A new phenomenological model to describe root-soil interactions based on percolation theory
Introduction
Plant growth and productivity are influenced by many factors, such as nutrient and light availability, adaptation, competition, soil substrate variability, grazing by herbivores, attacks by various pathogens, and climate variables. Mechanisms that explain observed differences in maximum tree height at different locations and patterns in height growth have eluded ecologists and plant physiologists (Ryan and Yoder, 1997). Clearly, the growth of trees can be restricted by any conditions that limit productivity. We suggest, however, that it may be possible that any of these limiting conditions is expressed through, or reflected by, a reduction in actual transpiration. Already more than a half a century ago, Rosenzweig (1968) argued that variability in productivity is well accounted for by (evapo)-transpiration. Rosenzweig's argument is elegant, though difficult to use predictively, on account of the many interacting factors that influence how much water is actually transpired by any individual plant. Although the physiological responses of plants to water stress, and the associated effects on plant growth, are well-studied on easy to access aboveground tissues, i.e., stems, branches, and leaves (Zhu, 2002; Jaleel et al., 2009; Venturas et al., 2017), there still remains a paucity of information on how plant growth is modulated by fundamental constraints over plant available soil water that arise from the interaction between roots and soil physical properties. While this interaction provides a basis for our guiding hypothesis, our goal here is to probe available literature for evidence that limitations in transpiration due to variability in a variety of local conditions, such as microclimate, soil conditions, and slope aspect or curvature, are reflected in corresponding reductions in tree height. With this investigation, we hope then to provide motivation for more detailed experimental studies that can isolate the dependence of growth rate on transpiration.
The basis for the application of percolation theory approach for explaining how root-soil interactions regulate transpiration was laid by considering limitations on root growth imposed by network properties of the soil (Hunt, 2017), and an interfacial constraint between the directed network of a plant and the random network of the soil (Hunt and Manzoni, 2016). Two recent large-scale studies of world data sets on tree growth confirmed the importance of percolation theoretical values of: (a) the two-dimensional optimal path exponent in the time dependence of tree height and (b) root radial extent growth rates, and the two-dimensional value of the percolation mass fractal dimensionality, df, to root fractal mass.
The goal of the current paper is to investigate whether variability in plant growth on local scales and within species is, in part, related to constraints placed on transpiration by soil structure that can be explained by percolation theory. The scope of the paper is to present the results of testing several scenarios including different terrain curvature, slope aspect, soil characteristics, and climate ranges. Particularly, we addressed the possibility that variability in tree height cited by Ryan and Yoder (1997), as well as several other cases, may be accounted for by a single analytical result for the growth of plants, suggested to be governed by root radial extent (RRE), but also shown to account for plant height (Hunt and Manzoni, 2016; Hunt, 2017). Note that the same result for extensional growth rates used here generates as well (Hunt, 2017) the quoted relationship of net primary productivity (NPP) to transpiration, the problem that originally interested Rosenzweig (1968).
Section snippets
Critical literature review
A literature review of publications on the variability of tree growth showed that multiple factors and processes can affect transpiration, such as soil moisture content, compaction and hydrophobicity, climate, slope aspect, and slope curvature. For example, Popova et al. (2016) found that the optimal path selection by roots in the soil is fundamental for resource acquisition. Popova et al. (2016) stated that “root apices may direct their growth through cracks or generally follow paths with a
Phenomenological model
The hypothesis of the relevance of percolation theory to root growth would imply that the exponent, γ should be the optimal paths exponent, Dopt, i.e., γ = δ/β = Dopt, or RL = RREDopt. For a relatively shallow soil layer, for a 2D flow pattern, the value of γ = 1.21 can be used, and RL ~ RRE1.21 implies that RRE ~ RL0.83 where 0.83 = 1/1.21. Since RL is proportional to time, t, RRE becomes proportional to t 0.83 (Watt et al., 2006; Hunt, 2016). Using the experimental data reported by
Results: implications of the phenomenological model
In this Section, we address a number of published studies where our model of tree growth may find support. As no investigations were actually conducted with the purpose of testing our specific model, though some investigators indeed investigated related hypotheses, we cannot, in general, exclude ambiguity of understanding a model of the tree growth. Nevertheless, the evidence compiled appears to relate to our predictions with regard to both the temporal and transpiration dependences of the tree
Discussion and conclusions
A possible application of the present results is to enhanced drought susceptibility of trees in the western continental USA and diminution of water resources. The recent increase in drought mortality may be partly due to higher temperatures, but it certainly also has a component related to higher tree density brought on by a century of fire suppression. At higher densities, less water is available per tree. Drought weakened trees are also more susceptible to pathogens. The increased (dead) tree
Statement outlining authors’ individual contributions
Allen Hunt: Original conceptualization, hypothesis formulation, data search and analysis, writing.
Boris Faybishenko: Data selection, interpretation, and analysis, writing.
Thomas Powell: Data interpretation, scope of testing, hypothesis revision, writing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors are thankful to two anonymous reviewers for their comments and suggestions, which helped improve the manuscript. AGH is grateful for correspondence with Michael Ryan, whose related work inspired the present manuscript, and to Stefano Manzoni for an informal review. BF and TP research was partially supported by the NGEE-Tropics and Deduce projects, funded by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, and Office of Advanced
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