Efficiency and evolution of water transport systems in higher plants: a modelling approach. I. The earliest land plants

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Abstract
The evolution of the stele was studied under the functional aspect of water transport problems by using a numerical approach. The underlying mathematical model describes the behaviour of a fluid-filled porous medium and is based on the coupling of Hooke’s law and Darcy’s law including a dynamic permeability approach which leads to a self-organization of the considered structure according to the resulting fluid- pressure field. Calculations dealing with two problems were performed. The essential demand of a water conducting system for a plant was demonstrated quantitatively. As soon as the plant shows an upright habit, the need for efficient water transport occurring through a highly porous apoplastic pathway becomes evident. In a second approach, the evolution of the protostele was simulated using the concept of dynamic permeability. The simulations of structures with self-regulating hydraulic conductivity yielded two strategies according to the pressure-permeability relationship. Increasing hydraulic conductivity with increasing negative fluid pressure results in peripheral layers of the conducting tissues, whereas the inverse pressure-permeability relationship yields a central position of the conducting tissues. The latter arrangement corresponds to the protostelar construction of early vascular plants.