A general model for allometric covariation in botanical form and function

Abstract

The West, Brown, and Enquist (WBE) theory for the origin of allometric scaling laws is centered on the idea that the geometry of the vascular network governs how a suite of organismal traits covary with each other and, ultimately, how they scale with organism size. This core assumption has been combined with other secondary assumptions based on physiological constraints, such as minimizing the scaling of transport and biomechanical costs while maximally filling a volume. Together, these assumptions give predictions for specific ''quarter-power'' scaling exponents in biology. Here we provide a strong test of the core assumption of WBE by examining how well it holds when the secondary assumptions have been relaxed. Our relaxed version of WBE predicts that allometric exponents are highly constrained and covary according to specific quantitative functions. To test this core prediction, we assembled several botanical data sets with measures of the allometry of morphological traits. A wide variety of plant taxa appear to obey the predictions of the model. Our results (i) underscore the importance of network geometry in governing the variability and central tendency of biological exponents, (ii) support the hypothesis that selection has primarily acted to minimize the scaling of hydrodynamic resistance, and (iii) suggest that additional selection pressures for alternative branching geometries govern much of the observed covariation in biological scaling exponents. Understanding how selection shapes hierarchical branching networks provides a general framework for understanding the origin and covariation of many allometric traits within a complex integrated phenotype.allometry ͉ fractal ͉ metabolism ͉ scaling ͉ traits S ince the pioneering work of Julian Huxley (1), questions concerning how selection influences specific traits within integrated phenotypes have been a prominent focus in comparative biology (2, 3). The phenotype is a constellation of traits that often covary with each other during ontogeny. Further, organism size is a central trait that influences how most biological structures, processes, and dynamics covary with each other (4, 5). The dependence of a given biological trait, Y, on organismal mass, M, is known as allometry. Allometric relationships are often characterized by power laws (1) of the form, Y ϭ Y 0 M , where is the scaling exponent and Y 0 is a normalization constant that may be characteristic of a given taxon. A sampling of intra-and interspecific data reveals that the central tendency of often approximates quarter-powers (4, 5) (e.g., 1/4, 3/4, 3/8, etc.), although for any given relationship considerable variability may exist (6).West, Brown, and Enquist (7-9) hypothesized that the value of for many biological allometries arises from the geometry of vascular networks and resource-exchange surfaces (e.g., cardiovascular or plant vascular systems). The core assumption of this theory is that many organismal, anatomical, and physiological traits are linked mechanistically by allometric scaling of...

Precision of allometric scaling equations for trees can be improved by including the effect of ecological interactions

“…This variability can be accounted for by measuring additional ecological factors at the level of the individual. Fitting both exponents and normalizations at the level of the individual (Mäkelä and Valentine 2006;Price et al 2007), and accounting for relationships between these parameters and ecological factors, could even further increase the predictive power of allometries. However, because of the strong interdependence between the two parameter values (Lumer 1939), one of the scaling parameters may have to be set to a predetermined value before the value of the other can be accurately estimated using merely statistical fit.…”

“…There have been only a few attempts to give a mechanistic explanation for the statistical variability although both the scaling exponent and the normalization constant may have an interpretation based on biological processes (Kozłowski et al 2003;Etienne et al 2006;Mäkelä and Valentine 2006;Chown et al 2007;Enquist et al 2007;Price et al 2007). As an alternative, some process-based models use conditional values of a and b, or additional variables to modify the values of a and b, instead of attempting to give a direct interpretation of the values of a and b by themselves (Duursma et al 2007;Holdo 2007).…”

“…Thus, the predictions are likely to be somehow biased, if a model uses any static scaling relationship that is directly or indirectly linked to crown ratio to predict stem properties in competing trees. In general, it appears that within constrained limits both scaling exponents and normalisation constants are strongly linked to the morphological and physiological traits of branching networks in plants Price et al 2007). Hence, they can be modified by any factor that influences the formation of those networks, such as competition.…”

Testing Metabolic Theories

“…The WBE-based models are now being applied in general ecological investigations and have been shown to predict numerous broad-scale physiological and ecological phenomena with remarkable accuracy (e.g., Enquist et al 2003Enquist et al , 2007bBrown et al 2004;Savage et al 2004;Gillooly et al 2005;Price et al 2007;Hou et al 2008). However, vociferous debate has ensued on the universality of the empirically observed scaling (Glazier 2005;White et al 2007;Makarieva et al 2008), the empirical and statistical validity of the temperature dependence term (Clarke 2004;Irlich et al 2009), fundamental principles of the models (Makarieva et al 2004;Suarez et al 2004;Kozłowski and Konarzewski 2005;O'Connor et al 2007;Apol et al 2008;Banavar et al 2010), and their predictive capacity (Algar et al 2007).…”

Morphospace: Measurement, Modeling, Mathematics, and Meaning

“…They have already extended this approach somewhat (Price, Enquist, and Savage, 2007 This proposal will develop a synthetic and predictive theory for plant biology that links physiological processes from the level of plant cells and hydraulic vascular systems to that of whole forests and the biosphere. Using theoretical, laboratory, and field based techniques, the research brings together plant physiologists, ecologists and theoretical biologists to advance existing theory in order to develop a unified and quantitative scaling approach.…”