Fig. 1: C–R and R–N base modules.

a Rosenzweig–MacArthur C–R module modelled with Holling type II functional response and logistic resource growth, where \(R\) is resource biomass and \(C\) is consumer biomass. Parameters: \(r\) is the intrinsic growth rate of \(R\), \(K\) is the carrying capacity of \(R\), \({a}_{{\mathrm {CR}}}\) is the attack rate of \(C\) on \(R\), \(e\) is the assimilation rate of \(C\), \({R}_{0}\) is the half-saturation density of \(C\), \({m}_{R}\) and \({m}_{C}\) are the mortality rates of \(R\) and \(C\), respectively. b R–N module modelled with a Monod nutrient uptake equation and external nutrient input, where \(N\) is a limiting-nutrient pool and \(R\) is the resource biomass. Parameters: \({I}_{N}\) is external nutrient input to \(N\), \({a}_{{RN}}\) is nutrient uptake rate by \(R\), \(k\) is the half-saturation density of \(R\), \({l}_{N}\) and \({l}_{R}\) are nutrient loss rates from \(N\) and \(R\), respectively.