For the (non-adaptive) fixed preference case, representative for passive filter feeders like cladocerans, including species with the ability to actively egest unfavourable prey (Uszko et al. 2015), \(p_{Z}\) was assumed to be a constant parameter (Eqs. 1-5). For the adaptive preference case, representative for active hunters like copepods (Ray et al. 2016), \(p_{Z}\) is not fixed, but itself a function of time (Eq. 6). We used a fitness gradient approach to describe the adaptive preference dynamics (Abrams and Matsuda 2004, Mougi and Iwasa 2010, Yamamichi et al. 2019). For this case, the value of \(p_{Z}\) depends on the fitness gradient of \(Z\), described by the effect of a change of\(p_{Z}\) on the net energy gain of zooplankton\(\left(\frac{\partial W_{Z}}{\partial p_{Z}}\right)\), where\(W_{Z}(t)=\frac{1}{Z}\cdot\frac{\text{dZ}}{\text{dt}}\) is the net-growth of zooplankton. This fitness gradient is multiplied by the speed of adaptation \(V\). This first term of Eq. 6 describes the ability of \(Z\) to adapt its prey preference \(p_{Z}\) to optimize its own fitness (net energy gain). The second additive term of Eq. 6 is a boundary function\(B\left(p_{Z}\right)=\frac{C}{p_{Z}^{2}}-\frac{C}{\left(1-p_{Z}\right)^{2}}\)with the scaling constant \(c\), which keeps the value of \(p_{Z}(t)\)within the range of [0,1] (Yamamichi et al. 2019).

Parameter values (Appendix S1: Table S1) and initial conditions (see section on model analysis) were taken from Miki et al. (2011), with the exception of the maximum growth rate of \(P_{I}\) (\(\mu_{max,I}\)), which was chosen to be higher than in the original parameterization. The latter was motivated by the fact that, dependent on species identity, the difference in maximum growth rate between edible and inedible phytoplankton species does not need to be very pronounced (Burson et al. 2018). Correspondingly, we decreased the difference in maximum growth rate between \(P_{E}\) and \(P_{I}\), to reduce the effect of principle physiological differences between the two phytoplankton species on system dynamics.