Community patterns for the fixed preference case
Along the enrichment gradient (\(N_{\max}\)), the superior resource competitor (edible phytoplankton) can establish at the lowest enrichment level (\(N_{\max}\) > \(0.055\)), independent of the preference value. The invasion threshold for zooplankton depends on the available prey biomass and the preference value for edible phytoplankton, the enrichment level for successful invasion increasing with decreasing preference for the phytoplankton. For enrichment levels slightly above the invasion threshold for zooplankton, the inedible phytoplankton and finally the parasitic fungi can successfully invade. The invasion boundaries for zooplankton, inedible phytoplankton and fungi are very close to each other, nearly overlapping, therefore only the coexistence boundary is indicated in Fig. 1 (red curve). Coexistence is not possible for too low enrichment levels and too strong preferences for fungi.
Within the coexistence area, the mean biomass of all food web compartments along the mycoloop increase with nutrient enrichment (Fig. 1a,b,d,e), whereas it decreases for edible phytoplankton (Fig. 1c). The community is dominated by either edible phytoplankton (at low nutrient availability) or zooplankton (at high nutrient availability, apart from regions with an almost exclusive preference for fungi) (see Appendix S2, Fig. S2.1).
The response of zooplankton along the preference gradient differs for low vs. high enrichment levels (Fig. 1a). For low enrichment levels, zooplankton increases with increasing preference for edible phytoplankton. For high enrichment levels, zooplankton shows a hump shaped relationship reaching the highest biomass at\(\ p_{Z}\approx\ 0.3\). With increasing preference for edible phytoplankton,\(\ \)the phytoplankton decreases due to stronger top-down pressure through zooplankton (Fig. 1c), while the biomass of fungi increases (Fig. 1b). The abundance of the fungal host (inedible phytoplankton) shows a hump shaped relationship with respect to the preference, peaking at \(p_{Z}\approx\ 0.3\), where its parasite is the preferred prey (Fig.1d). For high enrichment levels, the area with highest inedible phytoplankton biomass overlaps with the region of maximum biomass of zooplankton (Fig. 1a,d), indicating a strong top down control on both prey species, releasing the phytoplankton host from infection through fungi and from nutrient competition with edible phytoplankton.
At preference values close to one (i.e. strong preference for edible phytoplankton), the system exhibits oscillatory dynamics. This region extends towards lower preference levels with nutrient enrichment (area to the right of the black dashed line in Fig. 1). The oscillatory dynamics are characterized by small amplitude cycles for low enrichment and a pronounced increase of cycle amplitudes at high enrichment levels (Fig. 1f).
In the area with stable point equilibria (area to the left of the black dashed line in Fig.1), all compartments reach their maximum biomass at the highest investigated enrichment level (Fig. 1a-e). Only in the absence of zooplankton (edible phytoplankton-only state), for preference values close to zero, the edible phytoplankton increases with enrichment (area to the left of the red line in Fig. 1c). The maximum fungal biomass and freely available nutrient levels are observed at high preference values for edible phytoplankton (\(p_{Z}\approx\) 0.8) (Fig. 1b,e).
In comparison to the assumption of linear food uptake rates (Miki et al. 2011), there is no qualitative change in the biomass response pattern along the nutrient gradient under the assumption of nonlinear food uptake rates, as illustrated for \(p_{Z}=0.5\) (Fig. 2a,b). However, while the phytoplankton host is predicted to reach a higher biomass compared to its parasite throughout the nutrient gradient for the linear case, under the assumption of saturating food uptake terms the phytoplankton host only dominates at the highest nutrient levels (see Appendix S2, Fig. S2.2). Furthermore, zooplankton can invade at lower prey abundance (lower \(N_{\max}\)) compared to the linear case, so edible phytoplankton cannot reach as high biomass levels and decreases more steeply along the nutrient gradient compared to the linear case (Fig. 2a,b).