Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Growth of soil-borne fungi is poorly described and understood, largely beca use nondestructive observations on hyphae in soil are difficult to make. Ma thematical modelling can help in the understanding of fungal growth. Except for a model by Paustian & Schnurer (1987a), fungal growth models do not co nsider carbon and nitrogen contents of the supplied substrate, although the se nutrients have considerable effects on hyphal extension in soil. We intr oduce a fungal growth model in relation to soil organic matter decompositio n dealing with the detailed dynamics of carbon and nitrogen. Substrate with a certain carbon : nitrogen ratio is supplied at a constant rate, broken d own and then taken up by fungal mycelium. The nutrients are first stored in ternally in metabolic pools and then incorporated into structural fungal bi omass. Standard mathematical procedures were used to obtain overall-steady states of the variables (implicitly from a cubic equation) and the conditio ns for existence. Numerical computations for a wide range of parameter comb inations show that at most one solution for the steady state is biologicall y meaningful, specified by the conditions for existence. These conditions s pecify a constraint, namely that the 'energy' (in terms of carbon) invested in breakdown of substrate should be less than the 'energy' resulting from breakdown of substrate, leading to a positive carbon balance. The biologica l interpretation of the conditions for existence is that for growth the 'en ergy' necessary for production of structural fungal biomass and for mainten ance should be less than the mentioned positive carbon balance in the situa tion where all substrate is colonized. In summary, the analysis of this com plicated fungal growth model gave results with a clear biological interpret ation.