In a large diversity of engineering and biological applications we are interested in fast and reliable characterization of the relationship between inputs and outputs of a model, in which the outputs are de ned as the solution of a system of input-parametrized partial di erential equations. The basic idea of model reduction is that this relationship between inputs and outputs can often be reasonably well approximated by a much lower dimensional model generating nearly the same response characteristics, but leading to signi cantly reduced simulation times. The interactions between predators and preys, extensively studied in the invasion theory and biological control, represent dominant factors of the species distribution and composition in a community. These interferences are strongly in uenced by the preferences and type of predators, predator mediated apparent competition, as well as the vulnerabilities of di erent prey types. Generalist predators, that use a possibly rich variety of food sources, have profound impacts on the the dynamics of such communities. This work focusses on the numerical implementation of reduced order techniques { Proper Orthogonal Decomposition (POD) method, and the hybrid variant: POD combined with DEIM (Discrete Empirical Interpolation Method) { applied to spatial predator{prey systems in the presence of generalist predators. Comparative numerical results with respect to CPU time and errors of the approximate solutions in both high- delity and reduced models are presented.