Tikhonov–Fenichel reductions and their application to a novel modelling approach for mutualism

When formulating a model there is a trade-off between model complexity and (biological) realism. In the present paper we demonstrate how model reduction from a precise mechanistic “super model†to simpler conceptual models using Tikhonov–Fenichel reductions, an algebraic approach to singular perturbation theory, can mitigate this problem. Compared to traditional methods for time scale separations (Tikhonov’s theorem, quasi-steady state assumption), Tikhonov–Fenichel reductions have the advantage that we can compute a reduction directly for a separation of rates into slow and fast ones instead of a separation of components of the system. Moreover, we can find all such reductions algorithmically.