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).