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The origin of allometric scaling patterns that are multiples of 1/4 has longfascinated biologists. While not universal, scaling relationships withexponents that are close to multiples of 1/4 are common and have been describedin all major clades. Foremost among these relationships is the 3/4 scaling ofmetabolism with mass which underpins the 1/4 power dependence of biologicalrates and times. Several models have been advanced to explain the underlyingmechanistic drivers of such patterns, but questions regarding a disconnectbetween model structures and empirical data have limited their widespreadacceptance. Notable among these is a fractal branching model which predictspower law scaling of both metabolism and physical dimensions. While a power lawis a useful first approximation to many datasets, non-linearity in some largedata compilations suggest the possibility of more complex or alternativemechanisms. Here, we first show that quarter power scaling can be derived usingonly the preservation of volume flow rate and velocity as model constraints.Applying our model to the specific case of land plants, we show thatincorporating biomechanical principles and allowing different parts of plantbranching networks to be optimized to serve different functions predictsnon-linearity in allometric relationships, and helps explain why interspecificscaling exponents covary along a fractal continuum. We also demonstrate thatwhile branching may be a stochastic process, due to the conservation of volume,data may still be consistent with the expectations for a fractal network whenone examines subtrees within a tree. Data from numerous sources at the level ofplant shoots, stems, petioles, and leaves show strong agreement with our modelpredictions. This novel theoretical framework provides an easily testablealternative to current general models of plant metabolic allometry.

Flow similarity, stochastic branching, and quarter power scaling in plants