Stem Mechanics as a Theoretical Basis for the Self-Thinning Rule
The self-thinning law describes the relationship between maximum mean size and density in even-aged monocultures that are experiencing density due to overcrowding by the equation w = K•Pa (0.1) where w is mean size; K is the constant of proportionality; f is density; and a is typically -1.5. Currently, the law does not represent a body of theory and is a simple empirical relation. Experiments to test a set of hypotheses that would provide a theoretical basis for the law were done with stands of unmanaged, evenaged Pinus contorta var. latifolia Emglm. and with monocultures of greenhouse grown Trifolium pratense L.. The model is derived from two principles: (1) the main plant stem develops to equalize bending stress along its length; and (2) total stand leaf area reaches a site-specific equilibrium. The model puts mean size as a function of both total leaf area and density. It predicts the value of "a", -1.5, given perfect conformace with the uniform resistance to bending principle and states that K is a function of total stand leaf area. Zero (control), one and two leaflets were continously removed from young petioles of T. pratense to test the hypothesis that K is a function of total stand leaf area. K was reduced as much as 25 per cent in the two-leaflet removed treatment, but it was unaffected when the defoliation treatment did not significantly reduce leaf area. With leaf area included in eqn (0.1), "a" was -1.33 for the control group, and as much as 90 per cent of the variation in mean weight in selfthinning and nonself-thinning stands was explained with multiple linear regression. The hypothesis that "a" in eqn (0.1) results from stems uniformly resistant to bending was tested with P. contorta. The model, using observed mechanical relations for mature and sapling trees, predicted that "a" was -1.26 and -1.11, respectively. The observed values were -0.83 and -0.84, respectively. Even though P. contorta stems closely follow the stem forming principle, the model overpredicted the exponents for density. This study suggested that additional factors such as leaf area dynamics and canopy coverage are involved in the determination of "a". The mechanical relation used in this model is not only mechanism behind the self-thinning law. While the ultimate mechanism of the law may be physiological in nature, analysis of whole plant properties may provide the initial theory for the law.
Dean, Thomas J. (1986). Stem mechanics as a theoretical basis for the self-thinning rule. Diss. 89p.