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.