Tansley Review No. 119 Theoretical considerations of optimal conduit length for water transport in vascular plants

Abstract

Summary 196

I. INTRODUCTION 196

1. The neglected dimension 196

2. Basic concepts 197

(a) The heuristic notion of vessel-tiers 197

(b) Ohm's law 199

(c) Conductances, resistances and resistivities 199

(d) Lumen and pit resistances 199

(e) The importance of conduit radius and length in conductance 199

II. EVOLUTIONARY TRENDS IN CONDUIT DIMENSIONS 199

1. Nature and origin of xylem conduits 199

2. Increasing hydraulic conductance with increasing diameter and length 200

(a) Evolutionary trends in tracheid dimensions 200

(b) Origin of the vessel 200

3. Functional limitations to increasing vessel length 201

(a) Safety versus efficiency 201

(b) Containment of cavitation and embolism 202

III. MAXIMUM XYLEM TRANSPORT IN THE PRESENCE OF CAVITATION 203

1. Cavitation is linked to the driving force for transport 203

2. Transport models and extreme assumptions about conduit length 203

(a) Unitary cavitation response (n = 1) 203

(b) Infinitely partitioned response (n = ∞) 204

(c) ΔP and cavitation containment 204

IV. INCLUDING VESSEL LENGTH IN A TRANSPORT MODEL 205

1. Framing questions of optimal conduit length 205

2. A numeric model for flow through n conduit tiers 205

(a) Model structure 205

(b) Model solution 206

3. Optimization when f(P) is linear 206

(a) Isolating the effects of n on cavitation containment 206

(b) Optimal conduit tier-length distributions (OCLDs) 207

(c) Abrupt changes in conduit length 208

(d) Optimal frequency of end walls: incorporating R_pit 208

4. Optimization when f(P) is curvilinear 210

V. CONDUIT LENGTH IN MODERN TAXA: IMPLICATIONS FOR TRANSPORT 210

1. Limitations to the concept of conduit tiers 210

(a) Vessel ends are randomly distributed 210

(b) Dispersion around mean length within each ‘tier’ 210

2. Is the xylem optimally partitioned? 211

(a) Optimal number of end walls 211

(b) Conduit length distribution along the pathway 211

3. Hydraulic segmentation 212

(a) Segmentation in hydraulic resistance 212

(b) Segmentation in cavitation vulnerability 212

VI. CONCLUSIONS 212

1. Anatomy 212

2. Modelling flow 213

VII. APPENDIX: ANALYTICAL SOLUTIONS AND PROOFS 213

1. Analytic solution for Q_maxwith a single tier 213

2. The general case for n tiers 214

3. Analytic solution for Q_maxwith two tiers 214

4. Matric flux and n = ∞ 215

5. R_pit, variable pathway resistance and OCLD 215

6. Proof of Eqn 15 describing limited cavitation containment 215

Acknowledgements 216

References 216

Vascular plants have shown a strong evolutionary trend towards increasing length in xylem conduits. Increasing conduit length affects water transport in two opposing ways, creating a compromise that should ultimately define an optimal conduit length. The most obvious effect of increased length is to decrease the sequential number of separate conduits needed to traverse the entire pathway, and thereby to reduce the number of wall-crossings and the hydraulic resistance to flow within the xylem. This is an essential evolutionary pressure towards the development of the vessel, a conduit of multicellular origin whose length is not restricted by developmental constraints. The vessel has been an essential component in all plant lineages, achieving transport tissues with very high specific conductivity. A countering effect, however, arises from the partitioning of the cavitation response, a process whereby individual xylem conduits drain of water and lose conducting capacity. Flow in the xylem is down a gradient of negative pressure, which is necessarily most negative in the distal regions (i.e. near the foliage). Cavitation can be caused directly by negative pressures, and results in a total loss of the hydraulic conductance of the individual conduits within which it occurs. If cavitation is triggered by low pressure experienced only at the very distal end of a long conduit, the conduit nevertheless loses its conducting capacity along its entire length. Pathways composed of long conduits will therefore suffer greater total conductance loss for equivalent pressure gradients, because the effects of cavitation are not effectively restricted to the tissue regions within which the cavitation events are generated. By contrast, short conduits can restrict cavitation to distal regions, leaving trunk and root tissues less seriously affected. The increased total conductance loss of a system made entirely of very long conduits translates into a lower maximum rate of water transport in the xylem. The loss in hydraulic capacity associated with failure to partition the flow pathway fully, and locally contain the effects of cavitation, theoretically reaches a maximum of 50% for the extreme case in which a single set of conduits traverses the entire pathway. Shorter conduits confine individual cavitation events to smaller regions and permit the pathway as a whole to have a more gradual conductance loss in conjunction with the pressure gradient. A compromise exists between (1) minimizing total conductance loss from cavitation via fine partitioning of the pathway with many tiers of short conduits, and (2) reducing total wall resistance via coarse partitioning with a few tiers of long conduits. An analysis is presented of the optimal number of end walls (i.e. mean conduit length relative to total pathway length) to maximize transport capacity. The principle of optimal containment of cavitation also predicts that conduits should not be of equal length in all portions of the pathway. The frequency of end walls should rather be proportional to the magnitude of the water-potential gradient at each point, and conduits should be longest in the basal portion (roots) and progressively shortened as they move up the stems to the foliage. These concepts have implications for our understanding of the contrasting xylem anatomies of roots and shoots, as well as the limits to evolution for increased hydraulic conductance per xylem cross-sectional area. They also indicate that to model the hydraulic behaviour of plants accurately it is necessary to know the conduit length distribution in the water flux pathway associated with species-specific xylem anatomy.