Quasi-steady state approximation to a fungal growth model

In a previous paper, we proposed a fungal growth model (Lamour et al., 2001 IMA J. Math. Appl. Med. Biol., 17, 329-346), describing the colonization and decomposition of substrate, subsequent uptake of nutrients, and incorporation into fungal biomass, and performed an overall-steady-state analysis. In this paper we assume that where nutrient dynamics are much faster than the dynamics of fungal biomass and substrate, the system will reach a quasi-steady-state relatively quickly. We show how the quasi-steady-state approximation is a simplification of the full fungal growth model. We then derive an explicit fungal invasion criterion, which was not possible for the full model, and characterize parameter domains for invasion and extinction. Importantly, the fungal invasion criterion takes two forms: one for systems where carbon is limiting, another for systems where nitrogen is limiting. We focus attention on what happens in the short term immediately following the introduction of a fungus to a fungal-free system by analysing the stability of the trivial steady state, and then check numerically whether the fungus is able to persist. The derived invasion criterion was found to be valid also for the full model. Knowledge of the factors that determine invasion is essential to an understanding of fungal dynamics. The simplified model allows the invasion criterion to be tested with experimental data.