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During the past decade, several detailed models of plant vascular transport systems (i.e. xylem and phloem) have been presented in the literature, and many of them are currently capable of accurately modelling the hydraulic characteristics of trees, including tall trees. This marks a departure from earlier modelling exercises in plant water relations, when models were intended primarily to promote an understanding of the biophysical and physiological mechanisms of transport, but whose performance was comparatively poor when they were required to predict the behaviour of organisms spanning the logarithmic ranges from small seedlings to gigantic old trees. In addition, many of these modelling efforts have assumed, more or less explicitly, that a principle of optimality operates in the design of the transport systems, i.e. they have assumed criteria by which various aspects of the transport system should be optimised. Moreover, these models are characterised by very different approaches, structures and objectives, and differ significantly with regard to several other important characteristics. Because models formally organise our knowledge, we review them here, in the hope of highlighting the theoretical progress achieved so far and the challenges remaining in our understanding of the vascular transport systems of trees.
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Mencuccini, Hölttä, Martinez-Vilalta
Mencuccini et al. Optimality models in plant hydraulics 1
X. Comparative Criteria for Models of the
Vascular Transport Systems of Tall Trees
Maurizio Mencuccini
, Teemu Hölttä
and Jordi Martinez-Vilalta
Mencuccini, Hölttä, Martinez-Vilalta
, University of Edinburgh, School of GeoSciences, Crew Building, West
Mains Road, EH9 3JN Edinburgh (UK);
, Centre for Ecology Research and Forestry Applications (CREAF),
Universitat Autonoma de Barcelona, Bellaterra, Cerdanyola (Barcelona,
, to whom correspondence should be addressed.
, Department of Forest Ecology, University of Helsinki (Helsinki, Finland)
The authors thank the Catalan government (AGAUR - Generalitat de Catalunya) for a visiting 18
Professorship in UAB to Maurizio Mencuccini. 19
Table of contents
Abstract 22
Introduction 23
Comparative criteria for the construction of transport models of tall trees 24
Comparative criteria for models of xylem water transport in tall trees: empirical 25
evidence and optimality modelling 26
Comparative criteria for models of phloem water transport: empirical evidence and 27
optimality modelling 28
Empirical evidence for size- or age-related phloem sieve cell tapering 29
Critique: what have we learnt with regard to the modelling of the physiology of long-30
distance vascular transport in trees? 31
Optimal transport systems: future frontiers 32
Conclusions 33
Acknowledgements 34
Literature cited 35
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Keywords: ecological modelling; optimality; xylem conductance; phloem conductance; 39
xylem safety; xylem efficiency; phloem safety; phloem efficiency. 40
Mencuccini, Hölttä, Martinez-Vilalta
Abstract 42
During the past decade, several detailed models of plant vascular transport systems (i.e., xylem 43
and phloem) have been presented in the literature, and many of them are currently capable of 44
accurately modelling the hydraulic characteristics of trees, including tall trees. This marks a 45
departure from earlier modelling exercises in plant water relations, when models were intended 46
primarily to promote an understanding of the biophysical and physiological mechanisms of 47
transport, but whose performance was comparatively poor when they were required to predict 48
the behaviour of organisms spanning the logarithmic ranges from small seedlings to gigantic 49
old trees. 50
In addition, many of these modelling efforts have assumed, more or less explicitly, that a 52
principle of optimality operates in the design of the transport systems, i.e., they have assumed 53
criteria by which various aspects of the transport system should be optimised. In addition, these 54
models are characterised by very different approaches, structures and objectives, and differ 55
significantly with regard to several other important characteristics. Because models formally 56
organise our knowledge, we review them here, in the hope of highlighting the theoretical 57
progress achieved so far and the challenges remaining in our understanding of the vascular 58
transport systems of trees. 59
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Plants in general, and trees in particular, undergo tremendous transformations in size during 62
growth and development. The biomass of a mature tree can be ten or more orders of magnitude 63
larger than that of a small seedling and plant hydraulic systems must similarly be designed in 64
such a way that their performance is not impaired by these tremendous increases in size 65
(Mencuccini 2003). How this is achieved without incurring significant costs and limitations in 66
their physiological performance is still far from clear, but the literature of the last ten years, 67
including modelling attempts, has paid much more attention to these issues than earlier 68
literature. Hence, some reflections can be made. In much of this modelling literature, the main 69
insights into how plant transport systems are designed (especially in the case of large 70
organisms such as trees) have been obtained using ideas that owe much to the use of a principle 71
of optimality, i.e., the principle that the design of a transport system must satisfy some pre-72
defined criterion of optimal performance, which translates into a maximization or a 73
minimization function. We will look at these in detail later on. 74
While much of this theoretical and modelling literature has focussed on the upward transport of 76
water from roots to leaves via the xylem of plants, significant progress has also been made in 77
the understanding of downward solute plus water transport via plant phloem. Plants are 78
integrated units, with sub-systems that must be closely co-ordinated in order for the organism 79
to work well, hence examining one sub-system in isolation without proper consideration for the 80
interactions with other sub-systems is unlikely to be very productive in the long run (e.g., 81
Zimmermann & Brown, 1971; Holbrook & Zwieniecki 2005). We will therefore summarise 82
theoretical and modelling literature that contains valuable information on both xylem and 83
phloem transport sub-systems. 84
Because of the large quantity of resources necessary to construct water and solute transport 86
systems in large organisms, these findings have central importance in the understanding of the 87
whole-plant physiology of tall trees. A tight co-ordination between plant assimilation, 88
carbohydrate allocation (including storage) and respiration must be invoked to explain the 89
enormous evolutionary and ecological success of trees in colonising and retaining dominance 90
in large swaths of the terrestrial biosphere. In other words, our capacity to predict the 91
‘ecosystem physiology’ of forests over long time periods seems limited without a careful 92
consideration of how short-term processes such as gas exchange and long-distance transport are 93
Mencuccini, Hölttä, Martinez-Vilalta
coupled to long-term processes such as growth and development. Understanding tree transport 94
systems has a central role for two reasons, a) because transport systems of tall organisms are 95
expensive to build and maintain, and b) because their performance in delivering resources is 96
inextricably linked to the acquisition of other resources by the tree, either in the leaves by 97
photosynthesis, or by the roots in the form of nutrients to be transported to leaves. 98
An expanding number of studies have been published recently on the physiology of tall trees 100
and much of it is reflected in the chapters of this book. This literature is precious and absolutely 101
necessary to test the behaviour of models and to suggest further areas in which current models 102
are deficient. Because of space limitations, we do not review it unless absolutely necessary, and 103
focus instead on the literature directly relevant to the modelling of the physiology of tall trees. 104
We focus initially on presenting the main principles that we will use to summarize the 106
modelling literature concerned with the ‘optimal’ design of transport systems of tall trees. We 107
then present examples of such theoretical and modelling advances for xylem and phloem 108
transport. Finally, we look at the frontiers of this research and point out what remains to be 109
done and what can be achieved in the near future. 110
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There is a very large literature on the use of optimality criteria in ecology. It is not our intention 114
to review it here, not even briefly. We will only highlight those principles which we believe are 115
important for the construction of models of transport systems for tall trees and which have 116
already been discussed in different contexts in the ecological literature on optimality. 117
The modular construction of their bodies allows plants, and particularly trees, to increase their 119
sizes over several orders of magnitude. Correspondingly, plant functions must scale 120
accordingly (i.e., isometrically or allometrically). For example, Mencuccini (2003) reviewed 121
the literature on plant hydraulics and reported that the published data on hydraulic conductance, 122
(amount of water moved from soil to leaf per unit of time and per unit of drop in water 123
potential, i.e., mmol H
O s
), showed a log normal distribution profile, with changes in 124
the magnitude of this parameter of five orders of magnitude (from around 0.01 to more than 125
100 mmol H
O s
). The reason for this strongly right-skewed frequency distribution was 126
due to the logarithmic (and equally varying) distribution of leaf areas and biomasses across 127
plants. 128
Does this general increase in size, and specifically the need to build long-distance transport 130
systems, result in other physiological or ecological trade-offs? Is there a specific challenge that 131
tall trees have to face, compared to other ‘minor’ organisms within the plant kingdom? Or does 132
increased size provide unexpected benefits and possibilities for compensations? 133
Increased stature results in a number of different processes, i.e., increased costs of construction 135
of a long transport system, an accentuated impact of the hydrostatic effects of gravity, plus the 136
hydrodynamic effects due to water movement in conduits. In addition, the modular 137
construction itself leads to expanding crowns for much of the life cycle of trees, with the 138
consequent need to transport ever greater amounts of water and solutes. On the other hand, a 139
bulky structure may provide substantial benefits in terms of accumulated water, sugar and 140
nutrient storage capabilities and the possibility of a more effective exploration of above- and 141
below-ground biological spaces. 142
There probably exist challenges for plants (and especially trees) both in the sense of 144
constructing systems that can work under very different biophysical regimes as well as in the 145
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sense that the use and allocation of carbohydrates produced by photosynthesis is crucial to their 146
present and future performance. While many of these challenges are not unique to the plant 147
kingdom (large animals such as elephants in terrestrial environments or whales in marine ones 148
are likely to face analogous construction challenges), the unique feature of trees (and plants in 149
general) is in the direct link between the efficacy in the distribution of resources by the 150
transport systems (e.g., water from root tips to canopy leaves) and the capacity of other organs 151
of acquiring and processing food e.g., poorly designed xylem would affect stomatal opening 152
and carbon uptake). Similar examples can be derived with regard to the feedbacks between 153
photosynthesis and root functioning. This an important topic to which we will return later. 154
In part as a consequence of what was said above, there also exist challenges to scientists in 156
understanding the functionality of these transport systems. Typically, plant physiologists and 157
ecologists have focussed on developing models that explain the ‘working’ of a particular 158
system, i.e., the mechanisms necessary for that system to work properly. In the modern 159
literature, starting from Dixon and Joly (1895) for xylem transport and Münch (1927) for 160
phloem transport, physiological investigations have long focussed on understanding the 161
biophysical and physiological mechanisms by which transport occurred, with models being 162
constructed to summarise this sort of knowledge. Comparatively scant attention was paid to 163
how these principles applied when faced with the challenge of modelling transport systems of 164
large organisms. 165
However, it quickly becomes obvious that, once one starts to employ these models in the 167
context of understanding and predicting performance of both small and tall plants, very little 168
insight is provided by them. Most of the time, one has to resort to empirical parameter 169
calibration to adjust model performance across these vast ranges of allometric scaling. It is then 170
apparent that, in order for physiological models to be applicable across scales of logarithmic 171
magnitudes, different principles must be incorporated, in addition to the known physiological 172
mechanisms. We refer to models that incorporate these scaling (or allometric) principles as 173
scalable. A scalable model is one in which attention is paid to the allometry of the system, in 174
an empirical or a semi-mechanistic fashion, by incorporating components which scale with 175
size, thereby ensuring that the system behaves logically across logarithmic scales. The level of 176
detail of these representations in a scalable model can vary, from simple representations of the 177
overall biomass cost of plant transport systems, to those in which allometric scaling is 178
represented at the anatomical level. We will see a few examples later on. 179
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In addition to scalability, theoretical models differ in the way they represent plant efficiency in 181
constructing transport systems. Strictly speaking, efficiency can be defined as the ratio of 182
energy exiting a system (seen as a black box) divided by energy required, as an input, to make 183
that system work. If the two forms of inputs and outputs can be put on the same units, then 184
efficiency is unitless and varies between 0 and 1. Hence a car engine has an energy conversion 185
efficiency typically of 10 to over 40%, wind turbines of up to 60%, solar panels of around 50% 186
and plant photosynthesis of up to 6%. Expressing efficiency on common units allows broad 187
comparability across systems. Unfortunately, this practice is rare in the plant physiological 188
literature, and particularly so in the design of plant transport systems. In some cases, the 189
efficiency of a transport system is defined as the ratio of the water transportable per unit of time 190
and water potential difference divided by the amount of photosynthate required to construct it 191
(or more rarely, to construct and maintain it). This is still acceptable because it provides a 192
measure of costs of the inputs (carbon required to construct and maintain the system) against 193
which to assess the gains obtained by the system’s outputs (water transported and expended in 194
transpiration during photosynthesis). In many other cases, however, the concept of efficiency is 195
used in a looser sense, to indicate the efficacy of a system in transporting water (e.g., as judged 196
by the values of plant hydraulic conductances). While the difference is largely semantic, we 197
will use it here to differentiate between models that explicitly calculate transport costs and 198
those that do not. 199
In the first case (when costs and gains are compared), it is relatively easy to define a criterion 201
for the construction of an optimal conducting system. As a consequence, optimal models exist 202
that maximise transport efficiency per se (e.g., maximise hydraulic conductance gains given 203
fixed construction costs). However, in the second case this is more difficult, because there does 204
not exist an upper bound to how efficacious a transport system can be and, by definition, larger 205
values of hydraulic conductance are always preferable. Hence for this class of models, criteria 206
for optimal performance cannot be based on the maximisation of transport efficacy per se, but 207
must be based on arguments of functional balance, e.g., the maximization of the carbon return 208
by leaves given the hydraulic gains of the conducting system relative to other limiting factors 209
or the efficacy of transport relative to its loss of safety because of, e.g., embolisation. 210
A third criterion that we propose relates to the choice of the optimality criterion itself. How 212
should a transport system for tall trees be designed? Should it maximise the total conductance 213
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per se, the organ-level efficiency of the resources used in the construction of such system, the 214
total growth of the organism, the total net carbon gain (gross photosynthesis minus construction 215
and maintenance costs) or the tree-level efficiency of resource use (e.g., the amount of carbon 216
obtained by leaf photosynthesis divided by the amount required for organ construction, i.e., 217
leaves with their associated cohorts of conducting pipes)? The answer given is frequently that 218
the best optimality criterion is the one that relates more closely to evolutionary fitness, in the 219
sense of promoting the long term survival of the species. In this sense, it may be difficult to 220
decide which criterion is actually the ‘best’, because several of them are likely to be applicable 221
under different circumstances. Practice shows that, in fact, optimality models incorporate a 222
range of different criteria. 223
A fourth criterion by which modelling principles for plant transport systems can be assessed is, 225
as alluded to before, the level of physiological detail which they incorporate. Some transport 226
models have been developed primarily to allow scaling physiological processes against 227
logarithmic axes of plant size, whereas their level of anatomical detail is limited. The cost of 228
construction of a transport system may be assessed in terms of the total biomass invested in the 229
organ (branch, stem, roots) carrying out the transport function (typically upward xylem water 230
transport), without a detailed consideration of the other functions performed by that organ (e.g., 231
mechanical support, carbohydrate storage, etc.). Hence, by definition, the costs of the transport 232
system are overestimated and the corresponding efficiency under-estimated. Other models have 233
instead incorporated the concept of efficiency by focussing on the actual carbon costs involved 234
in constructing the individual units involved in water and solute transport, i.e, the conduits, in 235
an attempt to separate hydraulic transport costs from other costs. There is an expanding 236
empirical literature on the allometric scaling of various characteristics of individual conduits 237
which is useful for this purpose (e.g., Wheeler et al., 2005; Sperry et al., 2006; Pittermann et 238
al., 2006a and 2006b). Because of the complexities involved in scaling up the results obtained 239
at the anatomical level to the whole tree using this approach, empirical data on allometric 240
scaling at the level of a whole plant are particularly important tests of the performance of these 241
models. 242
Linked to the issue of the level of physiological detail embedded in the model, is our fifth and 244
last criterion of the scope of the model and of its transferability for the prediction at larger 245
scales. Models that attempt to represent many or all of the processes involved in plant transport 246
systems are more likely to be employed to predict processes at larger spatial and temporal 247
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scales; on the other hand, they are also likely to provide more synthetic descriptions of the 248
details of each process. Vice versa, more mechanistic models (which are constructed to 249
describe only one or a few processes in great detail) frequently pay the price of being unusable 250
for the description of processes at larger spatial and temporal scales because they cannot be 251
easily ‘contextualised’. 252
In the next section, we will review the plant transport models that have been employed in 254
recent years to study the role of tree size on tree performance. Hence, our main focus will be on 255
models centred at the organismal level while we will not attempt to review other models 256
operating clearly at lower (conduit) or larger (ecosystem) scales. We will use these five criteria 257
(i.e., a) presence/absence of model scalability, b) use of efficiency vs efficacy principles, c) 258
choice of the optimality criterion if one was present, d) level of physiological detail and e) 259
transferability to other scales) to highlight similarities and differences among them and to 260
explore how their differences have led to the advancement of our knowledge in the 261
understanding of the physiology of tall trees. It is not our intention to rank these models 262
according to our own preference of what constitutes the ‘best’ model. Our intention is rather to 263
use them as examples of logical summaries of our knowledge to illustrate what we have learnt 264
on the significance of transport systems in tall trees. 265
In dealing with the transport models appearing in the literature, we will refer to Table 1 (for the 267
xylem) and Table 2 (for the phloem), which summarise the main features of each model 268
relative to the five criteria previously introduced. 269
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X.3.1 Pipe model theory (Shinozaki et al., 1964a, b). 272
Since its inception, the pipe model theory (PMT) has been very successful at attracting the 273
attention of foresters, ecologists and modellers for its intellectual simplicity, which allows 274
understanding and modelling some important aspects of carbon allocation in plants. Hence, it is 275
an obligate, albeit old, starting point. In its original formulation (Shinozaki et al., 1964a, b), the 276
PMT assumed that, because of the need to support leaves both mechanically and hydraulically, 277
simple linear relationships were to be expected between amount of leaf mass (or, by extension, 278
area) on a plant and its branch, stem or root cross-sectional area (or, by extension, functional 279
sapwood area), either within a single tree from top to bottom, or across trees of different sizes 280
(Table 1). In some sense, it is the equivalent of the formulation of Corner’s rule for individual 281
leaves, which states that a constant ratio exists between petiole size and leaf area. The PMT has 282
been used innumerable times as the theoretical justification for the derivation of empirical 283
relationships between tree leaf area and stem cross-sectional or sapwood areas. 284
The original model was not scalable, in the sense that it did not account for size-related effects 286
on the functional ratios between leaf mass and stem cross-sectional areas. In the original 287
publication, Shinozaki et al. (1964a) noted that tapering at the bottom of trees caused 288
systematic departures from the predicted linear relationship between stem cross-sectional area 289
and leaf mass and attributed these departures to the accumulation of disused pipes after the 290
lower branches had been shed. It is now well known that, for a range of other reasons including 291
biomechanical effects, hydraulic compensation effects and sapwood ageing, large trees can 292
frequently maintain larger values of both cross-sectional area and sapwood area per unit of leaf 293
area (e.g., McDowell et al., 2002) than smaller trees (although the opposite pattern has also 294
been reported). It is also obvious that, other things being equal, both construction and 295
maintenance costs must increase more than proportionally with stem cross-sectional area 296
because of the associated increase in height. Mäkelä (1986, 1989) have subsequently proposed 297
versions of the pipe model which scale more realistically with tree size, as construction and 298
maintenance costs of longer pipes are explicitly accounted for. The concepts embedded in this 299
class of models have proved to be far more useful than those of the original theory and have 300
frequently been employed in whole forest carbon balance models (e.g., Mäkelä & Hari 1986). 301
Because the original PMT was primarily concerned with the functional balance between leaves 303
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and conducting stems, and without consideration for the actual costs involved, it was 304
essentially based on a criterion of efficacy. In addition, without any additional constraints, the 305
PMT was not an optimality model as such, but rather a proposal to interpret and understand the 306
frequently observed linear relationships between leaf mass and stem cross-sectional areas. The 307
level of physiological detail employed to represent the transport system was limited. Note 308
however that the PMT did not make any assumption about size or shapes of individual pipes, 309
which are better understood as strands of wood rather than individual conduits. Subsequent 310
studies (e.g., West et al., 1997; 1999; McCulloh et al., 2003), however, have interpreted it as 311
indicating that each pipe represented unbranched, untapered conduits. In any case, modelling of 312
factors such as the vertical changes in stem hydraulic conductance, or of the age-related 313
changes in anatomical properties, is not possible with the PMT. The biggest limitation of this 314
theory was probably also its main strength: because hydraulic and bio-mechanical functions 315
were jointly considered (albeit very empirically), its heuristic value was limited, but its 316
practical application was both straightforward and robust within the size range for which the 317
relationships were constructed. 318
Roderick & Berry (2001) published an extension of the PMT that linked the hydraulic 320
properties of a set of parallel rigid pipes to a macroscopic variable, wood density. This linkage 321
allowed the authors to make predictions of the expected direction of change of the hydraulic 322
properties with the change in important environmental variables (water temperature, nitrogen 323
availability, air CO
concentration) and to test these predictions against the observations of 324
changes in wood density reported in the wood technology literature. By and large, the model 325
predicted the qualitative direction of change in hydraulic properties correctly. 326
X.3.2 Hydrall (Magnani et al., 2000; Magnani et al., 2002) 328
As the name suggest, Hydrall was designed to increase our understanding of the allocational 329
constraints imposed on assimilation by the construction and maintenance of the xylem transport 330
system (i.e., roots and stems) (Magnani et al., 2002). The model was designed from the 331
beginning to scale with tree size, albeit not allometrically (Table 1). Also, because construction 332
and maintenance costs were accounted for, a tree’s carbon budget could be calculated. In 333
Hydrall the transport costs were equated with the total biomass costs for a particular organ, 334
without consideration for the various components within that organ. Hydrall was based on an 335
explicit optimization criterion, i.e., maximising stand level assimilation while keeping leaf 336
water potential just below the threshold for xylem embolism. Because of its flexibility and the 337
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incorporation of additional processes (mainly plant photosynthesis), it has been employed for 338
the description and analysis of additional processes, namely the description of C allocation 339
during growth, the age-related patterns of stand net primary productivity and the response of 340
forest C accumulation to a range of environmental variables (Magnani et al., 2002). More 341
recently, its central principle of allocational constraints based on plant water relations has been 342
incorporated in a regional model of carbon fluxes across Europe (Zaehle et al., 2006). Similar 343
hydraulic concepts have been incorporated into a wider model recently developed by Buckley 344
& Roberts (2005). 345
X.3.3. WBE (West et al., 1997; 1999) 347
The WBE model (sometimes, referred to as FBN, fractal branching network, cf., Weitz et al., 348
2006) has attracted enormous attention since its initial presentation in 1997. Its main strengths 349
have been in providing a new language, that of power law relationships applied to the quasi-350
fractal representation of plants, to the old problem of description of plant form and function. It 351
did so by formalising the description of plant form via a clever system of ratios which were 352
assumed to scale constantly across the hierarchical order of segments inside the plant (e.g., the 353
ratios of branch diameter and length, and conduit diameter of the mother branches against those 354
of the daughter branches). This allowed considerable simplification in the calculation of their 355
scaling as plant size increased. Volume filling by the branching network and scaling between 356
diameters and lengths to maintain elastic similarity were employed to constrain two of these 357
three allometric ratios. The third one, the allometric scaling of conduit diameter as a function of 358
distance from the apex (called conduit tapering) was constrained empirically (West et al., 1999; 359
Mäkelä & Valentine 2006), using the relationship between conduit diameter and number of 360
segments from the apex and assuming complete independence of transport resistance from 361
length, which resulted in universal scaling relationships. However, both higher and lower rates 362
of tapering are observed than the conduit tapering function in the model, especially close to the 363
apex and at the bottom of tree trunks, respectively (Mencuccini et al., 2007), and independence 364
of resistance from length can only very approximately be achieved, even theoretically. Note 365
that the use of the term ‘tapering’ is slightly confusing here, because in WBE the petiole 366
conduit size acts as the fixed reference conduit size. Hence, high rates of tapering effectively 367
indicate high rates of basipetal enlargement, rather than high rates of apical narrowing. Also, 368
individual conduits do not normally taper, therefore the proposed tapering represents the 369
diameter change occurring from one conduit to the next. 370
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Although by definition, the WBE model scales with plant size (because it was designed to do 372
precisely that), its success in doing so has been hotly debated, with questions raised about the 373
comparability of inter-specific with intra-specific and especially ontogenetic analyses (e.g., 374
Mencuccini, 2002). Conduit tapering obviously helps to reduce the height-related increase in 375
hydraulic resistance and several authors have reported rates of tapering consistent with the 376
predictions from WBE (e.g., Mencuccini, 2002, Anfodillo et al., 2006; Weitz et al., 2006; 377
Mencuccini et al., 2007; Petit et al., 2008). However, notable exceptions have also been 378
reported. For example, far from continually increasing their conduit size, tall gymnosperm and 379
angiosperm trees frequently appear to keep size constant or even reduce the size in their trunks 380
(Mencuccini et al., 2007; Petit et al., 2010), probably in order to minimise costs. Similarly, 381
departures from model predictions have been reported in very small plants (Sack et al., 2002), 382
in scaling nitrogen content and plant respiration across a range of sizes within a species (Reich 383
et al., 2006), in scaling leaf hydraulic conductance (Coomes et al., 2008), in scaling tree size-384
density distributions (Coomes et al., 2003) and in scaling net primary productivity and water 385
use with forest age (Magnani 1999). 386
The WBE model is based on an efficacy concept, since carbon costs specific to the transport 388
systems are not quantified. In addition, WBE is not really an optimality model, since larger 389
tapering exponents will always result in lower values of the total resistance of each pipe (albeit 390
with lower returns and with larger cross-sections required to fit the conduits; cf., Mäkelä & 391
Valentine, 2006). 392
The fundamental contribution of the WBE model compared to earlier descriptions of plant 394
water transport systems (e.g., the PMT) has been the introduction of conduit tapering. That 395
conduits tapered had been known for a long time, but WBE were the first to realise that this 396
process had important consequences that had not been explored. By assuming that a tapered 397
pipe resulted in a transport system whose hydraulic resistance was independent of length (such 398
that a small seedlings could be considered equivalent to a tall tree in terms of its transport 399
capacities and photosynthetic performance per unit of leaf area), they were able to extend their 400
model to a vast range of other processes and situations, up to ecosystem-scale analyses of gas 401
fluxes and ecosystem metabolism. Finally, the authors of the WBE model claimed that their 402
model could easily be extended to describe phloem transport in plants but so far, this extension 403
has not been carried out. 404
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Becker et al. (2003) examined the implications of including inter-conduit resistances in the 406
WBE model. They examined three possible scenarios, depending on how pit resistance was 407
assumed to scale with lumen resistance and found that the effect on the derived WBE 408
exponents depended on the particular assumption made. If the pit resistance was assumed to 409
represent a constant fraction of lumen resistance or if tracheid dimensions were scaled to 410
minimize wood resistivity, then the derived exponents would be identical to the ones obtained 411
by WBE. If instead, the proportion of resistance in pits increased with increasing conduit 412
diameter, the derived exponents doubled in magnitude approximating those obtained by 413
Murray’s law (see later section). It is unclear on what bases should the choice be made given 414
that each alternative has its own merit. Despite this empirical nature, this paper is important 415
because it shows that theoretical scaling exponents cannot be obtained without a complete 416
description of the hydraulic structure, which should incorporate pits. 417
X.3.4 Murray’s law (McCulloh et al., 2003; 2004; McCulloh and Sperry 2005) 419
Murray (1926) examined the scaling of conduit diameters in animal arteries. He derived a cubic 420
relationship between blood flow and vessel diameters at different positions along the vascular 421
network, thereby explaining why diameters rapidly decrease from the central aorta to the 422
peripheral arterioles. He also explained this relationship by showing that the cubic exponent 423
resulted from the maximisation of the conductance of a branched system containing a fixed 424
amount of blood (or, in his words, minimizing the total work carried out by the act of blood 425
flowing creating friction and the energy invested in blood). 426
McCulloh et al (2003) proposed that a similar relationship holds for plant xylem. They 428
reasoned that water, compared to blood, was cheap but that, conversely, substantial costs were 429
involved in building the walls to reinforce them against the potential threat of implosion caused 430
by the tension present in plant xylem. They proved that under such circumstances an identical 431
cubic scaling would result and they also showed that conduit furcation (i.e., the ratio of number 432
of conduits between distal and proximal ranks) would increase hydraulic conductance. They 433
also presented data confirming that, in peripheral leaflets and leaves of four species, the stems 434
of two vines and in the initial stages of branch ramification of one species of tree (Fraxinus), 435
conduit numbers did decrease from distal to basal positions (suggesting that the conduits were 436
furcating, thereby violating the assumptions of WBE, although not necessarily of PMT), while 437
their conduit diameters scaled following the proposed cubic relationship. Conversely, no 438
furcation was seen for the stems of the diffuse porous Acer and the coniferous Abies (McCulloh 439
Mencuccini, Hölttä, Martinez-Vilalta
et al., 2003; 2004; 2005). Murray’s law as applied to plants by McCulloh et al. (2003) does 440
show scalability with regard to conduit diameter. Murray’s law is based on efficiency and the 441
optimality criterion is to maximise hydraulic conductance for a fixed investment in conduit 442
wall reinforcement. The level of description of the transport system is greater than in previous 443
treatments, with a detailed representation of how conduits taper and of their furcation ratios, 444
but the scope of the theory is more limited. Murray’s law says nothing regarding the total 445
number of conduits necessary to support a certain leaf area, nor regarding the relationship 446
between tapering and distance from the apex. As such, it is not a scalable model. So far, the 447
theory has not been applied beyond its original aim to predict other processes. 448
Strictly speaking, the predictions of Murray’s law only apply to cases in which conduits do not 450
carry out a support function. Applying it to lignified organisms creates problems. For example, 451
in the absence of conduit furcation, Murray’s law predicts that the optimal investment in 452
hydraulic conductance occurs for totally untapered conduits. Hence, presence of conduit 453
furcation is crucial to obtain vertical profiles of tapered conduits. Empirical data show that 454
conduits generally do not furcate below the initial few bud scars in self-supporting trees, 455
particularly diffuse porous and conifers (McCulloh et al.,2004; Petit et al., 2008). However, 456
there is ample evidence that conduits continue to change their diameters all the way down the 457
trunk and into the roots (sometimes with inverted taper; cf., Mencuccini et al., 2007). 458
Consequently, this tapering cannot be explained by Murray’s law. 459
X.3.5 Net C gain model (Mencuccini et al., 2007) 461
Mencuccini et al. (2007) presented a scaling model of plant xylem water transport which 462
contained elements taken from many of the previous modelling approaches. The plant was 463
represented following the quasi-fractal system of WBE, ensuring scalability, and the costs of 464
conduit construction were estimated using the theory of conduit wall reinforcement outlined in 465
McCulloh et al. (2003), which means that hydraulic efficiency was determined. However, 466
Mencuccini et al. (2007) diverged in the choice of the optimality criterion. Rather than use the 467
efficiency in the use of resources for the construction of the xylem system, this model used the 468
combination of a constant leaf water potential plus the maximisation of the net C gains of the 469
whole-plant, i.e., it linked the costs of xylem water transport with the gains obtained by 470
photosynthesis in a manner resembling the approach of Hydrall. The rationale for choosing this 471
optimisation criterion is that it would be adaptive for a plant to construct an inefficient transport 472
system (with respect to the maximum set by Murray’s law), provided that it resulted in 473
Mencuccini, Hölttä, Martinez-Vilalta
proportionally more carbohydrates being photosynthesised or in proportionally lower transport 474
costs. This differs from the analysis based on Murray’s law, which predicts instead what the 475
maximum hydraulic conductance will be for a fixed, not a variable, amount of resources spent 476
on conduit walls. It is likely that the net carbon gains change considerably during ontogeny, 477
since the xylem is cheap to construct when a plant is small and becomes increasingly costly as 478
a plant grows in size, in which case resource conservation may became a predominant 479
consideration relative to resource use efficiency. This approach provides an explanation for 480
inverse tapering at the base of (especially coniferous) trees, an otherwise puzzling 481
phenomenon. The published version of the model maximised net C gains (gross photosynthesis 482
minus xylem construction costs) but essentially identical results in terms of the predictive 483
patterns were obtained by employing alternative formulations for the costs and gains (e.g., 484
incorporating xylem maintenance costs in addition to construction costs or incorporating a 485
mesophyll conductance term in series with stomatal conductance), or by using alternative 486
definitions of the optimality criterion to be maximised (i.e., by employing the ratio of total C 487
gained by photosynthesis divided by the total C costs of the xylem transport system). The level 488
of physiological detail of the model was relatively high compared to some of the other 489
examples previously examined, with conduit tapering, conduit number and conduit furcation all 490
considered (albeit the published version of the model was more restricted). Relative to Hydrall, 491
the Mencuccini et al. (2007) model incorporated a more mechanistic calculation of costs, which 492
are here based on the construction of conduit walls (whose thickness depends on conduit 493
diameter) and not on the total biomass invested in wood. Plant photosynthesis was represented 494
and made dependent on environmental variables. The high level of physiological detail resulted 495
in a loss of simplicity of the model, which did not provide analytical solutions to the problem 496
of optimal tapering, but required parameterization using site-specific and species-specific 497
parameters. 498
Mencuccini, Hölttä, Martinez-Vilalta
Our knowledge of the scaling principles to be applied to the design of phloem transport systems 501
for tall trees is considerably less advanced than the knowledge for the xylem. Thompson & 502
Holbrook (2003a; 2003b, 2004) have repeatedly attracted attention to the fundamental 503
importance played by phloem anatomical parameters in affecting sugar and water transport 504
properties in the phloem, and to the need to develop a sounder knowledge base of their 505
variation within and across individuals and species, and yet these fundamental details of tree 506
anatomy remain poorly known. 507
The paucity of data on tree phloem anatomy (particularly with regard to tall trees) is all the 509
more important when one considers the importance of phloem transport in the context of the 510
movement of carbohydrates from forest canopies to storage compartments, roots and 511
mycorrhiza and the relevance of this movement for the carbon cycle. In addition, recent 512
theories that attempt to explain age-related patterns in tree growth based on sink limitations 513
(Sala & Hoch, 2009) are directly concerned with the transport of sugars away from the crown 514
and the presence of potentially negative feedbacks between photosynthesis, sink activities and 515
efficacy of sugar export. As a consequence of the paucity of empirical information on phloem 516
structure and function of tall trees, theories and models that are useful for understanding 517
phloem transport systems of tall trees are limited. The most relevant ones are reviewed here 518
(Table 2). 519
X.4.1 Information-transmission model (Thompson and Holbrook 2003a; 2003b; 2004)) 521
Thompson and Holbrook (2003a, 2003b, 2004) significantly expanded the analytical scope of 522
phloem modelling relative to several previous theoretical exercises of phloem function (Tyree 523
et al. 1974, Goeschl et al. 1976, Philips and Dungan 1993). By using dimensionless quantities, 524
they greatly simplified the analysis of phloem transport in several important respects 525
(Thompson and Holbrook 2004). In the context of this review, perhaps the most important 526
innovation was the analysis of information transmission along phloem axes. Thompson (2006) 527
pointed out that, the smaller the turgor pressure differential between opposite ends of the 528
phloem translocation pathway, the better the whole-plant integrative control of phloem 529
transport, particularly in tall trees, where the turgor pressure drop would otherwise rapidly 530
build up over long distances. With more-or-less uniform turgor along the axis, information on 531
changes in water or sugar status would be transmitted rapidly from one end of the plant to the 532
Mencuccini, Hölttä, Martinez-Vilalta
other, and the behaviour of the sieve cell-companion cell complex would not need to depend 533
greatly on the knowledge of where these cells were located along the pathway. Information on 534
changes in source and sink activity and water status could be transmitted via individual 535
molecules moving at the solution bulk flow velocity or in the form of pressure and 536
concentration waves (Philips & Dungan, 1993; Thompson & Holbrook 2004). Following 537
Philips & Dungan (1993), Thompson & Holbrook (2003b) used dimensionless ratios to show 538
that, given realistic ranges of parameter values, tall plants (several metres of height) were likely 539
to behave like ‘reservoirs’ rather than a ‘rivers’, i.e., their rates of both phloem transport and 540
information transmission were likely to become sluggish and unresponsive to changes in 541
prevailing conditions. In addition, Thompson (2006) showed that of all the factors affecting 542
phloem transport, sieve tube length (potentially equal to total plant height) was by far the most 543
important, but that data on this dimension are lacking. 544
The Thompson & Holbrook (2003a; b) information-transmission model was not conceived to 546
be scalable, as changes in sieve tube anatomical properties and their number with tree size were 547
not considered, but it was intended as a tool to understand transport mechanisms per se. Indeed, 548
when their model was parameterised for giant sequoia trees of height equal to 100m, pressure-549
concentration waves were predicted to take at least a week to traverse the tree from canopy to 550
roots, raising questions on how regulation of phloem transport occurs in tall trees. The model 551
was based on an efficacy criterion, because construction costs were not calculated and, strictly 552
speaking, it was not an optimality model because no equation related to the behaviour of the 553
phloem tube was explicitly either maximised or minimised. In essence, the authors proposed a 554
‘workable’ regime of conditions, limited by the geometry of the system, under which flow of 555
material and information occurs efficaciously and certain critical conditions associated with 556
phloem transport (i.e., cell plasmolysis, water potential disequilibrium with the xylem and the 557
occurrence of the ‘reservoir’ regime) are avoided. An additional characteristic of this model is 558
that it describes in great detail the behaviour of a single conducting tube but it incorporates no 559
notion of the number of tubes required to sustain a certain level of sugar export from a leaf, nor 560
does it consider the possibility that tubes may be tapered, branched or contain solute relays. As 561
such, its main application is in process understanding, whereas scalability and transferability 562
are limited. 563
X.4.2 Minimum investment model (Hölttä et al., 2006; 2009b) 565
Mencuccini, Hölttä, Martinez-Vilalta
The Hölttä et al. (2009b) minimum investment model was designed to be scalable, by 566
incorporating principles (such as tube tapering or variable number of phloem tubes per leaf) 567
that allowed it to perform realistically across a range of tree sizes, although allometric theory 568
was not employed. It also explicitly considered the risk that phloem transport under steady-569
state conditions was limited by excessive viscosity caused by high solute concentrations. The 570
model contained an optimization function: given fixed photosynthetic and transpiration rates, it 571
calculated the minimum number of combined xylem and phloem tubes required to obtain 572
transport under steady-state conditions. 573
The rationale for analysing a coupled xylem / phloem transport system is that the structure and 575
flux rates in the xylem control the water potential, which in turn affects phloem transport. 576
Interestingly, because xylem water potential affects both xylem and phloem transport, the 577
conductance of the two systems must be coupled, such that large structural investments in the 578
xylem are predicted to reduce the need for investment in the phloem and vice versa. 579
Because the model incorporated the basic physiological mechanisms needed to describe 581
transport as well as the components required to make it scalable, its scope was larger than the 582
previous model. However, its transferability and applicability was limited by its increased 583
complexity, the lack of a mechanistic description of photosynthesis and the lack of coupling to 584
the final fate of the carbohydrates transported. 585
The system was designed to minimise the number of tubes required to achieve xylem and 587
phloem transport (rather than optimize information transmission). This condition should make 588
the predictions of this model very different from the predictions from the Thompson & 589
Holbrook model. For example, it should result in extremely slow transfer times of pressure-590
concentration waves for tall plants (i.e., in the same order of magnitude as molecule transfer 591
times or even slower), thereby negating the existence of a localised system of physiological 592
control, as invoked by Thompson & Holbrook (2004). In reality, this delay in transfer times 593
was greatly alleviated provided that the assumption was made that phloem conduits tapered 594
too. Relatively small linear rates of tapering proved to be sufficient to keep the dimensionless 595
ratios within the expected range, while wave propagation time and the minimum number of 596
required phloem tubes declined dramatically (Hölttä et al 2009b). 597
X.4.3 Speed-of-link model (Mencuccini & Hölttä, 2010) 599
Mencuccini, Hölttä, Martinez-Vilalta
Mencuccini & Hölttä (2010) built on the previous models developed by Hölttä et al. (2006 and 600
2009b) to expand the range of processes to which they could be applied. As such, the new 601
version did not contain any innovation compared to the previous models with regard to how the 602
transport system was optimised. It is reviewed separately here to illustrate the importance of 603
incorporating size-related processes to make a whole-plant phloem transport model scalable, 604
such that its applicability to explain additional processes is enhanced. 605
The coupled xylem-phloem model of Hölttä et al. (2006) was expanded by linking it to a new 607
routine that modelled root respiration and soil CO
gas diffusion as a function of soil 608
temperature, moisture content and the amount of sugars transported by phloem and respired by 609
roots. The coupled gas exchange / vascular transport / soil diffusion model was then employed 610
to help interpret the observed temporal patterns of movement of isotopic tracers introduced in 611
trees by photosynthetic labelling. Several studies have shown that, upon application of an 612
isotopic C label over plant canopies, a spike in either depleted
(e.g., Steinmann et al., 613
2004), enriched
(e.g., Johnson et al., 2002; Högberg et al., 2008) or
(e.g., Howarth 614
et al., 1994; Mikan et al., 2000) appeared in the soil respiratory flux after a delay of about 1 to 615
5 days, suggesting a close coupling between photosynthesis and soil/ecosystem respiration. 616
Similar conclusions were obtained by several other authors (e.g., Ekblad et al., 2005; Gärdenäs 617
2000) using simultaneous measurements of photosynthetic and respiratory fluxes, but without 618
employing isotopic tracers, although in this second case, the corresponding respiratory spikes 619
tended to occur much earlier and more closely in time to the changes in photosynthesis. 620
Mencuccini & Hölttä (2010) tested the hypothesis that the ‘speed-of-link’ between canopy 622
photosynthesis and soil respiration depended on whether the speed estimates were obtained by 623
using the isotopically-based approach or the flux-based approach (cf., Mencuccini & Hölttä, 624
2010). Fifty-four independent estimates of ‘speed-of-link’ were available across a range of 625
plant heights ranging from 0.1 m to around 40 m, i.e., over three orders of magnitude (Figure 626
1). 627
For the isotopically-based measurements, one would predict that the length of the phloem 629
transport system would exert significant constraints on the speed of the transfer of the 630
isotopically labelled molecules from the canopy, through the phloem and roots and out of the 631
soil as gaseous CO
, and particularly so in tall trees. However, the extent by which this 632
constraint would operate is open to question. Without any specific size-related adjustments in 633
Mencuccini, Hölttä, Martinez-Vilalta
phloem properties, the constraint imposed by the increase in height over three orders of 634
magnitude is likely to be extremely large, as shown by the results reported by Thompson & 635
Holbrook (2003b) for the model parameterised for giant sequoia trees. 636
The data did indeed show that the time delay between 1 and 5 days mentioned above was 638
largely the result of differences in plant size (longer times in tall trees compared to herbaceous 639
plants and tree seedlings). However, the measurements also showed an increase in the apparent 640
velocity of the isotopic signal as a function of plant size (Figure 1): the time required for the 641
isotopic tracer to emerge from the soil surface when applied to 40-m tall trees was longer by 642
only a few days compared to the time observed for much smaller plants (Figure 1). Two models 643
(the combined photosynthesis / phloem transport /gas diffusion model just mentioned and a 644
simplified version based on average properties) were then employed to understand the nature of 645
the mechanism(s) that could explain these observations. The authors found that they could only 646
be explained by assuming that the phloem transport system operated differently depending on 647
plant size, i.e,. by assuming that both the turgor drop along the phloem pathway and the phloem 648
specific conductivity increased as a function of plant size (Figure 1, dotted and dashed curves 649
and right axes). An alternative explanation could involve the presence of solute relays. If one 650
assumes that individual sieve tubes are shorter than the length of the whole pathway and are 651
connected in series with the solutes metabolically transferred from one sieve tube to the next 652
(as hypothesized by Lang, 1979), then a similar relationship would be found. Size-related 653
changes in sugar storage within the plant or in soil gas/water transport properties could not 654
explain the observations. Hence, the strong suggestion from these ecosystem-level observations 655
was that significant size-related adjustments had taken place in the phloem transport system of 656
tall trees and that size-related properties must be incorporated in phloem transport models to 657
increase their applicability across a range of plant sizes, i.e, to make them scalable. 658
Do phloem tubes taper in a manner similar to what is seen in the xylem? The (limited) 662
empirical evidence has never been systematically summarised and put into context. Because of 663
the importance of this process, such a review is provided here, together with additional 664
unpublished data (Table 3). 665
It appears that the large majority of the studies support the hypothesis that phloem sieve cells 667
Mencuccini, Hölttä, Martinez-Vilalta
taper basipetally, similarly to what is found in the xylem, but a few exceptions are present 668
(Table 3). Connor & Lanner (1990) studied xylem and phloem anatomy of Great Basin 669
bristlecone pines (Pinus longaeva D. K. Bailey) of various ages in California and Utah. They 670
found no age-related trend in phloem characteristics, i.e., annual increments and number of 671
sieve cells produced per year along a radial file, but sieve cell diameters were not measured. 672
For this report, it is unclear at which stem height the measurements refer to and, in addition, 673
those trees were likely to have had fairly similar heights and maturational processes were likely 674
to have ended, given the range of ages employed (site means ranging from 751 to 1,863 years). 675
Quilho et al (2000) also found no evidence of vertical sieve tube tapering in 15-yr-old 676
Eucalyptus globulus Labill. trees sampled at six height levels (from 5% to 75% of tree height), 677
possibly because, as in the xylem, much of the tapering may occur near the apex and a plateau 678
is then rapidly reached. A report for a conifer species (Picea abies (L.) Karst., in Rosner et al., 679
2001) showed evidence of an inverse pattern of reductions in sieve cell diameters at the bottom 680
of the stem compared to the base and the inside of the crown. The report by Enns et al. (2006) 681
on 21-days-old Zea mays seedlings is interesting because it showed clear evidence of furcation 682
in sieve tube cells: their number drastically declined towards the root tips of unbranched 683
primary roots. The decrease in sieve cell diameters in small leaf veins compared to major leaf 684
veins (Lush 1976) is qualitatively similar to the vessel tapering normally found in tree leaves 685
(Coomes et al., 2008). 686
Ewers & Fisher (1991) were probably the first to suggest that the concept of the trade-off 688
between safety and efficiency could also be applied to phloem transport. They collected 689
anatomical data along branches of different individuals of species of the genus Bauhinia (some 690
of which were lianas, some shrubs and some trees). They showed clear increases in both xylem 691
and phloem cross-sectional areas and in both vessel and sieve tube diameters with increases in 692
the amount of leaf area distal to the stem segment. Visual inspection of their graphs shows that 693
vertical sieve cell tapering was similar to vessel tapering in shrubs and trees, whereas phloem 694
cell tapering was slower than vessel tapering in vines. As far as we know, this is the only study 695
that simultaneously compared xylem and phloem anatomical properties along an axial gradient 696
and put them in relation to the leaf area distal to those segments (cf., Gartner 2002 for a similar 697
dataset comparing leaf-sapwood area ratios with leaf-inner bark area ratios along the stem of 698
Douglas fir (Pseudotsuga menziesii (Mirbel) Franco), trees). 699
Because of the paucity of data on these trends, we recently collected a similar dataset, using the 701
Mencuccini, Hölttä, Martinez-Vilalta
four chronosequences of Pinus sylvestris (at Guisachan and Selm Muir), Acer pseudoplatanus 702
and Fraxinus excelsior described in Mencuccini et al. (2005), Martinez-Vilalta et al. (2007a 703
and 2007b) and Hamid & Mencuccini (2009), all from Scotland (UK). Xylem and phloem 704
anatomical parameters were measured on cross-sections taken at breast height from trees of age 705
varying between 3 and 250 (Figures 2 and 3). Our results confirm the trends reported by Ewers 706
& Fisher (1991) for the genus Bauhinia. A highly significant correlation was found between 707
xylem sapwood area and functional phloem area (as estimated in regions of the cross-section 708
where uncrushed phloem could be measured), with a relationship that was broadly similar 709
across the three species studied at the four sites. The overall power-law scaling with a slope of 710
b=0.78 suggested a more rapid accumulation of functional tissue in the xylem than in the 711
phloem in large plants and the individual slopes for the four cases were all below 1.00 (Figure 712
2a). Changes in density and diameter of phloem sieve cells during ontogeny also broadly 713
matched the corresponding changes in xylem conduit density and diameters (Figure 2b and 2c). 714
Because functional areas of both xylem and phloem tissue increased during ontogeny, there 716
were negative relationships in the ratios of leaf area-sapwood area and leaf area-functional 717
phloem area, although for the pine such reductions were surprisingly very small. Because 718
functional xylem tissue accumulates faster than functional phloem tissue (Figure 3), the slopes 719
observed for the leaf-functional phloem area ratios are less steep than those for the leaf area-720
sapwood area ratios for the angiosperms. 721
Mencuccini, Hölttä, Martinez-Vilalta
Significant progress has taken place in understanding how to model the vascular transport 724
systems of trees, particularly tall ones. For the xylem the original pipe model has now been 725
replaced by a more detailed representation of a network of tapered and furcating conduits. 726
These two fundamental properties, tapering and furcation, allow models to address the question 727
of xylem transport in tall organisms and have provided some initial answers. Similar conduit 728
tapering (and possibly furcation) appears to occur in the phloem as well, and the implications 729
of the introduction of hypothetical solute relays for sugar transport have also begun to be 730
explored. 731
It has also become apparent that an examination of the size-related changes in the hydraulic 733
conductance of tall trees needs to consider construction and maintenance costs, again both for 734
the xylem and for the phloem. It had been hypothesised for some time that such costs would be 735
ecologically relevant (e.g., Magnani et al., 2000), but their significance has only become 736
apparent when a much more detailed approach was adopted, i.e., when the wall reinforcement 737
costs of individual conduits were considered, as opposed to generic biomass costs per unit of 738
hydraulic conductance. A challenge here is in separating the conduit wall costs associated 739
directly with hydraulic reinforcement versus those linked to mechanical reinforcement of the 740
structure. The advancement of our knowledge of the allometric scaling of anatomical properties 741
(conduit and pit diameter and length) should contribute to this objective. 742
Perhaps more strikingly, the last ten years have seen the explicit introduction of optimality 744
modelling of plant hydraulic architecture for both xylem and phloem transport systems. 745
Optimality models have proved useful and have contributed to explaining otherwise puzzling 746
phenomena. Most of these optimality models operate at the scale of entire organisms or above 747
(Magnani et al., 2000); perhaps a challenge now is to employ their predictive power at the scale 748
of individual conduits, to make sense of the emerging allometric datasets at the anatomical 749
scale (e.g., Lancashire & Ennos, 2002; Sperry & Hacke, 2004; Hacke et al., 2004). 750
Concomitantly to these advancements, new questions have arisen as a result of the application 752
of a specific optimality criterion. Specifically for the phloem, how can rapid information 753
transmission be obtained while the construction costs are also kept at relatively low levels? 754
How can xylem and phloem properties be simultaneously coordinated with leaf-level 755
Mencuccini, Hölttä, Martinez-Vilalta
transpiration and photosynthetic rates? 756
Collectively these modelling exercises have increased our understanding of the significance of 758
the structural adjustments that allow tall trees to maintain levels of physiological activity 759
identical or similar to the ones of small trees. In turn, by forcing us to examine and incorporate 760
size-dependent properties into xylem and phloem transport models, these models have also 761
achieved scalability, i.e., they can now be applied successfully on both small and large trees. 762
It is remarkable that the models reviewed above give reasonably realistic answers to the 766
questions of the optimal behaviour of tree vascular-transport systems, when many important 767
properties are either not represented or represented only in a very crude fashion. For example, 768
the predicted tapering that minimised the dependency of hydraulic resistance on path length in 769
the WBE model depended crucially on the assumption of how pit resistance scaled with 770
conduit lumen resistance (Becker et al., 2003). Similarly, none of the current models 771
incorporate information on conduit packing or on conduit spatial arrangement, and only very 772
crudely on conduit length, three components which are also likely to be important, because of 773
their impact on the connectivity of the system (cf., Loepfe et al., 2007; Mencuccini et al., 774
2010). Without a mechanistic description of pit resistance, none of the existing optimality 775
models can provide a picture of the expected profile of plant water potentials. The significance 776
of this deficiency is that the trade-off between system efficiency (or efficacy) and safety from 777
embolism cannot presently be incorporated in any of these optimality models. 778
It is interesting to note that much of the recent literature on the topic of tall trees has focussed 780
on the description of the anatomical and physiological features occurring along the branches 781
(e.g., Burgess et al., 2006; Ishii et al., 2008; Domec et al., 2008), in leaves (e.g., Koch et al., 782
2004; Woodruff et al., 2004, 2007, 2008) or in trunks (Domec et al., 2008) at various heights in 783
a tree or at the top of trees of various heights, without linking these parameters to the rate of 784
tapering occurring within individual axes. These two strands of investigation (one dealing with 785
the effects of gravity, the other with the minimization of the hydraulic resistance caused by 786
longitudinal growth, i.e., in other words, the effects of height versus those of length) should be 787
reconciled and brought together. 788
Mencuccini, Hölttä, Martinez-Vilalta
Secondly, while progress has been made in avoiding empirical descriptions of the carbon costs 790
of hydraulic conductance, it is still not clear how these costs should be represented 791
mechanistically at the anatomical level. For example, it is very difficult to separate the costs 792
due to the hydraulic versus the mechanical support function carried out by conduit walls. An 793
optimality model that incorporated both hydraulic and mechanical properties at the anatomical 794
level would probably be a significant step forward. 795
Thirdly, similar uncertainties remain with regard to how to incorporate hydraulic capacitance 797
into optimality models, because we still do not understand to what extent the use of capacitance 798
water by trees results from the emptying of embolised conduits (i.e., a trade-off with 799
conductance, Hölttä et al., 2009a) or from processes independent from embolism (e.g., Meinzer 800
et al., 2003, 2006; Scholz et al., 2007). Incidentally, if water capacitance resulted largely from 801
the use of stored water in the inner bark, this would likely impact the transport properties of the 802
phloem in ways currently not predicted by the existing models. The significance of our inability 803
to model the optimal xylem structure that simultaneously maximises both hydraulic transport 804
and storage is that, among other things, we cannot account for the fact that significant increases 805
in xylem hydraulic resistances are both generally found in tall trees and theoretically predicted 806
to occur (Mencuccini, 2003; Mencuccini et al., 2007; Sperry et al., 2008), while major 807
limitations to their photosynthesis and growth are generally not found (e.g., Ryan et al., 2006; 808
Sillett et al., 2010). Many recent papers have highlighted the importance of capacitance in 809
regulating the scaling of important physiological properties (e.g., Sperry et al., 2008). 810
Finally, the persisting lack of suitable empirical methods to estimate phloem physiological 812
properties (water and solute fluxes, turgor pressure, hydraulic conductivity) still slows our 813
progress in understanding the significance of phloem physiology at the whole plant level and 814
slows our progress in obtaining a clearer picture of the integration and the interactions 815
occurring between these two conducting systems. 816
Mencuccini, Hölttä, Martinez-Vilalta
Models of the transport systems of trees have progressed enormously in the past ten years. We 818
identified and used five criteria to compare models with a common set of terminology. Many 819
of these models have paid attention to the peculiarities of transport in tall trees and the need to 820
incorporate properties that allow their deployment across a range of plant sizes. In practice, this 821
has involved the identification of properties that show size-dependent adjustment or, in other 822
words, properties allowing the model to perform realistically for both large and small trees. A 823
wide range of approaches have been employed to define these properties. Similarly, the criteria 824
by which to assess the optimality of a particular function are also very varied, reflecting the 825
particular questions posed by the researchers. In addition to the xylem, such models have also 826
been applied to understand phloem behaviour and many similarities in the scaling of the two 827
systems are apparent. The future development of models will continue to help direct empirical 828
research that has the potential to advance our understanding of long-distance transport 829
substantially. 830
The authors thank the Catalan government (AGAUR - Generalitat de Catalunya) for a visiting 833
Professorship in UAB to Maurizio Mencuccini. Thanks are due to two anonymous reviewers, 834
for providing useful suggestions that improved the manuscript. 835
Mencuccini, Hölttä, Martinez-Vilalta
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Mencuccini, Hölttä, Martinez-Vilalta
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characteristics and chemical composition of Acer pseudoplatanus and Fraxinus excelsior trees. 876
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water flows in trees according to cohesion theory and Münch hypothesis. Trees: Struct Funct 889
20:67-78. 890
Mencuccini, Hölttä, Martinez-Vilalta
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Mencuccini, Hölttä, Martinez-Vilalta
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and D.C. Shaw. 2006. Dynamics of water transport and storage in conifers studied with 943
deuterium and heat tracing techniques. Plant, Cell Environ 29:105-114.
Mencuccini, Hölttä, Martinez-Vilalta
Mencuccini M (2002) Hydraulic constraints in the functional scaling of trees. Tree Physiol 945
22:553–565. 946
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changes in the xylem architecture of trees. Ecol Lett 10:1084-1093. 953
Mencuccini M, Martinez-Vilalta J, Piñol J, Loepfe L, Burnat M, Alvarez X, Camacho J, Gil D 954
(2010) A quantitative and statistically robust method for the determination of xylem conduit 955
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Mencuccini M, Martinez-Vilalta J, Vanderklein D, Hamid HA, Korakaki E, Lee S, Michiels B 957
(2005) Size-mediated ageing reduces vigour in tall trees. Ecol Lett 8:1183-1190. 958
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and N availability on the belowground carbon and nitrogen dynamics of aspen mesocosms. 960
Oecol 124: 432–445. 961
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the cost of blood volume. PNAS USA 12:207-214. 964
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and the hydraulic efficiency of conifer wood: the role of tracheid allometry and cavitation 970
protection. Am J Bot 93:1265-1273. 971
Mencuccini, Hölttä, Martinez-Vilalta
Pittermann J, Sperry JS, Wheeler JK, Hacke UG, Sikkema EH (2006b) Mechanical 972
reinforcement of tracheids compromises the hydraulic efficiency of conifer xylem. Plant Cell 973
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proportions in Eucalyptus globulus. IAWA J 21:31– 40. 976
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Mencuccini, Hölttä, Martinez-Vilalta
Table 1. Classification of xylem water transport models based on five criteria of model structure, philosophy and applicability. 1050
Model scalability
Efficiency vs. efficacy of
transport system
Choice of optimality
Level of physiological
detail for transport
Scope of theory /
transferability to other
Pipe model
No (at least originally).
Subsequent applications by
Mäkelä (see text).
Efficacy. Computes cross-sectional
area required to transport water and
give mechanical support to a given
Not an optimality model in
original formulation
Limited to functional balance
between leaves and stem.
Somehow incorporates
biomechanical constraints.
Yes: 1) C allocation
Efficiency. Computes total biomass
costs of transport system.
Maximises net photosynthesis,
while maintaining constant plant
water potential.
Limited to computation of total
biomass costs of transport
system and total hydraulic
conductance of roots and stems.
Yes: 1) C allocation; 2) response
to environmental variables.
Yes, both ontogenetically and
Efficacy, bounded by
biomechanical and fractal
constraints. Computes conductance
of each tapered pipe.
Not an explicit optimality
Incorporates conduit tapering in
successive hierarchical levels of
quasi-fractal organism
Yes, very large range of
Murray’s law
Yes, for conduit diameter.
No, for other aspects.
Efficiency. Computes costs of
conduit wall construction.
Maximises xylem hydraulic
conductance while keeping wall
investment constant.
Models conduit tapering and
furcation in successive branches
of furcated pipe.
Limited so far.
Net C gain
Yes, with regard to conduit
numbers, diameters and
Efficiency. Computes costs of
conduit wall construction.
Maximises net whole-plant C
gains (gross gains minus costs)
or C use efficiency (ratio of C
gross gains over C costs), while
maintaining constant plant water
Conduit tapering and number are
included. Derives optimal size-
dependent patterns of plant
photosynthesis. Pits are not
Yes: 1) C allocation; 2) response
to environmental variables. So
far limited to heuristic solutions.
Mencuccini, Hölttä, Martinez-Vilalta
potential. included.
Mencuccini, Hölttä, Martinez-Vilalta
Table 2. Classification of phloem water transport models based on five criteria of model structure, philosophy and applicability. 1053
Model scalability
Efficiency vs. efficacy of
transport system
Choice of optimality criterion
Level of physiological detail for
transport system
Scope of theory /
transferability to
other processes
No. Distance is incorporated
but it fails to represent
transport realistically in large
Efficacy in solute and water
transport and information
transmission in one single tube.
Not an optimality model in original
Highly detailed for the physiological
processes occurring within a single tube;
does not incorporate notions of conduit
numbers, conduit tapering or conduit
branching. Additional solutes or relays are
not represented.
Understanding physiology.
Little transferability.
Only if the ratio of number of
conduits to leaf area supplied
is specified.
Efficiency. Computes costs of
conduit wall construction and
number of pipes required to
transport sugars.
Minimise number of pipes required,
given the photosynthesis.
Conduit tapering and number of conduits
are included. Incorporates relays and
additional solutes.
Understanding physiology.
No transferability.
Net C gain
Yes, with regard to conduit
numbers, diameters and
Efficiency. Computes costs of
conduit wall construction and
number of pipes required to
transport sugars.
Maximises net whole-plant C gains
(gross gains minus costs) or C use
efficiency (ratio of C gross gains over C
costs) based on combined xylem and
phloem costs.
Conduit tapering, number and furcation are
included. Phloem and xylem transport
systems are jointly represented and
Yes: 1) C allocation; 2)
response to environmental
variables; 3) Estimates of
turnover times of
photosynthetic C.
Mencuccini, Hölttä, Martinez-Vilalta
Table 3. Synthesis of published studies on age-related changes in phloem sieve cell diameters 1054
Species Type of measurement Observed trend Author(s)
Acacia nilotica var. Telia Along the stem Downward increase Ghouse & Iqbal (1977)
Betula pendula Along the stem
Downward increase
Trockenbrodt (1994)
Bauhinia aculeata (srhub)
Bauhinia galpinii (srhub)
Bauhinia blakeana (tree)
Bauhinia variegata (tree)
Along the stem
Downward increase
Ewers & Fisher (1991)
Bauhinia fassoglensis (vine)
Bauhinia vahii (vine)
Along the stem
Downward increase
Ewers & Fisher (1991)
Fagus sylvatica Along the stem Downward increase Schulz and Behnke (1986)
Fagus sylvatica Young vs old trees more numerous and smaller
sieve tubes in 10-m compared
to 30-m-tall trees
Vollenweider et al. (1994)
Eucalyptus globulus Along the stem No trend Quilhó et al (2000)
Populus deltoides Along the stem Downward increase MacDaniels (1918)
Populus euramericana cv.
Along the stem Downward increase Stahel (1968)
Populus tremula Along the stem Downward increase Raskatov & Kosicenko, (1968)
Populus tremula Along the stem
Downward increase
Trockenbrodt (1994)
Prosopis spicigera Along the stem Downward increase Ghouse & Iqbal (1977)
Quercus robar Along the stem
Downward increase
Trockenbrodt (1994)
Ulmus Americana Along the stem Downward increase MacDaniels (1918)
Ulmus glabra Along the stem Downward increase Trockenbrodt (1994)
Picea abies Along the stem Smaller sieve cells at the stem
bottom compared to base and
inside of crown
Rosner et al. (2001)
Pinus longaeva Stems of trees of age
varying between 751
and 1863 years
No change in phloem
increment or in number of
sieve cells
Connor & Lanner (1990)
Lolium temulentum Along leaf veins Diameter increase in major
compared to minor veins
Lush (1976)
Panicum maximum Along leaf veins Diameter increase in major
compared to minor veins
Lush (1976)
Mencuccini, Hölttä, Martinez-Vilalta
Zea mays Along the primary
unbranched root
Diameter increase and fewer
cells towards the tip
Enns et al. (2006)
Mencuccini, Hölttä, Martinez-Vilalta
Figure 1. Summary of the empirical and modelling results obtained by Mencuccini & Hölttä 1059
(2010) related to the effective transport velocities of isotopically labelled sugars in the pathway 1060
from canopy leaves to the soil surface (i.e., via phloem transport, root respiration and soil 1061
gaseous diffusion). The dotted surface represents the range of calculated transport velocities 1062
and the continuous black line the calculated mean velocity (in m/day, left axis), based on the 1063
observed times of appearance of the isotopic spikes out of the soil as gaseous CO
after the 1064
time of labelling of canopy photosynthesis, for a range of organisms ranging from small 1065
herbaceous plants to tall trees. The dashed and the dotted lines represent the inferred changes in 1066
phloem specific conductivity (m
, inner right-hand side axis) and in phloem turgor pressure 1067
gradient (MPa, outer right-hand side axis), respectively, that must have taken place in the 1068
phloem transport systems of these organisms to account for the observed velocities. Sugar 1069
storage in the system and gaseous diffusion in the soil were also accounted for in the model but 1070
did not explain the observed size-related pattern. 1071
Figure 2. Simultaneous changes in xylem and phloem properties during ontogeny in three 1073
different tree species, i.e., Acer pseudoplatanus (crossed squares), Fraxinus excelsior (crossed 1074
circles) and Pinus sylvestris (white and black triangles) at four sites across Scotland (UK). 1075
Xylem and phloem properties were obtained by sampling tree cores at breast height from a 1076
range of age and size classes. Top Panel: Average xylem and phloem functional areas; Middle 1077
Panel: Average xylem and phloem conduit density; Bottom Panel: Average xylem and phloem 1078
conduit radius. Numbers in the panels refer to the slopes of the log-log scaling relationships 1079
between the various properties, when significant. 1080
Figure 3. Size-related changes in the ratios of leaf to functional sapwood area and leaf to 1082
functional phloem area across three species of trees studied in Scotland (UK). Top Panel: Acer 1083
pseudoplatanus. Middle Panel: Fraxinus excelsior; Bottom Panel: Pinus sylvestris. Note that 1084
the ratios are plotted on a log scale to accommodate the different values present for phloem 1085
versus xylem-based calculations. Figures in the panels refer to the slopes of the log-log scaling 1086
Mencuccini, Hölttä, Martinez-Vilalta
relationships between the various properties plotted against stem diameter, when these were 1087
significant. 1088
Mencuccini, Hölttä, Martinez-Vilalta
xylem sapwood area (cm
0 1000 2000 3000 4000
functional phloem area (cm
b=0.78, R
xylem conduit density (n mm
1 10 100 1000
phloem tube density (n mm
xylem conduit radius, µm
0 20 40 60 80 100
phloem tube radius, µm
not sign
Pinus (Selm Muir)
Pinus (Guisachan)
Acer + Fraxinus b=0.37
Pinus b=0.53
Mencuccini, Hölttä, Martinez-Vilalta
0 20 40 60 80 100 120
leaf-functional phloem area or
leaf-xylem area ratios, m
leaf-sapwood ratio, b=-0.71
leaf-phloem ratio, b=-0.26
0 20 40 60 80 100
leaf-functional phloem area or
leaf-xylem area ratios, m
leaf-sapwood ratio, b= -0.88
leaf-phloem ratio, b= -0.42
tree diameter, cm
0 20 40 60 80 100
leaf-functional phloem area or
leaf-xylem area ratios, m
Selm Muir Al : Asap, not sign
Selm Muir Al: Aphl, not sign
Guisachan Al : Asap, not sign
Guisachan Al: Aphl, b= -0.21
Acer pseudoplatanus
Fraxinus excelsior
Pinus sylvestris
... This may have been suggested by the fact that the values of L are given for different species (graphs and Table 1 in Shinozaki et al.'s paper) with no details on the corresponding environmental conditions. This may have led to the interpretation that the PMT is not scalable, in the sense that it does not account for size-related effects on the leaf mass-to-SW area ratio (Mencuccini et al., 2011). This property of non-scalability, or at least changes in L with stand density or growth stages, is in fact acknowledged by Shinozaki et al.: they report variations of L within a growth season in a dense stand of 3-year-old Ulmus parvifolia (Fig. 11 in their paper) and with combinations of different growth stages and densities in maize (Zea mays) and buckwheat (Fagopyrum esculentum) in their Table 2. ...
... As argued above and by other authors (Normand et al., 2008;Mencuccini et al., 2011;Holtta et al., 2013), the PMT does not provide any details about the nature of 'pipes', thus leading to different interpretations of their structure. First, the analogy between the structure of a stem as described by Shinozaki et al. (i.e. a longitudinally oriented set of pipes) and the anatomical structure of a plant stem has led to the interpretation of Shinozaki et al.'s pipe as a tracheary element (i.e. a vessel or tracheid) (Rennolls, 1994;West et al., 1997West et al., , 1999Roderick and Berry, 2001;McCulloh et al., 2003). ...
... Consequently, the PMT has been misinterpreted as a species-specific isometric relationship between leaf area and conductive SW area. As no rule describing the variation of the parameter L with tree size was given by Shinozaki et al., a key criticism of the PMT is its non-scalability (Mencuccini et al., 2011). ...
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Background: More than a half century ago, Shinozaki et al. (Shinozaki K, Yoda K, Hozumi K, Kira T. 1964a. A quantitative analysis of plant form – the pipe model theory. I. Basic analyses. Japanese Journal of EcologyB: 97–105) proposed an elegant conceptual framework, the pipe model theory (PMT), to interpret the observed linear relationship between the amount of stem tissue and corresponding supported leaves. The PMT brought a satisfactory answer to two vividly debated problems that were unresolved at the moment of its publication: (1) What determines tree form and which rules drive biomass allocation to the foliar versus stem compartments in plants? (2) How can foliar area or mass in an individual plant, in a stand or at even larger scales be estimated? Since its initial formulation, the PMT has been reinterpreted and used in applications, and has undoubtedly become an important milestone in the mathematical interpretation of plant form and functioning. Scope: This article aims to review the PMT by going back to its initial formulation, stating its explicit and implicit properties and discussing them in the light of current biological knowledge and experimental evidence in order to identify the validity and range of applicability of the theory. We also discuss the use of the theory in tree biomechanics and hydraulics as well as in functional–structural plant modelling. Conclusions: Scrutinizing the PMT in the light of modern biological knowledge revealed that most of its properties are not valid as a general rule. The hydraulic framework derived from the PMT has attracted much more attention than its mechanical counterpart and implies that only the conductive portion of a stem cross-section should be proportional to the supported foliage amount rather than the whole of it. The facts that this conductive portion is experimentally difficult to measure and varies with environmental conditions and tree ontogeny might cause the commonly reported non-linear relationships between foliage and stem metrics. Nevertheless, the PMT can still be considered as a portfolio of properties providing a unified framework to integrate and analyse functional–structural relationships.
... It has been shown theoretically that, without size-related adjustments in phloem dimensions to increase phloem-specific conductivity, phloem sap flow velocity would decrease with increasing tree height Hölttä 2010, Mencuccini et al. 2011). Phloem conduit widening is thus thought to compensate for the increased resistance with increasing tree height (Hölttä et al. 2009, Mencuccini et al. 2011. Several studies report variations in sieve cell dimensions with height in trees (Petit andCrivellaro 2014, Jyske andHölttä 2015), but most have addressed these variations along individual stems rather than among different trees of various dimensions (Mencuccini et al. 2011). ...
... Phloem conduit widening is thus thought to compensate for the increased resistance with increasing tree height (Hölttä et al. 2009, Mencuccini et al. 2011. Several studies report variations in sieve cell dimensions with height in trees (Petit andCrivellaro 2014, Jyske andHölttä 2015), but most have addressed these variations along individual stems rather than among different trees of various dimensions (Mencuccini et al. 2011). Alongtree comparisons are nevertheless a prerequisite to obtaining stand-level estimates of phloem carbon translocation. ...
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At stand level, carbon translocation in tree stems has to match canopy photosynthesis and carbohydrate requirements to sustain growth and the physiological activities of belowground sinks. This study applied the Hagen-Poiseuille equation to the pressure-flow hypothesis to estimate phloem carbon translocation and evaluate what percentage of canopy photosynthate can be transported belowground in a hinoki cypress (Chamaecyparis obtusa Sieb. et Zucc.) stand. An anatomical study revealed that, in contrast to sieve cell density, conductive phloem thickness and sieve cell hydraulic diameter at 1.3 m in height increased with increasing tree diameter, as did the concentration of soluble sugars in the phloem sap. At tree level, hydraulic conductivity increased by two orders of magnitude from the smallest to the largest trees in the stand, resulting in a stand-level hydraulic conductance of 1.7 × 10-15 m Pa-1 s-1. The osmotic potential of the sap extracted from the inner bark was -0.75 MPa. Assuming that phloem water potential equalled foliage water potential at predawn, the turgor pressure in the phloem at 1.3 m in height was estimated at 0.22 MPa, 0.59 MPa lower than values estimated in the foliage. With this maximal turgor pressure gradient, which would be lower during day-time when foliage water potential drops, the estimated stand-level rate of carbon translocation was 2.0 gC m-2 day-1 (30% of daily gross canopy photosynthesis), at a time of the year when aboveground growth and related respiration is thought to consume a large fraction of photosynthate, at the expense of belowground activity. Despite relying on some assumptions and approximations, this approach, when coupled with measurements of canopy photosynthesis, may further be used to provide qualitative insight into the seasonal dynamics of belowground carbon allocation.
... It has been shown the- oretically that, without size-related adjustments in phloem dimensions to increase phloem-specific conductivity, phloem sap flow velocity would decrease with increasing tree height Hölttä 2010, Mencuccini et al. 2011). Phloem conduit widening is thus thought to compensate for the increased resistance with increasing tree height ( Hölttä et al. 2009Hölttä et al. , Mencuccini et al. 2011). Several studies report variations in sieve cell dimensions with height in trees (Petit andCrivellaro 2014, Jyske andHölttä 2015), but most have addressed these variations along individual stems rather than among different trees of various dimensions ( Mencuccini et al. 2011). ...
... Phloem conduit widening is thus thought to compensate for the increased resistance with increasing tree height ( Hölttä et al. 2009Hölttä et al. , Mencuccini et al. 2011). Several studies report variations in sieve cell dimensions with height in trees (Petit andCrivellaro 2014, Jyske andHölttä 2015), but most have addressed these variations along individual stems rather than among different trees of various dimensions ( Mencuccini et al. 2011). Along- tree comparisons are nevertheless a prerequisite to obtaining stand-level estimates of phloem carbon translocation. ...
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Phloem failure has recently been recognized as one of the mechanisms causing tree mortality under drought, though direct evidence is still lacking. We combined 13C pulse-labelling of 8-year-old beech trees (Fagus sylvatica L.) growing outdoors in a nursery with an anatomical study of the phloem tissue in their stems to examine how drought alters carbon transport and phloem transport capacity. For the six trees under drought, predawn leaf water potential ranged from -0.7 to -2.4 MPa, compared with an average of -0.2 MPa in five control trees with no water stress. We also observed a longer residence time of excess 13C in the foliage and the phloem sap in trees under drought compared with controls. Compared with controls, excess 13C in trunk respiration peaked later in trees under moderate drought conditions and showed no decline even after 4 days under more severe drought conditions. We estimated higher phloem sap viscosity in trees under drought. We also observed much smaller sieve-tube radii in all drought-stressed trees, which led to lower sieve-tube conductivity and lower phloem conductance in the tree stem. We concluded that prolonged drought affected phloem transport capacity through a change in anatomy and that the slowdown of phloem transport under drought likely resulted from a reduced driving force due to lower hydrostatic pressure between the source and sink organs.
... Phloem width, is relatively stable irrespectively of plant height [51], thus suggesting potential of intrinsic nutrient reallocation crucial for regenerated after damage [58,59]. Leaf gas exchange is related to transport of assimilates through phloem [60], supporting the complex response of phloem width to R, Y, and O light ( Figures 1D and 2C), which generally facilitate efficiency of photosynthesis [14,16,18,20]. ...
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Micropropagation of forest reproductive material is becoming an increasingly important tool of climate-smart forest management, whose efficiency is depending on artificial illumination, which in turn can have species-specific effects. To improve the energy-efficiency of micropropagation, light emitting diodes (LED) are becoming more popular; however, they emit light of narrow spectral composition, synergic effects of which can alter plantlet development. Regarding the in vitro cultures of trees, such effects have been scarcely studied. In this study, three clones of silver birch (Betula pendula Roth.) and three clones of hybrid aspen (Populus tremuloides Michx. × Populus tremula L.) from the eastern Baltic region were tested. The responses of leaf and stem anatomy of in vitro cultures to three LED light illumination treatments differing by spectral composition and to illumination by fluorescent tubes were estimated by linear (mixed) models. The studied light treatments had non-interacted effects on stomata density and on the secondary xylem cell wall in the stem of silver birch and in the stomata length, stem radius, and phloem width of hybrid aspen. Furthermore, clone-specific responses to illumination were observed for number of chloroplasts and phloem width of silver birch and for leaf thickness and xylem cell wall thickness of hybrid aspen, implying different mechanisms of shade avoidance. In general, the responses of plantlet anatomy differed according to the width of the light spectrum in case of LED, as well as for fluorescent tubes. Considering the legacy effects of early development of plantlets, adaptability of illumination in terms of spectral composition according to the requirements of genotypes appear highly beneficial for micropropagation of sustainable forest reproductive material.
... Similarly, under drought stress environmental conditions, for declining trees, phloem formation has priority over xylem formation for the long-term survival of a tree (Gričar et al. 2009). Our results here support earlier findings that the ratio of annually produced phloem to xylem cell number was related and phloem:xylem area is larger for smaller trees than for larger trees (e.g., Mencuccini et al. 2011;Jyske and Hölttä 2015). In addition, PCA analysis showed that a large xylem area was associated with a high growth rate. ...
Key messageAbies fargesii var. faxoniana (Rehder et E.H. Wilson) Tang S Liu seedlings at high elevations compensate for the low efficiency of their water conducting system and high phloem hydraulic resistance by the enhancement in xylem:leaf area, phloem:leaf area, and phloem:xylem area.ContextMaintenance of xylem and phloem transport is particularly important for the survival and growth of trees at the treeline. How plants modify the allocation to leaf, xylem, and phloem structures to adapt to the treeline environment is an important issue.AimsThe purpose of this study was to estimate how xylem and phloem anatomy and volume as well as leaf functional traits of A. fargesii seedlings vary with elevation.Methods We examined elevation-related differences in a variety of phloem and xylem functional areas and hydraulic conduit diameters of A. fargesii seedlings growing at elevations between 2600 and 3200 m in the subalpine conifer forest of southwest China.ResultsXylem area, last xylem ring area, and leaf:sapwood area significantly decreased, while xylem:leaf area, phloem:leaf area, and non-collapsed phloem:xylem area significantly increased with elevation. Principal components analysis showed that xylem area, non-collapsed phloem area, and xylem:phloem area were positively correlated with growth rates.Conclusion Our results showed that A. fargesii tree seedlings at the treeline tend to facilitate growth and maintain functional water and sugar balance between stem and leaves by the enhancement in xylem:leaf area, phloem:leaf area, and phloem:xylem area, but not through differences in vessel lumen diameter.
... This means that more wood is allocated in the lower parts of the stem, resulting in a more tapered stem. Stem thickening is also related to tree physiology and mechanics, as a taller tree with a larger crown needs more supporting structures and xylem for enhanced resilience and water transportation [20][21][22][23]. ...
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Tree growth is a multidimensional process that is affected by several factors. There is a continuous demand for improved information on tree growth and the ecological traits controlling it. This study aims at providing new approaches to improve ecological understanding of tree growth by the means of terrestrial laser scanning (TLS). Changes in tree stem form and stem volume allocation were investigated during a five-year monitoring period. In total, a selection of attributes from 736 trees from 37 sample plots representing different forest structures were extracted from taper curves derived from two-date TLS point clouds. The results of this study showed the capability of point cloud-based methods in detecting changes in the stem form and volume allocation. In addition, the results showed a significant difference between different forest structures in how relative stem volume and logwood volume increased during the monitoring period. Along with contributing to providing more accurate information for monitoring purposes in general, the findings of this study showed the ability and many possibilities of point cloud-based method to characterize changes in living organisms in particular, which further promote the feasibility of using point clouds as an observation method also in ecological studies.
... This is only possible when the tree reaches a certain size (Domec et al. 2008;Mencuccini et al. 2007;Woodruff et al. 2008). Size affects the distribution of nutrients as well as the ratio of tissues synthesizing and consuming assimilates, thereby determining the physiological status of the organism (Mencuccini et al. 2011). Changes in physiology cause changes in gene expression. ...
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The influence of scions donor tree age on the morphological variability of needles, shoots, and branching pattern was studied in 7-year-old grafted scions of Siberian stone pine (Pinus sibirica Du Tour). We analyzed clones of four age groups: seedlings (4–7 years), young trees (38–62 years), mature trees (238–376 years), and old trees (549–700 years). The results showed that during the first 7 years after grafting, the age of the scion donor tree greatly affects branching patterns and leaf morphology of grafted trees. The age of the scion donor tree also significantly affects the growth of grafts in length, albeit to a lesser extent. Grafts derived from seedlings, young, mature, and old trees had different ratios of shoot elongation and branching: weak growth and abundant branching, strong growth and abundant branching, strong growth and medium branching, weak growth and branching, respectively. The degree of needle xeromorphy, the level of apical dominance, and the number of epicormic buds increased significantly with the age of scion donor trees. Premature (late summer and autumn) growth of dormant buds was typical only for grafts derived from seedlings and, to a lesser extent, from young trees. The closer the scion donor tree is to the ontogenetic growth peak, the more elongated and abundant the branching of the grafts derived from it.
... Similar tapering patterns are also seen in phloem conduits, partly as a consequence of the fact that both xylem and phloem cells derive from the same cambial initials (e.g. Hölttä et al. 2013;Jyske & Hölttä 2014;Mencuccini et al. 2011). ...
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Much progress has been made in understanding the physiology and biochemistry of organ-level senescence. By comparison, ageing and senescence at the organismal level remain poorly known, especially so for perennial plants, for which model systems have been developed only recently. It has become clear that in perennials, ageing is accompanied by meristem-extrinsic size-related effects, even though separating these effects from meristem endogenous senescence is often challenging. Several experimental approaches have been identified that allow exploring whether the physiology and biochemical processes in perennials change systematically throughout the ontogenetic cycle and whether these changes are primarily age driven or size driven. Further progress can come from a more basic understanding of the metabolic, hormonal and molecular controls of these transitions in perennial plants and by framing our physiological and biochemical understanding within a clear evolutionary framework of the evolution, or lack thereof, of senescence.
Premise: The dimensions of phloem sieve elements have been shown to vary as a function of tree height, decreasing hydraulic resistance as the transport pathway lengthens. However, little is known about ontogenetic patterns of sieve element scaling. Here we examine within a single species (Quercus rubra) how decreases in hydraulic resistance with distance from the plant apex are mediated by overall plant size. Methods: We sampled and imaged phloem tissue at multiple heights along the main stem and in the live crown of four size classes of trees using fluorescence and scanning electron microscopy. Sieve element length and radius, the number of sieve areas per compound plate, pore number, and pore radius were used to calculate total hydraulic resistance at each sampling location. Results: Sieve element length varied with tree size, while sieve element radius, sieve pore radius, and the number of sieve areas per compound plate varied with sampling position. When data from all size classes were aggregated, all four variables followed a power-law trend with distance from the top of the tree. The net effect of these ontogenetic scalings was to make total hydraulic sieve tube resistance independent of tree height from 0.5 to over 20 m. Conclusions: Sieve element development responded to two pieces of information, tree size and distance from the apex, in a manner that conserved total sieve tube resistance across size classes. A further differentiated response between the phloem in the live crown and in the main stem is also suggested.
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Trees present a critical challenge to long-distance transport because as a tree grows in height and the transport pathway increases in length, the hydraulic resistance of the vascular tissue should increase. This has led many to question whether trees can rely on a passive transport mechanism to move carbohydrates from their leaves to their roots. Although species that actively load sugars into their phloem, such as vines and herbs, can increase the driving force for transport as they elongate, it is possible that many trees cannot generate high turgor pressures because they do not use transporters to load sugar into the phloem. Here, we examine how trees can maintain efficient carbohydrate transport as they grow taller by analysing sieve tube anatomy, including sieve plate geometry, using recently developed preparation and imaging techniques, and by measuring the turgor pressures in the leaves of a tall tree in situ. Across nine deciduous species, we find that hydraulic resistance in the phloem scales inversely with plant height because of a shift in sieve element structure along the length of individual trees. This scaling relationship seems robust across multiple species despite large differences in plate anatomy. The importance of this scaling becomes clear when phloem transport is modelled using turgor pressures measured in the leaves of a mature red oak tree. These pressures are of sufficient magnitude to drive phloem transport only in concert with structural changes in the phloem that reduce transport resistance. As a result, the key to the long-standing mystery of how trees maintain phloem transport as they increase in size lies in the structure of the phloem and its ability to change hydraulic properties with plant height.
Xylem and phloem tissue samples were collected from various-aged Great Basin bristlecone pine (Pinus longaeva D. K. Bailey) stems in southern Utah and southeastern California to determine whether the vascular cambia of older trees produce fewer xylem rays, shorter-lived xylem and phloem ray cells, fewer phloem sieve cells, and a thinner phloem. Increment cores were examined to determine whether ‘aged’ cambia produced narrower tracheids that might reduce water translocation. Sapwood thickness was measured and sapwood growth layers were counted on these cores. Regression and Classification and Regression Tree (CART) analyses of sample data found no age-related changes in cambial products. Phloem and xylem production appeared normal at all ages, with no evidence of cambial malfunction.
To test the applicability of the pipe model theory to actual tree form, the frequency distribution of the thickness of woody organs in a tree was examined in 10 different species. The frequency f(D) of a certain diameter class D proved to have a definite pattern of distribution in the root, branch and trunk respectively, with only a little difference between the species. The obtained f(D)〜D curves showed that a root system could well be approximated by the assemblage of many pipes of unit thickness, a trunk by a few cones piled up one upon another, and a branch system by a geometric model intermediate between the two. The results were well consistent with the pipe model theory of tree form. As an application of the theory in forest ecology, a new method for estimating the amounts of leaves or branches of trees and stands was also proposed, based on the direct proportionality found between those amounts and the cross-sectional area of the trunk at the height just below the lowest living branch.
Vascular Transport in Plants provides an up-to-date synthesis of new research on the biology of long distance transport processes in plants. It will be a valuable resource and reference for researchers and graduate level students in physiology, molecular biology, physiology, ecology, ecological physiology, development, and all applied disciplines related to agriculture, horticulture, forestry and biotechnology. The book considers long-distance transport from the perspective of molecular level processes to whole plant function, allowing readers to integrate information relating to vascular transport across multiple scales. The book is unique in presenting xylem and phloem transport processes in plants together in a comparative style that emphasizes the important interactions between these two parallel transport systems. * Includes 105 exceptional figures * Discusses xylem and phloem transport in a single volume, highlighting their interactions * Syntheses of structure, function and biology of vascular transport by leading authorities * Poses unsolved questions and stimulates future research * Provides a new conceptual framework for vascular function in plants.
The relationships between leaf area and sapwood and inner bark quantities (widths, areas, and volumes) were studied in an attempt to understand the design criteria for sapwood quantity in eighteen 34-year-old Douglas-fir (Pseudotsuga menziesii) trees with a wide range of leaf areas, sapwood areas, and dry masses of leaf, xylem, bark, and branch. Cumulative leaf area increased from the tip to the base of the crown, and then was constant; none of the other variables had the same distribution, and so whereas there were many significant correlations, none of the factors can be related to leaf area in a simple, causal manner. Leaf area/sapwood area was extremely variable from tree to tree at a given height, and within a tree from height to height. Sapwood width was relatively constant from the tip down the stem, supporting the hypothesis that sapwood quantity in this species is related to radial gas diffusion causing either a lethal buildup Of CO2 or a lethal depletion of O-2 at the sap /heart boundary. However, there was no significant correlation between leaf area and either total sapwood density (dry weight/ green volume) or the average latewood density in the sapwood which were used as proxies for radial diffusion rate; further research on actual radial gas diffusion in green wood may be informative.
Many theories have been formed to account for the ascent of sap in high trees, when root pressure is not acting. All have been found, on careful examination, unsatisfactory. Our attention was particularly directed to the problem as we were together in Bonn, in the Summer of 1893, when Professor E. Strasburger was kind enough to show us some of his experiments on the question, and since then we have, at intervals, occupied ourselves with some considerations as to the cause of the ascent of liquids in trees. It was not, however, till late last Spring that we had leisure to enter definitely on the research. We wish to acknowledge the kindness of Professor E. Perceval Wright in giving us the benefit of his advice on all occasions, and also the advantage we derived from Professor G. F. FitzGerald’s suggestive ideas.
Munch's pressure-flow mechanism is the most popular hypothesis for phloem translocation; however, difficulties with it are not resolved. The metabolic pumping hypotheses on the other hand often run into complications with the high flux-density requirement of translocation. A 'relay' mechanism is proposed for solute translocation in plants, which is a hybrid between pressure flow and one or another of the, at present, alternative candidates for the task of driving phloem translocation. Such a compromise may make sense of the confusing experimental and ultrastructural evidence.