Hydraulic trade-offs and space filling enable better predictions of vascular structure and function in plants

Abstract

Plant vascular networks are central to botanical form, function, and diversity. Here, we develop a theory for plant network scaling that is based on optimal space filling by the vascular system along with trade-offs between hydraulic safety and efficiency. Including these evolutionary drivers leads to predictions for sap flow, the taper of the radii of xylem conduits from trunk to terminal twig, and how the frequency of xylem conduits varies with conduit radius. To test our predictions, we use comprehensive empirical measurements of maple, oak, and pine trees and complementary literature data that we obtained for a wide range of tree species. This robust intra-and interspecific assessment of our botanical network model indicates that the central tendency of observed scaling properties supports our predictions much better than the West, Brown, and Enquist (WBE) or pipe models. Consequently, our model is a more accurate description of vascular architecture than what is given by existing network models and should be used as a baseline to understand and to predict the scaling of individual plants to whole forests. In addition, our model is flexible enough to allow the quantification of species variation around rules for network design. These results suggest that the evolutionary drivers that we propose have been fundamental in determining how physiological processes scale within and across plant species. U nderstanding the coevolution of plant internal vascular networks and external branching networks is essential to predict botanical form and function (1-4). Seminal studies have attempted to unite these internal and external networks (3,5,6). A decade ago West, Brown, and Enquist (3) proposed a model (WBE) that focuses on the primacy of vascular networks, predicts myriad aspects of plant form and function (3, 7), and has subsequently been tested by the collection of new data for vascular networks (8, 9) and analyses of fluxes through plants (10, 11), forests, and ecosystems (12, 13). Since the publication of the WBE model, several criticisms have been published that question its basic framework, assumptions, and generality (14-16). Indeed, focusing on plant models, several studies have: (i) highlighted how hydraulic safety and efficiency may have shaped the evolution of vascular networks (2, 17), (ii) questioned whether vascular safety and efficiency are adequately described by the WBE model (8,18,19), and (iii) revealed empirical patterns that contradict parts of the WBE model (9,(20)(21)(22)(23). For example, building on earlier work (24, 25), Sperry and colleagues (2) compiled data for the xylem conduits that transport water in plants, and they documented a general principle termed the "packing rule"-the frequency of xylem conduits varies approximately inversely with the square of conduit radius. This packing rule contradicts the WBE model's assumption that conduit frequency remains unchanged as conduit radii taper, decreasing in size from trunk to terminal twig. Safety and efficiency considerations have been pr...

Testing the packing rule across the twig–petiole interface of temperate woody species

“…Numerous attempts have been made to relate hydraulic architecture to overall plant morphology with varying degrees of success, e.g., the pipe model (Shinozaki et al 1964a, b), Murray's model (Murray 1926;McCulloh et al 2003), and the West, Brown, and Enquist (WBE) model (West et al 1999;Enquist 2002;Petit et al 2008;Anfodillo et al 2006; see also Savage et al 2010). However, nearly all of these models have been criticized on empirical or theoretical grounds (e.g.…”

“…Indeed, even the predictions of the most recent revisions of the metabolic theory of ecology (MTE), which incorporate tradeoffs between hydraulic safety and efficiency, fail to comply with some empirical observations (e.g. Savage et al 2010).…”

“…For example, one common assumption in plant hydraulic models is that the area-preserving rule of Leonardo da Vinci holds true across different branching levels (e.g. West et al 1997West et al , 2009Enquist et al 2009;Savage et al 2010). According to this rule, the sum of the crosssectional area of xylem conduits (tracheids or vessels) is constant across different levels of branching.…”

“…In turn, this leads to two other predictions: (1) the number of conduits (N) should vary inversely and isometrically with the cross-sectional area of xylem conduits (A), i.e., N µ A -1 , or the scaling exponent for the relationship between N and conduit diameter (D) should equal -2, i.e. N µ D -2 , and (2) the scaling exponent for the relationship between the 'conduit diameter ratio' (DR, which is the distal to proximal diameter ratio between adjacent branch ranks, i.e., DR = D n?1 /D n ) and the 'conduit number ratio' (NR, which is the distal to proximal number of conduits between adjacent branch ranks, i.e., NR = N n?1 /N n ) should equal -1/2 (Savage et al 2010), i.e., DR = NR -1/2 . These relationships, which are collectively called the ''packing rule'' (Sperry et al 2008;Savage et al 2010), make up a core assumption in many plant scaling models (e.g.…”

“…N µ D -2 , and (2) the scaling exponent for the relationship between the 'conduit diameter ratio' (DR, which is the distal to proximal diameter ratio between adjacent branch ranks, i.e., DR = D n?1 /D n ) and the 'conduit number ratio' (NR, which is the distal to proximal number of conduits between adjacent branch ranks, i.e., NR = N n?1 /N n ) should equal -1/2 (Savage et al 2010), i.e., DR = NR -1/2 . These relationships, which are collectively called the ''packing rule'' (Sperry et al 2008;Savage et al 2010), make up a core assumption in many plant scaling models (e.g. McCulloh et al 2003;Savage et al 2010).…”