Rg drives root and mycorrhizal growth according to their respective growth yields (Yg) estimated from biochemical composition (e.g. Waring and Running, 1998)
and associated assimilation of N and P according to set ratios for roots. Growth rate (δMC/δt) drives extension of root and mycorrhizal lengths (L) according to their specific volumes (ν), densities (ρ), internal porosities (θP), radii (r) and an assumed cylindrical geometry
Root and mycorrhizal lengths and resulting surface areas (A) determine uptake (U) of inorganic N and P, for example, NH4+ in eq. (17), by determining the nutrient concentrations at root and mycorrhizal surfaces at which radial transport by mass flow and diffusion, driven by the nutrient concentrations in the soil solution (eq. 17a), equals active uptake by the root and mycorrhizal surfaces, driven by maximum specific uptake (U′) and the half-saturation constant (eq. 17b)
Parameters for root and mycorrhizal uptake ( in eq. 17b) are the same as those for microbial uptake in eq. 8b) with which in eq. (17b) competes. Products of U are added to nonstructural N and P pools (σN and σP) in root and mycorrhizae which are coupled with σC generated from CO2 fixation, in mycorrhizae, roots and branches. Transfers among these pools (eq. A7a,b in Grant et al., 2010) are driven by concentration gradients generated by acquisition versus consumption of nonstructural N and C in mycorrhizae, roots and branches (eq. A7c,d in Grant et al., 2010). Ratios of nonstructural N and C in branches govern CO2 fixation (eqs A7f,g,h in Grant et al., 2010) by (1) setting ratios of structural N and C in leaves (eq. A7e in Grant et al., 2010) and hence maximum carboxylation rates (eqs A7i,j in Grant et al., 2010), and (2) determining rubisco activation through product inhibition (eq. A7k in Grant et al., 2010). Ra of above-ground phytomass is calculated from non-structural C pools for each species (i), branch (j), organ (k= leaves, twigs, branches, boles, reproductive) and node (n) in the same manner as is the Ra of roots and mycorrhizae in eqs. (11)–(14) above. Above-ground growth is thus modelled as
with associated assimilation of N and P, calculated for organ k= leaf from ratios of nonstructural C, N and P as
from which ratios of nonstructural N and C are derived as MN:MC.
Growth in leaf mass drives expansion of leaf area (A) constrained by leaf turgor (ψt) in eq. (20), assuming uniform growth of individual leaves (MC divided by population y) in three dimensions (Grant and Hesketh, 1992)
Similarly, growth in twig, branch and bole masses drive extension of twig, branch and bole lengths (Grant and Hesketh, 1992). Values of Ai,j,k,n, further resolved into layer, azimuth and inclination, are used to calculate radiation absorption and hence CO2 fixation coupled to leaf water and nutrient status (Grant, 2004; Grant et al., 2007a,b, 2009a,b, 2010).
Each plant population is initialized only with a small non-structural C reserve at planting which is transferred to σC in branches and roots during germination. These σC then drive initial Ra (eq. 12) and δMC/δt (eq. 15) and hence root elongation (eq. 16) and leaf expansion (eq. 20) required for nutrient uptake (eq. 17) and CO2 fixation. Upon exhaustion of this reserve, each population must sustain further nutrient uptake and CO2 fixation from root elongation and leaf expansion driven by the non-structural products of nutrient uptake and CO2 fixation. No areas or lengths of roots, mycorrhizae or leaves are prescribed. This creates feedback during plant growth, which can be positive when growth exceeds litterfall, or negative when growth does not.