Self-thinning and community persistence in a simple size-structured dynamical model of plant growth

EFFECT OF TOXIC METAL ON THE STRUCTURAL DRY WEIGHT OF A PLANT: A MODEL

A two compartment mathematical model for the individual plant growth under the stress of toxic metal is studied. In the model it is assumed that the uptake of toxic metal by the plant is through root compartment. The toxic metal present in the soil interfere with the uptake and distribution of essential nutrients in plant causing decrease in the nutrient uptake eventually damaging the root structure. In the model it is further assumed that the resistance to nutrient transport from root to shoot compartment increases and nutrient use efficiency decreases due to the presence of toxic metal. In order to visualize the effect of toxic metal on plant growth, we have studied two models, that is, model for plant growth with no toxic effect and model for plant growth with toxic effect. From the analysis of the models the criteria for plant growth with and without toxic effects are derived. The numerical simulation is done using Matlab to support the analytical results.

Insights into plant size-density relationships from models and agricultural crops

There is general agreement that competition for resources results in a tradeoff between plant mass, M, and density, but the mathematical form of the resulting thinning relationship and the mechanisms that generate it are debated. Here, we evaluate two complementary models, one based on the space-filling properties of canopy geometry and the other on the metabolic basis of resource use. For densely packed stands, both models predict that density scales as M(-3/4), energy use as M(0), and total biomass as M(1/4). Compilation and analysis of data from 183 populations of herbaceous crop species, 473 stands of managed tree plantations, and 13 populations of bamboo gave four major results: (i) At low initial planting densities, crops grew at similar rates, did not come into contact, and attained similar mature sizes; (ii) at higher initial densities, crops grew until neighboring plants came into contact, growth ceased as a result of competition for limited resources, and a tradeoff between density and size resulted in critical density scaling as M(-0.78), total resource use as M(-0.02), and total biomass as M(0.22); (iii) these scaling exponents are very close to the predicted values of M(-3/4), M(0), and M(1/4), respectively, and significantly different from the exponents suggested by some earlier studies; and (iv) our data extend previously documented scaling relationships for trees in natural forests to small herbaceous annual crops. These results provide a quantitative, predictive framework with important implications for the basic and applied plant sciences.

An analytical model of stand dynamics as a function of tree growth, mortality and recruitment: the shade tolerance-stand structure hypothesis revisited

Light competition and interspecific differences in shade tolerance are considered key determinants of forest stand structure and dynamics. Specifically two main stand diameter distribution types as a function of shade tolerance have been proposed based on empirical observations. All-aged stands of shade tolerant species tend to have steeply descending, monotonic diameter distributions (inverse J-shaped curves). Shade intolerant species in contrast typically exhibit normal (unimodal) tree diameter distributions due to high mortality rates of smaller suppressed trees. In this study we explore the generality of this hypothesis which implies a causal relationship between light competition or shade tolerance and stand structure. For this purpose we formulate a partial differential equation system of stand dynamics as a function of individual tree growth, recruitment and mortality which allows us to explore possible individual-based mechanisms--e.g. light competition-underlying observed patterns of stand structure--e.g. unimodal or inverse J-shaped equilibrium diameter curves. We find that contrary to expectations interspecific differences in growth patterns can result alone in any of the two diameter distributions types observed in the field. In particular, slow growing species can present unimodal equilibrium curves even in the absence of light competition. Moreover, light competition and shade intolerance evaluated both at the tree growth and mortality stages did not have a significant impact on stand structure that tended to converge systematically towards an inverse J-shaped curves for most tree growth scenarios. Realistic transient stand dynamics for even aged stands of shade intolerant species (unimodal curves) were only obtained when recruitment was completely suppressed, providing further evidence on the critical role played by juvenile stages of tree development (e.g. the sampling stage) on final forest structure and composition. The results also point out the relevance of partial differential equations systems as a tool for exploring the individual-level mechanisms underpinning forest structure, particularly in relation to more complex forest simulation models that are more difficult to analyze and to interpret from a biological point of view.