Responses of petiole sap flow to light and vapor pressure

PrePrints
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Responses of petiole sap flow to light and vapor pressure deficit in the tropical tree
Tabebuia rosea (Bignoniaceae)
27
Running title: LEAF-LEVEL SAP FLOW RESPONSES TO VPD AND LIGHT
ADAM B. RODDY1,2, KLAUS WINTER3, TODD E. DAWSON1
1
Department of Integrative Biology, University of California, Berkeley, CA, 94720 USA
Present address: School of Forestry and Environmental Studies, Yale University, New
Haven, CT, 06511 USA
3
Smithsonian Tropical Research Institute, Apartado 0843-03092, Balboa, Ancón,
Republic of Panama
2
Author of contact:
Adam B. Roddy
370 Prospect St
New Haven, CT 06511
USA
tel: +1 510 224 4432
email: [email protected]
Keywords: leaf, transpiration, hydraulics, hysteresis, tropics
28
29
30
31
32
33
1
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
PrePrints
34
35
ABSTRACT
Continuous measurements of sap flow have been widely used to estimate water flux
36
through tree stems and branches. However, stem-level measurements lack the
37
resolution necessary for accurately determining fine-scale, leaf-level responses to
38
environmental variables. We used the heat ratio method to measure sap flow rates
39
through leaf petioles and leaflet petiolules of saplings of the tropical tree Tabebuia rosea
40
(Bignoniaceae) to determine how leaf and leaflet sap flow responds to variation in
41
photosynthetically active radiation (PAR) and vapor pressure deficit (VPD). In the
42
morning sap flow rates to east-facing leaves increased 26 minutes before adjacent
43
west-facing leaves. Integrated daily sap flow was negatively correlated with daily mean
44
VPD, and sap flow declined when VPD exceeded 2.2 kPa whether this occurred in the
45
morning or afternoon, consistent with a feedforward response to humidity. Indeed,
46
changes in VPD lagged behind changes in sap flow. In contrast, changes in PAR often
47
preceded changes in sap flow. The sap flow-VPD relationship was characterized by two
48
distinct patterns of hysteresis, while the sap flow-PAR relationship displayed three types
49
of hysteresis, and the type of VPD hysteresis that occurred on a given day was
50
correlated with the type of PAR hysteresis occurring on that day. These patterns
51
highlight how multiple environmental drivers interact to control leaf sap flux and that the
52
development of sap flow sensors capable of measuring individual leaves could
53
drastically influence the amount of data recordable for these structures.
54
55
56
57
2
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
PrePrints
58
INTRODUCTION
59
Approximately 90% of all water converted from the liquid phase to the vapor phase
60
in terrestrial ecosystems moves through plants (Jasechko et al. 2013); in the tropics this
61
amounts to an estimated 32x1015 kg of water per year (Hetherington and Woodward
62
2003). Almost all of this water transits through plant leaves. Understanding how leaves
63
respond to abiotic drivers is important for understanding controls on water balance at
64
scales from leaves to landscapes (Jarvis and McNaughton 1986), yet our understanding
65
of leaf-level transpiration processes derives almost entirely from cuvette measurements
66
on parts of leaves and from inferring leaf-level processes from measurements on main
67
stems or branches. In the present study, we deploy a new sap flow sensor to measure
68
short- and long-term variability in leaf-level sap flux, thus highlighting the types of
69
questions and measurements its development may enable for future research.
70
Various sap flow methods are commonly used to estimate almost continuously tree
71
responses to environmental conditions for extended time periods (Marshall 1958;
72
Granier 1985; Burgess et al. 2001; Vandegehuchte and Steppe 2012). These
73
measurements are most often made on boles or large branches of trees and can be
74
used to estimate canopy-level responses to changing environmental conditions (Oren et
75
al. 1999; Ewers and Oren 2000; Traver et al. 2010). Despite technical advancements in
76
using sap flow measurements in stems to estimate canopy processes, a number of
77
problems remain. First, resistance and capacitance in stems and branches create time
78
lags in water movement between different points in the hydraulic pathway (Köcher et al.
79
2013). For tropical trees, these lags between canopy branches and the stem base can
80
approach an hour (Meinzer et al. 2004). Second, different parts of the canopy respond
81
to environmental conditions largely independently, such that sap flow measurements on
82
branches or boles may provide only an average response of many leaves or of a subset
83
of branches (Brooks et al. 2003; Nadezhdina et al. 2013). For example, east-facing
84
branches of Sequoiadendron giganteum reached their maximum daily sap flow rates 6
85
hours before west-facing branches at the same height (Burgess and Dawson 2008).
86
Although sap flow measurements on boles and branches have provided useful
87
estimates of whole-tree water use (Wullschleger et al. 1998), their utility for describing
3
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
88
leaf-level processes can be limited by time lags, capacitance, hydraulic resistance, and
89
variation in these factors along the root-to-leaf continuum.
PrePrints
90
Rarely have researchers attempted to measure sap flow rates through petioles of
91
individual leaves (Sheriff 1972). Recently, Clearwater et al. (2009) adapted the heat
92
ratio method (HRM; Burgess et al. 2001) originally used for measuring sap flow through
93
large stems to measure sap flow through small diameter stems. Slight modifications to
94
this method have proven useful in measuring sap flow through petioles under field
95
conditions in the neotropics (Roddy and Dawson 2012; 2013; Goldsmith et al. 2013) and
96
through small stems of anatomically and phylogenetically diverse species of the South
97
African fynbos flora (Skelton et al. 2013). Placing sensors in close proximity to the
98
transpiring leaves has the advantage of fine-scale measurements akin to leaf gas
99
exchange without the disadvantage of enclosing leaves in a cuvette that removes the
100
leaf boundary layer and otherwise modifies the leaf microenvironment.
101
In the present study, we measured sap flow rates through petioles and petiolules
102
of saplings of the tropical tree Tabebuia rosea (Bignoniaceae) to characterize how sap
103
flow responds to variation in light and vapor pressure deficit (VPD). We used plots of
104
functional responses of sap flow to environmental drivers in order to characterize
105
patterns of hysteresis in the diurnal relationships between sap flow and these drivers.
106
Hysteresis occurs when, for example, at a given VPD that occurs both in the morning
107
and again in the afternoon, sap velocity is higher in the morning (when VPD is
108
increasing) than in the afternoon (when VPD is decreasing), creating a clockwise
109
pattern of hysteresis throughout the day (Meinzer et al. 1997; O'Grady et al. 1999;
110
O'Brien et al. 2004; Zeppel et al. 2004). Hysteresis in a relationship indicates that
111
factors other than the primary descriptor variable are constraining the response variable.
112
For leaves, two types of hysteresis in the sap flow-VPD relationship have been
113
observed: (1) a clockwise pattern in which morning sap flow is higher than afternoon
114
sap flow, and (2) an intersected loop resulting from midday depression of sap flow and
115
higher peak afternoon sap flow than peak morning sap flow (Roddy and Dawson 2013).
116
Because hysteresis may result from interacting effects of multiple variables, in the
117
present study we also measured photosynthetically active radiation (PAR) levels on
4
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
118
each leaf or leaflet and used cross-correlation analysis to determine whether different
119
types of hysteresis were associated with different time lags between environmental
120
variables and sap flow.
121
122
METHODS
123
Plant Material
T. rosea grows to become a canopy tree in the lowland forests of central
125
Panama. While adults are often deciduous, seedlings are evergreen with five palmate
PrePrints
124
126
leaflets of varying size encircling the petiole. Three individuals were grown from seed in
127
20-liter, insulated pots outdoors under a glass roof at the plant growth facilities of the
128
Smithsonian Tropical Research Institute in Gamboa, Panama, until a few days before
129
sap flow measurements were begun. When the tops of the plants were ~70 cm above
130
the soil surface, they were transferred to a glass chamber (2 x 2 m square) to protect
131
them from strong afternoon winds. The lower 1.5 m of this 5 m tall chamber was made
132
of cement painted white, and doors on east- and west-facing sides of the chamber were
133
left ajar to allow air circulation. At the beginning of the sap flow measurements, the tops
134
of the plants were even with the top of the cement wall at the base of the chamber, and
135
during the course of the experiment two new sets of leaves were produced. Pots were
136
kept well-watered except for one week when water was withheld to characterize
137
changes in leaf-level sap flow rates in response to declining soil water. This week
138
coincided with higher than normal VPD. Sensors were installed when plants were
139
approximately eight months old, a few days after transferring them to the glass
140
chamber.
141
142
143
Sap flow measurements
On each of the three plants, two adjacent leaves on opposite sides of the plant
144
were chosen for measurement (for a total of six leaves and six leaflets). On each
145
measured leaf, sap flow sensors were installed on the leaf petiole and on the petiolule of
146
the middle, largest leaflet. At the time of installation, these leaves were the newest,
147
fully-expanded leaves on each plant. Plants were positioned so that the axis defined by
5
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
148
the two measured leaves on each plant were oriented east-west. Of the total 12
149
sensors installed, five failed at some point in the study, leaving two sensors on
150
petiolules and five sensors on petioles. Thus, two plants each had two sensors on
151
petioles and the third plant had one sensor on a petiole. The two petiolules with
152
sensors were on different plants and on different sides of these two plants.
153
Sap flow sensors and measurements were based on the design and theory of
Clearwater et al. (2009) with some slight modifications described previously (Roddy and
155
Dawson 2012; 2013) and again briefly here. Sensors were constructed from a silicone
PrePrints
154
156
backing and were connected to 10 cm leads with Molex connectors that were then
157
connected by 10 m leads to an AM16/32 multiplexer and CR23X datalogger (Campbell
158
Scientific Inc., Logan, UT). Sensors were held in place against the petiole or petiolule
159
surface with parafilm, and sensors and connections were insulated with multiple layers
160
of bubblewrap and aluminum foil at least 2 cm above and below the sensor. Consistent
161
with previous applications of the HRM, we measured initial temperatures for 10 seconds
162
prior to firing a 4-second heat pulse, monitored temperatures every 2 seconds for 200
163
seconds after the heat pulse, and initiated the measurement routine every 10 minutes.
164
The heat pulse velocity, vh (cm s-1), was calculated from the temperature ratio as:
165
166
where vh is the heat pulse velocity in cm s-1, k is the thermal diffusivity (cm2 s-1), x is the
167
distance from the heater to each of the thermocouples (cm), and δT1 and δT2 are the
168
temperature rises (oC) above and below the heater, respectively (Marshall 1958;
169
Burgess et al. 2001; Clearwater et al. 2009). We estimated the thermal diffusivity as:
170
171
where tm is the time (seconds) between the heat pulse and the maximum temperature
172
rise recorded x cm above or below the heater under conditions of zero sap flow
173
(Clearwater et al. 2009). We measured tm every morning before dawn when
174
atmospheric vapor pressures were lowest (between 0500 and 0600 hrs). At this time,
175
the vapor pressure deficit was almost always below 0.3 kPa, and therefore we assumed
6
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
vh was approximately zero. Thermal diffusivity, k, was calculated for each thermocouple
177
(upstream and downstream) from these predawn measurements of tm, averaged for
178
each sensor, and used to calculate vh from the heat ratios for the subsequent 24 hours.
179
Measurements of k on nights with VPD always above 0.3 kPa were discarded and
180
replaced with the most recently measured k when VPD < 0.3 kPa. We estimated the
181
temperature ratio under zero-flow conditions by excising petioles and petiolules above
182
and below the sensor at predawn at the end of the experiment, greasing the cut ends,
183
placing the segments in a darkened box, and recording the temperature ratios for the
PrePrints
176
184
subsequent ~4 hours. The average of these zero-flow temperature ratios corresponded
185
very well with the temperature ratios recorded predawn under low VPD (less than ~0.3
186
kPa) conditions. The sensor-specific average temperature ratio under zero-flow
187
conditions was subtracted from all calculated heat ratios. This corrected heat ratio was
188
then used to calculate vh.
189
190
191
Measurements of PAR and VPD
Light measurements were made using S1787 photodiodes (Hamamatsu
192
Photonics, Hamamatsu City, Japan). Photodiodes were connected to 15 cm long
193
copper wires with Molex connectors and then to 10 m leads, which were connected to a
194
CR5000 datalogger measuring in differential mode. Circuits created by each
195
photodiode were closed with a 100 ohm resistor. Photodiodes were positioned just
196
above each leaflet with a sap flow sensor, parallel to the axis of the central vein. Light
197
measurements were made every minute and averaged every 10 minutes. Voltage
198
measurements from the photodiodes were converted to PAR based on a calibration of
199
all photodiodes against a PAR sensor (LI-SB190, LiCor Biosciences, Logan, UT), during
200
which time all sensors were situated adjacent to each other in a clearing that received
201
full sunlight.
202
203
Vapor pressure deficit was calculated as (Buck 1981):
(
)
17.502*Ta
RH &
#
VPD = 0.61121 × e Ta +240.97 % 1 −
$ 100 ('
7
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
204
where Ta and RH are air temperature and relative humidity, respectively. Ta and RH
205
measurements were made every 10 minutes with a HOBO U23 datalogger (Onset
206
Computer Corp., Bourne, MA) that was covered in a white, PVC, Y-shaped tube and
207
hung level with the tops of the plants. This tube shielded the instrument from direct
208
solar radiation while allowing air flow through the housing and over the sensor.
209
210
PrePrints
211
Data analysis
All analyses were performed using R (R Core Team 2012). Raw vh
212
measurements were smoothed using the ‘loess’ function, which fits a polynomial to a
213
subset of the data in a moving window of 35 points, consistent with previous
214
applications (Roddy and Dawson 2012; 2013; Skelton et al. 2013). These points have
215
tricubic weighting proportional to their distance away from the center point.
216
Functionally, this means that while a large moving window is used for the averaging,
217
points within 80 minutes of the center point contribute ~80% of the total weight used to
218
calculate the loess-smoothed value for the center point. Conveniently, for smaller
219
windows consisting of just a few points (e.g. the six points recorded in a one-hour
220
window) when sap flow changes are consistently unidirectional, the loess smooth
221
approaches a linear regression.
222
For analyses of structure (leaf vs. leaflet) or aspect (east- vs. west-facing leaves),
223
vh measurements from individual sensors in each group were averaged. To estimate
224
the total sap flow during the day and night, we integrated the time course of vh
225
measurements for each day and night using the ‘auc’ function in the package MESS,
226
which calculates the area under the curve using the trapezoid rule. Daytime was
227
defined as being between 600 and 1800 hours, which corresponded to morning and
228
evening twilight. To minimize the effects of nocturnal refilling, we defined nighttime as
229
being between 100 and 600 hours, which assumed that leaf and stem water potentials
230
had equilibrated within seven hours after sunset. To analyze the effects of VPD on
231
integrated sap flow rates, we linearly regressed integrated sap flow against mean VPD.
232
In all regressions for leaves and leaflets in the day and in the night, the linear model was
8
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
233
determined to be as good as or better than both the logarithmic and power functions by
234
comparing the residual standard errors.
235
Differences in the timing of morning sap flow between east- and west-facing
leaves were compared at a critical vh of 1.5 cm hr-1, chosen because it was higher than
237
any measured nighttime velocities and lower than most daytime velocities.
238
Furthermore, at this time of day the loess-smoothed values almost equalled the raw,
239
measured sap flow velocities. We estimated the time at which vh = 1.5 cm hr-1 by
240
assuming a linear relationship (y = mx + b) between the two sequential morning
PrePrints
236
241
measurements that spanned vh of 1.5 cm hr-1. To compare east- versus west-facing
242
leaves and leaves versus leaflets, we used linear mixed effect models with day as the
243
random variable, which accounts for repeated measures.
244
To analyze patterns of sap flow hysteresis with VPD and light, we used cross-
245
correlation analysis (the ‘ccf’ function in the stats package). For each day and each
246
sensor, we determined the time lag with the highest correlation coefficient for the
247
relationships between sap flow and either VPD or PAR. We visually categorized the
248
types of hysteresis for VPD and PAR. For VPD, there were two types of hysteresis: (1)
249
clockwise and (2) intersected loop described earlier. For the sap flow-PAR relationship,
250
hysteresis was either (1) clockwise, (2) counterclockwise, or (3) counterclockwise with
251
an intersected loop. This last type of hysteresis was characterized by a predominant
252
counterclockwise pattern with a slight inversion at high light. We tested whether the
253
types of hysteresis had different associated time lags using a linear mixed effects model
254
with type of hysteresis as the fixed effect and day nested within sensor as the random
255
effect. To determine whether the type of VPD hysteresis was associated with the type
256
of PAR hysteresis, we used a chi-squared test.
257
258
259
RESULTS
Daily maximum VPD varied from 2.8 kPa to 6.9 kPa during the experiment, while
260
daily maximum PAR at the top of the canopy varied from 1125 to 1640 µmol m-2 sec-1.
261
The daily maximum vh through petioles varied between 1.4 cm hr-1 to 4.5 cm hr-1. This
262
lowest daily maximum vh occurred at the end of a week without water, during which time
9
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
263
five of the seven hottest, driest days occurred. Overall, thermal diffusivity, k, ranged
264
from 0.00136 to 0.00170 cm2 s-1. There were slight differences in k between sensors,
265
but k was relatively constant throughout the experiment for each sensor and consistent
266
with previously reported values for k from a diverse set of plant structures and species
267
(Clearwater et al. 2009; Roddy and Dawson 2012; 2013; Skelton et al. 2013).
268
On every morning, vh to east-facing leaves increased more quickly than it did to
west-facing leaves (Figure 1). Sap flow rates reached 1.5 cm hr-1 on average 26
270
minutes earlier for east-facing leaves than for west-facing leaves (t = 5.67, df = 23, P <
PrePrints
269
271
0.001), and on 18 of 25 days, west-facing leaves reached their daily peak vh later in the
272
day than east-facing leaves. However, vh to east-facing leaves did not decline any
273
earlier in the evening than it did to west-facing leaves.
274
Patterns of sap flow to leaves and leaflets also differed. Daily integrated sap flow
275
was lower through petiolules than through petioles (t = 7.42, df = 24, P < 0.001; Figure
276
2). While water was withheld for one week, daily maximum vh for both leaves and
277
leaflets declined such that leaflet sap flow rates were about half of those to leaves
278
(Figure 2a). On the day immediately following re-watering, leaves and leaflets had
279
almost equivalent sap flow rates, which continued to increase on subsequent days
280
despite declining daily maximum VPD. Daytime integrated sap flow to leaves and
281
leaflets was negatively correlated with mean VPD (Figure 2b), both when including all
282
days and when the last five days of the drought treatment were excluded (Table 1).
283
Nighttime integrated sap flow to leaflets was negatively correlated with mean nighttime
284
VPD, but only when including data during the drought (Table 1). Maximum vh for leaves
285
occurred at a slightly higher VPD than it did for leaflets (2.21 kPa vs. 2.06 kPa; grey
286
symbols in Figure 2b).
287
Patterns of sap flow hysteresis can be grouped into two main classes,
288
exemplified by data from two days from the same leaf shown in Figure 3. The first type
289
of hysteresis pattern was characterized by clockwise hysteresis in the relationship
290
between vh and VPD (Figure 3a). On this day, hysteresis in the vh-PAR relationship
291
predominantly followed a clockwise pattern (Figure 3b). Of the 35 instances of
292
clockwise hysteresis in the vh-VPD relationship, 23 of them occurred with a clockwise
10
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
pattern of hysteresis in the vh-PAR relationship. The second type of hysteresis was
294
defined by an intersected loop in the relationship between vh and VPD (Figure 3d).
295
When this occurred, the vh-PAR relationship was generally counterclockwise, but could
296
also have an intersection in the otherwise counterclockwise relationship (Figure 3e). Of
297
the 60 instances of an intersected loop in the vh-VPD relationship, 34 of them occurred
298
with counterclockwise hysteresis for vh-PAR and 18 of them occurred with a
299
counterclockwise intersected loop for the vh-PAR relationship. The patterns of
300
hysteresis in the vh-VPD and vh-PAR relationships were not independent of each other
PrePrints
293
301
(Χ2 = 30.31, df=2, P < 0.001). Regardless of the relationships between the
302
environmental variables and vh, the relationship between PAR and VPD showed a
303
counterclockwise pattern (Figure 3c,f).
304
The types of VPD and PAR hysteresis differed significantly in their associated
305
time lags (Figure 4). For VPD, the time lag with the highest correlation was significantly
306
later for clockwise hysteresis (118 minutes) than it was for the intersected loop (27
307
minutes; t = 16.44, df = 143, P < 0.001). Similarly, for the vh-PAR relationship, the
308
average time lag with the highest correlation was significantly later for clockwise
309
hysteresis (33.9 minutes) than it was for either counterclockwise (-60.5 minutes) or
310
counterclockwise-intersected hysteresis (-11.2 minutes; t = 6.15, df = 86, P < 0.001).
311
312
313
DISCUSSION
A variety of leaf physiological processes respond rapidly to changes in the leaf
314
microenvironment (Simonin et al. 2013). These rapid responses in leaves may protect
315
stems from low water potentials that can lead to loss of xylem functioning (Zimmermann
316
1983; Sperry 1986; Tyree and Ewers 1991; Hao et al. 2008; Chen et al. 2009; 2010;
317
Johnson et al. 2011; Bucci et al. 2012; Zhang et al. 2013; Skelton et al. 2015). As a
318
result, there has been burgeoning interest in the diurnal variability of leaf hydraulic
319
functioning (Brodribb and Holbrook 2004; 2007; Johnson et al. 2009; Johnson et al.
320
2011; Wheeler et al. 2013). The techniques for measuring sap flow through leaf
321
petioles used here may become critical in quantifying this diurnal variability and in
322
linking leaf hydraulic architecture with leaf water use.
11
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
323
East- and west-facing leaves differed significantly in their patterns of daily sap
flow (Figure 1). Midday depression of vh occurred in leaves on both sides of the plant,
325
although not always at the same time of day, and vh to east-facing leaves increased, on
326
average, 26 minutes earlier in the morning than it did to west-facing leaves. Differences
327
in the timing of morning increases are commonly observed at the branch level
328
(Steinberg et al. 1990; Akilan et al. 1994; Martin et al. 2001; Alarcón et al. 2003;
329
Burgess and Dawson 2008), and our results show that even adjacent leaves can differ
330
significantly in their temporal patterns of sap flow. Without concurrent measurements of
PrePrints
324
331
stem sap flow, however, understanding how these differences between leaves affect
332
branch and stem sap flow remains unclear.
333
Patterns of sap flow through petioles were similar to patterns observed for
334
petioles of other tropical species (Roddy and Dawson 2012; 2013), but, in some cases,
335
different from patterns observed in other species for main stems. A clockwise loop in
336
the vh-VPD relationship is commonly observed in main stems of canopy trees, and the
337
intersected loop has been reported for main stems, although infrequently (Meinzer et al.
338
1997; O'Grady et al. 1999; 2008; Zeppel et al. 2004). Whereas the clockwise vh-VPD
339
hysteresis results from a single peak of sap flow in the late morning, the intersected loop
340
requires bimodal peaks in the daily vh pattern (i.e. midday depression of gas exchange).
341
There were significant associations between the type of VPD hysteresis and the type of
342
PAR hysteresis. A clockwise pattern of vh-VPD hysteresis was associated with a
343
clockwise pattern in the vh-PAR relationship (Figure 3), and on these days both VPD
344
and PAR lagged behind changes in vh (Figure 4). In contrast, days with intersected
345
hysteresis for VPD generally displayed either counterclockwise or counterclockwise-
346
intersected hysteresis in the vh-PAR relationship. On these days, the timing of vh
347
changes was more well coupled to changes in PAR and VPD, with PAR generally
348
preceding changes in vh (Figure 4). This is in contrast to data from stems, for which a
349
clockwise vh-VPD loop is normally accompanied by a counterclockwise vh-PAR loop
350
(O'Brien et al. 2004; Zeppel et al. 2004).
351
352
The causes of hysteresis generally and the patterns of hysteresis described
herein specifically are unclear. For trees, hysteresis in the sap flow-VPD relationship is
12
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
thought to result from variation in hydraulic capacitance, resistance, or stomatal
354
sensitivity to VPD (O'Grady et al. 1999). First, while trees often supply their morning
355
transpiration from capacitive stores, which could elevate morning sap flow above that
356
observed if there were no capacitance (Cowan 1972; Waring and Running 1978; Waring
357
et al. 1979; Goldstein et al. 1998; Meinzer et al. 2004; 2008), at the leaf level this is
358
unlikely to be the primary cause of hysteresis because leaf water can turn over rapidly
359
during the day (Zwieniecki et al. 2004; Zwieniecki et al. 2007; Simonin et al. 2013).
360
Second, hysteresis has been thought to result from increasing hydraulic resistance
PrePrints
353
361
throughout the day as xylem embolisms accumulate (Brodribb and Holbrook 2004;
362
Meinzer et al. 2009). Increasing hysteresis in the vh-VPD relationship with progression
363
through the dry season (Jiménez et al. 2010) and with increasing maximum daily VPD
364
for both stems and leaves support hydraulic failure as the cause of hysteresis (Zeppel et
365
al. 2004; Roddy and Dawson 2013), but for Eucalyptus globulus there was no
366
relationship between daily declines in plant hydraulic conductance and sap flow
367
hysteresis (O’Grady et al. 2008). Third, hysteresis indicates a decoupling of sap flow
368
from its environmental drivers. In our experiment, instantaneous and daily integrated
369
sap flow declined above a threshold VPD of 2.2 kPa, a response which was remarkably
370
well conserved across days for both leaves and leaflets and was the same whether
371
maximum vh occurred in the morning or in the afternoon (Figures 2b, 3a,d). Decreasing
372
vh with increasing VPD may result from declining hydraulic conductance (Oren et al.
373
1999; Brodribb and Holbrook 2004) or from an apparent feedforward response to
374
humidity (Farquhar 1978; Franks et al. 1997; Buckley 2005).
375
The most probable cause underlying such different patterns of hysteresis for
376
individual leaves and for main stems is likely to be a matter of scale. Sap flow through
377
stems integrates the individual sap flow responses of many leaves in drastically different
378
microclimates. Some of this variation is due to variation in incident PAR between
379
different leaves and different branches (Figure 1; Burgess and Dawson 2008). Other
380
factors, such as leaf temperature and its effects on the vapor pressure gradient driving
381
transpiration, could also cause differences in sap flow between individual leaves that
382
would not be apparent in stem level measurements. In addition to microclimatic
13
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
383
variation, leaves and stems differ in their hydraulic architecture. Leaf water balance
384
changes rapidly as efflux and influx of water vary asynchronously even on the timescale
385
of seconds (Sheriff and Sinclair 1973; Sheriff 1974). Water balance of stems probably
386
does not change as dramatically over such short timescales because having numerous
387
parallel pathways for water entry and loss may mitigate the effects of any single
388
pathway. Thus, transpiration and sap flow probably vary more and more rapidly for
389
leaves than for stems.
PrePrints
390
391
392
CONCLUSIONS
Understanding leaf-level responses to abiotic conditions is critical for
393
understanding plant responses to future climate change. In the present study, we found
394
that leaves often exhibit sap flow responses to light and VPD that are notably different
395
from responses of stems. Two possible explanations for these differences between
396
scales are: (1) stems integrate over many leaves, each with their own microclimate and
397
(2) moving the sap flow sensor closer to the sites of transpiration removes the
398
confounding influence of stem hydraulic architecture on stem sap flow measurements.
399
Thus, sap flow measurements on main stems may not accurately describe leaf-level
400
processes. Significant differences in sap flow patterns and the timing of specific
401
responses between adjacent leaves highlights the need for more leaf-level
402
measurements made with sap flow methods. Such methods can better characterize the
403
responses of transpiration and sap flow to their environmental drivers without the effects
404
of changing the leaf microclimate by enclosing the leaf in a gas exchange cuvette.
405
Future measurements of sap flow through petioles could better elucidate how abiotic
406
drivers interact with biotic factors, such as leaf hydraulic architecture, to influence
407
diurnal variation in leaf-level sap flow and water use.
408
409
ACKNOWLEDGMENTS
410
Jorge Aguilar, Alexander Cheesman, Anna Schuerkmann, Kevin Tu, and Joseph Wright
411
provided technical assistance, and Daniel Johnson, Nathan Phillips, and an anonymous
412
reviewer provided useful comments on a previous version of the manuscript. This work
14
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
was supported by grants from the American Philosophical Society and the Smithsonian
414
Tropical Research Institute and a National Science Foundation Graduate Research
415
Fellowship to A.B.R.
PrePrints
413
15
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
416
REFERENCES
417
Akilan K., Considine J.A. and Marshall J.K. 1994. Water use by Geraldton wax
418
(Chamelaucium uncinatum Schauer) as measured by heat balance stem flow
419
gauges. New Zealand Journal of Crop and Horticultural Science 22:285-294.
420
Alarcón J.J., Domingo R., Green S.R., Nicolás E. and Torrecillas A. 2003. Estimation of
421
hydraulic conductance within field-grown apricot using sap flow measurements.
422
Plant and soil 251:125-135.
PrePrints
423
Brodribb .J. and Holbrook .M. 2007. Forced depression of leaf hydraulic conductance
424
in situ: effects on the leaf gas exchange of forest trees. Functional Ecology
425
21:705-712.
426
Brodribb T.J. and Holbrook N.M. 2004. Diurnal depression of leaf hydraulic conductance
427
in a tropical tree species. Plant, Cell & Environment 27:820-827.
428
Brooks R.J., Schulte P.J., Bond B.J., Coulombe R., Domec J.C., Hinckley T.M.,
429
McDowell N. and Phillips N. 2003. Does foliage on the same branch compete for
430
the same water? Experiments on Douglas-fir trees. Trees-Structure and Function
431
17:101-108.
432
Bucci S.J., Scholz F.G., Campanello P.I., Montti L., Jimenez-Castillo M., Rockwell F.A.,
433
Manna L.L., Guerra P., Bernal P.L., et al. 2012. Hydraulic differences along the
434
water transport system of South American Nothofagus species: do leaves protect
435
the stem functionality? Tree Physiology 32:880-893.
436
437
438
439
Buck A.L. 1981. New equations for computing vapor pressure and enhancement factor.
Journal of Applied Meterology 20:1527-1532.
Buckley T.N. 2005. The control of stomata by water balance. New Phytologist 168:275292.
440
Burgess S.S., Adams M.A., Turner N.C., Beverly C.R., Ong C.K., Khan A.A. and Bleby
441
T.M. 2001. An improved heat pulse method to measure low and reverse rates of
442
sap flow in woody plants. Tree Physiology 21:589-598.
443
Burgess S.S.O. and Dawson T.E. 2008. Using branch and basal trunk sap flow
444
measurements to estimate whole-plant water capacitance: a caution. Plant and
445
Soil 305:5-13.
16
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
446
Chen J.W., Zhang Q., Li X.S. and Cao K.F. 2009. Independence of stem and leaf
447
hydraulic traits in six Euphorbiaceae tree species with contrasting leaf phenology.
448
Planta 230:459-468.
449
Chen J.W., Zhang Q., Li X.S. and Cao K.F. 2010. Gas exchange and hydraulics in
450
seedlings of Hevea brasiliensis during water stress and recovery. Tree Physiol
451
30:876-885.
Clearwater M.J., Luo Z., Mazzeo M. and Dichio B. 2009. An external heat pulse method
453
for measurement of sap flow through fruit pedicels, leaf petioles and other small-
PrePrints
452
454
455
456
457
458
459
460
diameter stems. Plant, Cell & Environment 32:1652-1663.
Cowan I.R. 1972. An electrical analogue of evaporation from, and flow of water in
plants. Planta 106:221-226.
Ewers B.E. and Oren R. 2000. Analyses of assumptions and errors in the calculation of
stomatal conductance from sap flux measurements. Tree Physiology 20:579-589.
Farquhar G.D. 1978. Feedforward responses of stomata to humidity. Functional Plant
Biology 5:787-800.
461
Franks P.J., Cowan I.R. and Farquhar G.D. 1997. The apparent feedforward response
462
of stomata to air vapour pressure deficit: information revealed by different
463
experimental procedures with two rainforest trees. Plant, Cell & Environment
464
20:142-145.
465
466
Goldsmith G.R., Matzke N.J. and Dawson T.E. 2013. The incidence and implications of
clouds for cloud forest plant water relations. Ecol Lett 16:307-314.
467
Goldstein G., Andrade J.L., Meinzer F.C., Holbrook N.M., Cavelier J., Jackson P. and
468
Celis A. 1998. Stem water storage and diurnal patterns of water use in tropical
469
forest canopy trees. Plant, Cell & Environment 21:397-406.
470
471
Granier A. 1985. Une nouvelle méthode pour la mesure du flux de sève brute dans le
tronc des arbres. Annales des Sciences Forestieres 42:193-200.
472
Hao G.Y., Hoffmann W.A., Scholz F.G., Bucci S.J., Meinzer F.C., Franco A.C., Cao K.F.
473
and Goldstein G. 2008. Stem and leaf hydraulics of congeneric tree species from
474
adjacent tropical savanna and forest ecosystems. Oecologia 155:405-415.
17
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
475
476
477
478
479
480
481
PrePrints
482
Hetherington A.M. and Woodward F.I. 2003. The role of stomata in sensing and driving
environmental change. Nature 424:901-908.
Jarvis P.G. and McNaughton K.G. 1986. Stomatal control of transpiration: scaling up
from leaf to region. Advances in ecological research 15:1-49.
Jasechko S., Sharp Z.D., Gibson J.J., Birks S.J., Yi Y. and Fawcett P.J. 2013.
Terrestrial water fluxes dominated by transpiration. Nature 496:347-350.
Jiménez E., Vega .A., Pérez-Gorostiaga P., Fonturbel T. and Fernández C. 2010.
Evaluation of sap flow density of Acacia melanoxylon R. Br. (blackwood) trees in
483
overstocked stands in north-western Iberian Peninsula. European Journal of
484
Forest Research 129:61-72.
485
Johnson D.M., McCulloh K.A., Meinzer F.C., Woodruff D.R. and Eissenstat D.M. 2011.
486
Hydraulic patterns and safety margins, from stem to stomata, in three eastern
487
U.S. tree species. Tree Physiology 31:659-668.
488
Johnson D.M., Meinzer F.C., Woodruff D.R. and McCulloh K.A. 2009. Leaf xylem
489
embolism, detected acoustically and by cryo-SEM, corresponds to decreases in
490
leaf hydraulic conductance in four evergreen species. Plant Cell Environ 32:828-
491
836.
492
Köcher P., Horna V. and Leuschner C. 2013. Stem water storage in five coexisting
493
temperate broad-leaved tree species: significance, temporal dynamics and
494
dependence on tree functional traits. Tree Physiol 33:817-832.
495
496
497
Marshall D.C. 1958. Measurement of sap flow in conifers by heat transport. Plant
Physiology 33:385-396.
Martin T.A., Brown K.J., Kučera J., Meinzer F.C., Sprugel D.G. and Hinckley T.M. 2001.
498
Control of transpiration in a 220-year-old Abies amabilis forest. Forest Ecology
499
and Management 152:211-224.
500
Meinzer F.C., Hinckley T.M. and Ceulemans R. 1997. Apparent responses of stomata to
501
transpiration and humidity in a hybrid poplar canopy. Plant, Cell & Environment
502
20:1301-1308.
18
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
503
Meinzer F.C., James S.A. and Goldstein G. 2004. Dynamics of transpiration, sap flow
504
and use of stored water in tropical forest canopy trees. Tree Physiology 24:901-
505
909.
506
Meinzer F.C., Johnson D.M., Lachenbruch B., McCulloh K.A. and Woodruff D.R. 2009.
507
Xylem hydraulic safety margins in woody plants: coordination of stomatal control
508
of xylem tension with hydraulic capacitance. Functional Ecology 23:922-930.
509
PrePrints
510
511
Meinzer F.C., Woodruff D.R., Domec J.C., Goldstein G., Campanello P.I., Gatti M.G.
and Villalobos-Vega R. 2008. Coordination of leaf and stem water transport
properties in tropical forest trees. Oecologia 156:31-41.
512
Nadezhdina N., David T.S., David J.S., Nadezhdin V. and Pinto C.A. 2013. Mapping the
513
water pathways in stem xylem by sap flow measurements during branch severing
514
experiments. Acta Horticulturae 991:223-230.
515
O'Brien J.J., Oberbauer S.F. and Clark D.B. 2004. Whole tree xylem sap flow responses
516
to multiple environmental variables in a wet tropical forest. Plant, Cell &
517
Environment 27:551-567.
518
O'Grady A.P., Eamus D. and Hutley L.B. 1999. Transpiration increases during the dry
519
season: patterns of tree water use in eucalypt open-forests of northern Australia.
520
Tree Physiology 19:591-597.
521
Oren R., Phillips N., Ewers B.E., Pataki D.E. and Megonigal J.P. 1999. Sap-flux-scaled
522
transpiration responses to light, vapor pressure deficit, and leaf area reduction in
523
a flooded Taxodium distichum forest. Tree Physiology 19:337-347.
524
Oren R., Sperry J.S., Katul G.G., Pataki D.E., Ewers B.E., Phillips N. and Schäfer
525
K.V.R. 1999. Survey and synthesis of intra-and interspecific variation in stomatal
526
sensitivity to vapour pressure deficit. Plant, Cell & Environment 22:1515-1526.
527
O’Grady A.P., Worledge D. and Battaglia M. 2008. Constraints on transpiration of
528
Eucalyptus globulus in southern Tasmania, Australia. Agricultural and Forest
529
Meteorology 148:453-465.
530
531
R Core Team. 2012. <http://www.R-project.org/> Vienna, Austria: R Foundation for
Statistical Computing.
19
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
532
533
534
Roddy A.B. and Dawson T.E. 2012. Determining the water dynamics of flowering using
miniature sap flow sensors. Acta Horticulturae 951:47-53.
Roddy A.B. and Dawson T.E. 2013. Novel patterns of hysteresis in the response of leaf-
535
level sap flow to vapor pressure deficit. Acta Horticulturae 991:261-267.
536
Sheriff D.W. 1972. A new apparatus for the measurement of sap flux in small shoots
537
with the magnetohydrodynamic technique. Journal of Experimental Botany
538
23:1086-1095.
PrePrints
539
540
541
542
543
Sheriff D.W. 1974. Fluctuations in water uptake into and vapour efflux from leaves.
Journal of Experimental Botany 25:580-582.
Sheriff D.W. and Sinclair R. 1973. Fluctuations in leaf water balance, with a period of 1
to 10 minutes. Planta 113:215-228.
Simonin K.A., Roddy A.B., Link P., Apodaca R., Tu K.P., Hu J., Dawson T.E. and
544
Barbour M.M. 2013. Isotopic composition of transpiration and rates of change in
545
leaf water isotopologue storage in response to environmental variables. Plant,
546
Cell & Environment 36:2190-2206.
547
Skelton R.P., West A.G., Dawson T.E. and Leonard J.M. 2013. External heat-pulse
548
method allows comparative sapflow measurements in diverse functional types in
549
a Mediterranean-type shrubland in South Africa. Functional Plant Biology
550
40:1076-1087.
551
552
553
Skelton R.P., West A.G. and Dawson T.E. 2015. Predicting plant vulnerability to drought
in biodiverse regions using functional traits. Proc Natl Acad Sci U S A .
Sperry J.S. 1986. Relationship of xylem embolism to xylem pressure potential, stomatal
554
closure, and shoot morphology in the palm Rhapis excelsa. Plant Physiology
555
80:110-116.
556
Steinberg S.L., McFarland M.J. and Worthington J.W. 1990. Comparison of trunk and
557
branch sap flow with canopy transpiration in pecan. Journal of experimental
558
botany 41:653-659.
559
Traver E., Ewers B.E., Mackay D.S. and Loranty M.M. 2010. Tree transpiration varies
560
spatially in response to atmospheric but not edaphic conditions. Functional
561
Ecology 24:273-282.
20
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
562
563
Tyree M.T. and Ewers F.W. 1991. The hydraulic architecture of trees and other woody
plants. New Phytologist 119:345-360.
564
Vandegehuchte M.W. and Steppe K. 2012. Sapflow+: a four-needle heat-pulse sap flow
565
sensor enabling nonempirical sap flux density and water content measurements.
566
New Phytol 196:306-317.
567
568
PrePrints
569
Waring R.H., Whitehead D. and Jarvis P.G. 1979. The contribution of stored water to
transpiration in Scots pine. Plant, Cell & Environment 2:309-317.
Waring R.H. and Running S.W. 1978. Sapwood water storage: its contribution to
570
transpiration and effect upon water conductance through the stems of old-growth
571
Douglas-fir. Plant, Cell & Environment 1:131-140.
572
Wheeler J.K., Huggett B.A., Tofte A.N., Rockwell F.E. and Holbrook N.M. 2013. Cutting
573
xylem under tension or supersaturated with gas can generate PLC and the
574
appearance of rapid recovery from embolism. Plant Cell Environ 36:1938-1949.
575
576
577
Wullschleger S.D., Meinzer F.C. and Vertessy R.A. 1998. A review of whole-plant water
use studies in tree. Tree physiology 18:499-512.
Zeppel M.J.B., Murray B.R., Barton C. and Eamus D. 2004. Seasonal responses of
578
xylem sap velocity to VPD and solar radiation during drought in a stand of native
579
trees in temperate Australia. Functional Plant Biology 31:461.
580
Zhang Y.J., Meinzer F.C., Qi J.H., Goldstein G. and Cao K.F. 2013. Midday stomatal
581
conductance is more related to stem rather than leaf water status in subtropical
582
deciduous and evergreen broadleaf trees. Plant Cell Environ 36:149-158.
583
Zimmermann M.H. 1983. Xylem structure and the ascent of sap. Springer-Verlag.
584
Zwieniecki M.A., Boyce C.K. and Holbrook N.M. 2004. Hydraulic limitations imposed by
585
crown placement determine final size and shape of Quercus rubra L. leaves.
586
Plant, Cell & Environment 27:357-365.
587
588
Zwieniecki M.A., Brodribb T.J. and Holbrook N.M. 2007. Hydraulic design of leaves:
insights from rehydration kinetics. Plant, Cell & Environment 30:910-921.
589
21
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
PrePrints
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
Figure legends
Figure 1. (a) Three days of sap flow for east- (dashed) and west-facing (solid) leaves.
Tick marks on the horizontal axis indicate midnight. (b) Boxplot of the time lag in sap
flow rates between east- and west-facing leaves.
Figure 2. (a) Eight days of sap flow for leaves (solid) and leaflets (dashed). The first five
days corresponded to the end of a week without watering. Tick marks on the horizontal
axis indicate midnight. (b) The relationship between daily integrated sap flow and mean
daily VPD for leaves (triangles) and leaflets (circles). Black points represent the last five
days during the drought treatment. Grey points at the bottom mark the mean VPD (and
standard error) at which maximum daily sap flow occurred for leaves and leaflets.
Integrated daily sap flow was, on average, 30% lower for leaflets than it was for leaves.
Figure 3. The pairwise relationships between vh, VPD, and PAR for two days (top and
bottom rows). (a,d) The vh-VPD relationship differed between the two days, as did the
(b,e) vh-PAR relationship. (c,f) However, the VPD-PAR relationship was approximately
the same for the two days.
Figure 4. Boxplots of time lags (in minutes) associated with different types of hysteresis
in the relationship between vh and (a) VPD and (b) PAR. ‘CW’ = clockwise, ‘CCW’ =
counterclockwise, ‘CCW-Int’ = counterclockwise-intersected (see Methods for
descriptions).
Table 1. Summary statistics for the linear regressions between integrated sap distance
and mean VPD for leaves and leaflets in the day and in the night, whether including
data from the week of drought or not.
22
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
Figure 1
PrePrints
617
618
619
23
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
Figure 2
PrePrints
620
621
622
24
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
Figure 3
PrePrints
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
25
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
Figure 4
PrePrints
642
643
644
26
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015
645
646
Table 1
Leaves
R2
Day
PrePrints
Night
t
Leaflets
d.f.
P
R2
t
d.f.
P
All
0.26 3.05
23
<0.01
0.40
4.15
23
<0.00
1
No drought
0.22 2.51
18
0.02
0.20
2.42
18
0.03
All
0.04 0.94
23
0.36
0.28
3.19
23
<0.01
No drought
0.02 0.55
18
0.59
0.13
1.98
18
0.06
647
648
27
PeerJ PrePrints | https://dx.doi.org/10.7287/peerj.preprints.1017v1 | CC-BY 4.0 Open Access | rec: 30 Apr 2015, publ: 30 Apr 2015