Consequences of insufficient equations in models of the Münch hypothesis of phloem transport
Abstract The suggestion of concentration dependent unloading as a necessary assumption for a closed-form mathematical expression of the Munch hypothesis of phloem transport (Goeschl et at., 1976) has been recently questioned (Ferrier & Christy, 1977). Also questioned was whether previous models, known to have one less equation than dependent variables, have produced erroneous or misleading results. A review of Munch's original concepts and recent comments by several researchers indicate that an equation describing the exit of solutes from sieve tubes is essential for consistency with the Munch hypothesis. Evidence is presented to show that previous mathematical predictions and interpretations regarding ‘runaway velocities’ have resulted in part from mathematical inconsistencies and characteristics of the numerical solution procedures. Likewise, a proposal that different steady-state velocities and concentrations of transport at a given loading rate might be determined by ‘previous history’ of the system can be explained on the basis of implied relationships hidden in models with insufficient equations. Finally it is concluded that concentration dependent unloading in models of the Munch hypothesis will not detract, but rather will contribute to their usefulness in experimental testing and other research regarding phloem transport.