Model system
We investigated the biomass distribution and dynamics of a planktonic food web consisting of two types of primary producers (phytoplankton) which share a limiting nutrient source \(N\), assumed to be phosphorus [µg P·L-1], a zooplankton species \(Z\), and parasitic fungi \(F\). The food web is based on the following assumptions: one phytoplankton species \(P_{E}\) is well-edible for Z, while the other phytoplankton species \(P_{I}\) is inedible for \(Z\). \(P_{E}\) is the superior resource competitor, while\(P_{I}\) is the inferior resource competitor. Furthermore, \(P_{E}\) is insusceptible to fungal infection, while\(\ P_{I}\) is susceptible to infection by \(F\). \(F\) is edible for \(Z\), thereby creating an alternative nutrient pathway from the otherwise inedible \(P_{I}\) to\(Z\), i.e. the mycoloop.
The food web was translated into a corresponding differential equation system (Eqs 1-5). All biomasses are expressed in units of phosphorus [µg P·L-1]. Nutrient dynamics were assumed to follow chemostat dynamics with maximum nutrient availability\(N_{\max}\) and dilution rate \(q\) (Eq. 1). In contrast to the basic model presented in Miki et al. (2011), we assumed a saturating functional response for the nutrient uptake of both phytoplankton species following Monod kinetics with maximum growth rate\(\mu_{max,i\ },\ i\in\ \left\{E,I\right\}\), and half saturation constant K (Eqs. 2, 3). Similar to Miki et al. (2011) and in line with published dependencies of infection rate on host density (Gerla et al. 2013, Frenken et al. 2020), we assumed a linear dependency of the infection of \(F\) on host biomass \(P_{I}\) with infection rate\(\beta\) and conversion efficiency \(f_{F}\) (Eq. 4). We furthermore assumed a saturating functional response type III (Holling 1959) for the food uptake term of \(Z\) with food uptake rate \(a_{Z}\) and handling time \(h_{\text{i\ }},\ i\in\ \left\{P_{E},F\right\}\) (Eq. 5). A functional response type III has been shown to be representative for zooplankton species with a selective feeding behavior, like raptorial copepods, but also for filter feeders with the ability to down regulate their filtration rate if prey density is low, which has been reported for several daphnia species (Uszko et al. 2015, Kiørboe et al. 2018, Sandhu et al. 2019). Correspondingly, we assume a functional response type III to mimic the (disproportional) release of low abundant prey from predation pressure - not captured by a functional response type II (Wollrab and Diehl 2015). In addition to this density dependent food uptake term, we consider a prey preference parameter \(p_{Z}\) which defines the preference level of \(Z\) for \(F\) vs. \(P_{E}\). For this, the food uptake rate \(a_{Z}\) is multiplied by the preference parameter\(p_{Z}\in\left[0,1\right]\), with \(p_{Z}\) indicating the preference for \(P_{E}\), and \(\left(1-p_{Z}\right)\)indicating the preference for \(F\), respectively. Correspondingly, a value of \(p_{Z}=0\ (1)\) indicates that \(Z\) feeds exclusively on\(F\ (P_{E})\), where \(p_{Z}=0.5\) indicates no preference. Consumed prey biomass was converted to zooplankton biomass by conversion efficiencies \(e_{P}\) and \(e_{F}\) for edible phytoplankton and fungi, respectively.