Models for adaptive feeding and population dynamics in plankton

Traditionally, differential-equation models for population dynamics have considered organisms as “fixed” entities in terms of their behaviour and characteristics. However, there have been many observations of adaptivity in organisms, both at the level of behaviour and as an evolutionary change of traits, in response to the environmental conditions. Taking such adaptiveness into account alters the qualitative dynamics of traditional models and is an important factor to be included, for example, when developing reliable model predictions under changing environmental conditions. In this thesis, we consider piecewise-smooth and smooth dynamical systems to represent adaptive change in a 1 predator-2 prey system. First, we derive a novel piecewise-smooth dynamical system for a predator switching between its preferred and alternative prey type in response to prey abundance. We consider a linear ecological trade-off and discover a novel bifurcation as we change the slope of the tradeoff. Second, we reformulate the piecewise-smooth system as two novel 1 predator-2 prey smooth dynamical systems. As opposed to the piecewise-smooth system that includes a discontinuity in the vector fields and assumes that a predator switches its feeding strategy instantaneously, we relax this assumption in these systems and consider continuous change in a predator trait. We use plankton as our reference organism because they serve as an important model system. We compare the model simulations with data from Lake Constance on the German-Swiss-Austrian border and suggest possible mechanistic explanations for cycles in plankton concentrations in spring.