Allocation of new growth between shoot, root and mycorrhiza in relation to carbon, nitrogen and phosphate supply: teleonomy with maximum growth rate.

Treating resource allocation within plants, and between plants and associated organisms, is essential for plant, crop and ecosystem modelling. However, it is still an unresolved issue. It is also important to consider quantitatively when it is efficient and to what extent a plant can invest profitably in a mycorrhizal association. A teleonomic model is used to address these issues. A six state-variable model giving exponential growth is constructed. This represents carbon (C), nitrogen (N) and phosphorus (P) substrates with structure in shoot, root and mycorrhiza. The shoot is responsible for uptake of substrate C, the root for substrates N and P, and the mycorrhiza also for substrates N and P. A teleonomic goal, maximizing proportional growth rate, is solved analytically for the allocation fractions. Expressions allocating new dry matter to shoot, root and mycorrhiza are derived which maximize growth rate. These demonstrate several key intuitive phenomena concerning resource sharing between plant components and associated mycorrhizae. For instance, if root uptake rate for phosphorus is equal to that achievable by mycorrhiza and without detriment to root uptake rate for nitrogen, then this gives a faster growing mycorrhizal-free plant. However, if root phosphorus uptake is below that achievable by mycorrhiza, then a mycorrhizal association may be a preferred strategy. The approach offers a methodology for introducing resource sharing between species into ecosystem models. Applying teleonomy may provide a valuable short-term means of modelling allocation, avoiding the circularity of empirical models, and circumventing the complexities and uncertainties inherent in mechanistic approaches. However it is subjective and brings certain irreducible difficulties with it.