Regime shifts caused by adaptive dynamics in prey-predator models and their relationship with intraspecific competition

The paper concerns with regime shifts between multiple attractors in ecological predator-prey models and hysteresis phenomena caused by evolution. We present a survey of eco-evolutionary models with an adaptive trait affecting the prey defence or activity that influence predator functional response and give overview of typical consequences of the trait evolution to the predator-prey dynamics together with important references to related adaptive dynamics research. The selection and mutation process is modelled by a resident-mutant model (possible mutant invasion into a monomorphic resident population). Model derivations are given in detail for all of the common functional responses (Holling's type I, II, III and generalized). Different types of adaptive trait value dependences with respect to transient dynamics are distinguished according to the effect to the eco-system: we prove that if the prey adaptive trait evolution influence only the functional response of the predator, stable dynamics and irreversible abrupt regime changes are typical, whereas reversible regime shifts or more complex dynamics caused by adaptivity of the prey trait occur for trait adaptations that bring an advantage against predator together with intraspecific competition asymmetry. We confirm possibility of hysteresis eco-evolutionary cycle, persistent oscillations between different attractors of the ecological subsystem driven by adaptive trait dynamics.