpler model than that used for hydrogen could be used since an effect
of group (pre-spike and control only) was neither expected, nor found. The fixed part of the
model contained main effects and interactions of species, plant functional type, and season. In
the random part of the model, random effects of tree pairs, trees within pairs, and tree/grass
2
observational units were allowed to take care of the experimental design, but none of these
appeared to be important. Residual variances were different for different grass/tree and
season combinations. The largest variance was found in the dry-wet transition (Nov 2010),
and smallest variance in the wet 2011 (Jan 2011) period. Trees had slightly larger variance
than grass.
3
Appendix 2
14
Vachellia nilotica
Topsoil Subsoil
soil moisture content (%)
12
10
8
6
4
2
0
Philenoptera violacea
Topsoil Subsoil
soil moisture content (%)
14
12
10
8
6
4
2
0
14
Terminalia sericea
Topsoil
soil moisture content (%)
12
Subsoil
10
8
6
4
2
0
Monthly variation in average top and sub-soil volumetric moisture content (%) under three
savanna tree species. The dotted arrow indicates start of dry top-soil and the long-dashed
arrow depicts the start of dry sub-soil (2.5m) during the study period (Jan 2010 to Jan 2011).
The black solid arrow represents sub-soil water recharge (Jan 2010 data is not shown since
the loggers were not set up during that time and Oct data is not available due to the loss of
loggers in September 2010)
4
Appendix 3
2
Table 1: Summary of ANOVA for the differences in δ H between pre-spiked and control
groups. The F-tests for the differences were extracted from a larger mixed linear model. The
analysed responses are Box-Cox transformed Odds ratio’s.
Effects
Pre-spike Vs. Control
F
P
DF
Tree species
0.64 0.530
2, 286
Plant functional type
1.96 0.162
1, 286
Season
6.17 0.0002* 3, 286
Species x Plant functional type
0.01 0.990
2, 286
Species x Season
1.83 0.071
8,286
Plant functional type x Season
3.08 0.016* 4, 286
Species x Plant functional type x Season 1.06 0.392
8, 286
*P<0.05
2
Table 2: Summary of comparisons of differences in least square means of δ H as obtained
from the repeated measures mixed linear model. The term “ftype” indicates the plant
functional type.
Group comparisons of pre-spike Vs.
control
P
T
Wet 10 (season)
Differences
between LS
Means
(± 1SEM)
0.002 (± 0.003)
0.60
0.59
Wet-dry transition (season)
-0.003(±0.004)
0.45
-0.75
Dry (season)
0.020 (±0.004)
<0.0001*
4.84
Dry-wet transition (season)
0.006 (±0.003)
0.043*
2.03
Wet 11 (season)
0.006 (±0.002)
0.025*
2.26
Wet 10 (ftype x season)
Grass
-0.002 (±0.003)
0.555
-0.59
Wet-dry transition (ftype x season)
Grass
-0.014 (±0.001)
<0.0001*
-9.91
Dry (ftype x season)
Grass
0.030 (±0.008)
<0.0001*
4.00
Dry-wet transition (ftype x season)
Grass
0.004 (±0.004)
0.268
1.11
Wet 11 (ftype x season)
Grass
0.002 (±0.003)
0.410
0.83
Wet 10 (ftype x season)
Tree
0.005(±0.005)
0.305
1.03
Wet-dry transition (ftype x season)
Tree
0.007 (±0.008)
0.360
0.92
Dry (ftype x season)
Tree
0.010 (±0.004)
0.004*
2.87
Dry-wet transition (ftype x season)
Tree
0.009 (±0.005)
0.087
1.71
Wet 11 (ftype x season)
Tree
0.010 (±0.005)
0.034*
2.13
*P<0.05
5