Community patterns for the adaptive preference case
Following the optimal preference values \(p_{Z}^{*}\) (average equilibrium value of \(p_{Z}(t)\) in case of oscillatory dynamics) which are reached along nutrient enrichment for the adaptive preference case (Eqs. 1-6), two different regimes can be distinguished for low vs. high enrichment levels (Fig. 1, 2c). In Regime I (\(N_{\max}\ \)< 40 μgP·L-1), edible phytoplankton clearly dominates total available prey for zooplankton and correspondingly the optimal preference is almost exclusive for edible phytoplankton (\(p_{Z}\) close to 1) (Fig. 2c, 3c). In Regime II (\(N_{\max}\ \)> 40 μgP·L-1), with biomass of fungi and its relative contribution to total prey biomass reaching a critical threshold (Fig. 3d), optimal preference exhibits a pronounced shift towards preference for fungi with further enrichment, even though edible phytoplankton still dominates the total available prey (Fig. 2c). In Regime I, the qualitative pattern of the community response to nutrient enrichment is identical to the fixed preference case (Fig. 2b,c), even edible phytoplankton is only slightly decreasing. In Regime II, the freely available nutrient (N) and mean biomasses of both zooplankton prey remain constant (Fig. 1e, 2c, 3d), keeping relative contribution of fungi to total available prey biomass at 33% (Fig. 3c, 2d). Only zooplankton and inedible phytoplankton (host) increase with further nutrient enrichment (Fig 2c). Zooplankton biomass increases more steeply with nutrient enrichment compared to Regime I (Fig. 2c) and reaches a higher maximum biomass compared to the case without prey preference (pZ = 0.5) (Fig. 3a). The equilibrium dynamics exhibit the same stable vs. oscillatory behavior as the fixed preference case for the respective parameter combination on the \(p_{Z}-N_{\max}\) plane.
It is notable that the adaptive preference values neither follow maximum zooplankton biomass (Fig. 3a) nor values with highest top-down control and, therefore, lowest total prey biomass (Fig. 3b). They also do not follow the highest biomass values of fungi, albeit being the more profitable prey for zooplankton (greater conversion efficiency of fungi than edible phytoplankton) (Fig. 3c). So, what governs the optimal preference value along the enrichment gradient and how is this related to total and relative prey densities?
Analyzing the equilibrium condition for the fitness gradient term of Eq. 6 (\(\frac{\partial W_{Z}}{\partial p_{Z}}=0\)), which optimizes zooplankton net-growth (\(W_{Z}=\frac{1}{Z}\cdot\frac{\text{dZ}}{\text{dt}})\), reveals a negative correlation between the relative contribution of fungi to total prey biomass\(\ (F/(P_{E}+F))\) and total prey biomass (\(P_{E}+F)\)(Fig. 3d). Comparing these optimal prey availabilities (black dash-dotted line in Fig 3d) with the simulated equilibrium values for the mycoloop food web (Eqs. 1-6) (black solid line in Fig. 3d) reveals that the optimal value of the fitness gradient term cannot be reached before prey composition along the enrichment gradient reaches the optimal prey availability (black dot in Fig. 3d). Once reached, total and relative prey values are preserved at these values with further enrichment, while the optimal preference value keeps decreasing (increasing preference for fungi) with further nutrient enrichment (for further details see Appendix S3).