On the measurement of growth with applications to the modelling and analysis of plant growth

Abstract

1. In this paper, a theoretical framework for the analysis of growth is described. Growth is equated with change in volume (V) and the growth rate is given by the equation; d V/dt = (dm/dt)(1/ρ) - (dρ/dt)(m/ρ2) where m is the mass and p the density. The volume is inclusive of internal air spaces. 2. The second term of the growth equation (see above) can be ignored if density is constant over time. Data for humans (and presumably other large animals) show that while composition changes over time, the density is approximately constant at about that of water. In that case, the growth rate can be estimated from measures of the rate of change of mass. However, the density of plants is variable (c. 0.4-1.2 g cm-3) and measures of mass and density are necessary to analyse plant growth. 3. To use the theory as the basis of plant growth models, it is necessary to develop simple methods for estimating the surface area of roots, stems and leaves assuming that the mass and volume are known. A literature review found that the surface area to volume ratios of leaves and roots generally increase with the mass concentration of water. Theoretical arguments are used to predict that in woody stems, the situation should be reversed such that the surface area to volume ratio increases with the mass concentration of dry matter. Those relationships should be very useful in the development of plant growth models. 4. Measures of plant dry mass and estimates of the rate of change in dry mass are shown to be very difficult to interpret because of differences in the mass concentration of dry matter between individuals and over time. 5. It is concluded that measures of mass and density will be necessary before plant growth analysis can achieve its full potential. A framework for extending the theory to include the forces necessary for growth to occur is described. Show more