Plato's Plant: On the Mathematical Structure of Simple Plants and Canopies. - Review - book reviews

Schieving, Feike. 1998. Backhuys, Leiden, The Netherlands. xi + 360 p. $93.50, Dutch Guilders 168.00, ISBN: 90-5782-003-X.

In the early part of this century, the classical works of D'Arcy Thompson, Cecil Murray, and Julian Huxley inspired the viewpoint that the complexity of whole-organism form could be shown to follow general principles. These principles were hypothesized to stem from physical and biological constraints and were reflected in mathematical regularities such as phyllotaxy, allometry, morphology, branching patterns, and numerous other aspects of whole organism anatomy and physiological functioning. Certain aspects of this viewpoint were integrated into the development of modern zoology. In contrast, botany has not traditionally been guided by such mathematical formalisms. In last few decades, however, several integrative themes of botanical research have emerged

including: allometry, hydraulic architecture, biomechanics, whole-plant physiological modeling, and applications of fractal geometry. Together these approaches have shown how physical and biological principles influence whole-plant form, function, and evolution. For example, recent work by K. J. Niklas has proposed that the evolution of vascular plant form represents a reconciliation of a few critical constraints such as: (a) light interception, (b) biomechanics, (c) hydraulic limitations of transporting resources, and (d) the need for maximizing reproductive output in differing environments.

Plato's Plant is a provocative attempt to treat plants as entities reflecting a deeper truth. As in the studies mentioned above, its central thesis is that plant form and function are integrated by a set of principles following physical and biological laws. This thesis is based on the premise that in any given environment plant form represents an optimal configuration of various functions. Natural selection is assumed to act upon each component (canopy, root, and reproductive components) to maximize net photosynthesis, reproductive output, and growth. The author's goal is "to determine [the] ideal principles by which a plant is driven."

The book is organized around the development of the idealized "Plato Plant" model. Chapter 1, "On canopies, light, and nitrogen," focuses on the interactions of nitrogen distribution and canopy leaf area. Here Schieving does not distinguish individuals and only models the canopy as an entity. Under simple assumptions of nitrogen limitation the author derives an optimal canopy leaf area and leaf-photosynthesis-light curve. Chapter 2, "A leaf area game," considers the consequences of optimal canopies consisting of individuals. The rates of net photosynthesis for various plant "types" are allowed to vary in canopy area and nitrogen distribution. The author demonstrates that an evolutionary stable strategy (ESS) exists where for a given leaf area nitrogen use efficiency is maximized at every height. By considering the ESS it is shown how the total canopy leaf area and nitrogen distribution of stands consisting of individuals must be higher than the "optimal canopies" derived in Chapter 1. In other words, within Schieving's framework, any individual that maximizes its leaf photosynthetic nitrogen efficiency will eventually outcompete plants having an optimal nitrogen distribution and leaf canopy area.

Individuals are allowed to grow in size in Chapter 3. Change in biomass is modeled by a series of differential equations and kinetic reaction equations of carbon and nitrogen uptake in shoots and roots. In non-fluctuating environments, maximization of growth is shown to represent a "functional balancing between roots and shoots" which depends on the limiting resource (nitrogen or light). This also gives the interesting prediction that increases in accessible nitrogen should lead to an increase in the concentration of plant tissue nitrogen and decreases in net carbon content. In contrast, increases in light intensity will lead to an increase in net carbon content.

The last three chapters, "An optimal control of Plato's Plant," "Equations of functional equilibrium," and "Equations of motion" include extensions of dynamic optimization models of allocation. Here the central problem is how to best allocate biomass to leaf, stem, and reproductive biomass at any given time so as to maximize the production of reproductive mass. Plant allocation is modeled through differing growth strategies including sudden and gradual transitions from vegetative to reproductive allocation. Most importantly, Schieving shows how variation in resources can influence seed production. The chapter "Equations of functional equilibrium," includes the addition of "hormonal" control of leaf and root growth. Its production is modeled to be dependent upon soil nitrogen concentration. As a consequence, changes in nitrogen availability results in divergent growth of roots and/or shoots. An interesting result is mathematically showing how plants, under such control, could adaptively respond to herbivory. The final section in the book is a disappointingly short three-page epilogue entitled, "On ecological concepts." It essentially states that the "Plato Plant" model may provide a basis for ecological investigations. However, none are presented. For example, there is no indication of how these plant "types" influence local coexistence by the partitioning of resources or space.