  Predator prey interactions are one of ecology's central research themes, but
with many interdisciplinary implications across the social and natural
sciences. Here we consider an often-overlooked species in these interactions,
namely parasites. We first show that a simple predator prey parasite model,
inspired by the classical Lotka Volterra equations, fails to produce a stable
coexistence of all three species, thus failing to provide a biologically
realistic outcome. To improve this, we introduce free space as a relevant
eco-evolutionary component in a new mathematical model that uses a
game-theoretical payoff matrix to describe a more realistic setup. We then show
that the consideration of free space stabilizes the dynamics by means of cyclic
dominance that emerges between the three species. We determine the parameter
regions of coexistence as well as the types of bifurcations leading to it by
means of analytical derivations as well as by means of numerical simulations.
We conclude that the consideration of free space as a finite resource reveals
the limits of biodiversity in predator prey parasite interactions, and it may
also help us in the determination of factors that promote a healthy biota.
