There exists an urgent need in fisheries science for simple models for assessing the impact of fishing on the dynamics of fish communities. We present a new class of predator prey models that describe the relationship between predators and their prey by piecewise-linear differential equations. Interactions are governed by threshold values for population abundances. The simplest model has four distinct cases with different asymptotic stable states. The model allows for fishing mortality on both predator and prey. If fishing mortality on either the predator, the prey or both are varied, the system might move to new stable states. The threshold values act as reference points for fishing exploitation, as they indicate a structural change in the predator-prey relationship. The model is demonstrated for several predator-prey couples in the Celtic Sea.