Population dynamics of intraguild predation in a lattice gas system

In the system of intraguild predation (IGP) we are concerned with, species that are in a predator-prey relationship, also compete for shared resources (space or food). While several models have been established to characterize IGP, mechanisms by which IG prey and IG predator can coexist in IGP systems with spatial competition, have not been shown. This paper considers an IGP model, which is derived from reactions on lattice and has a form similar to that of Lotka-Volterra equations. Dynamics of the model demonstrate properties of IGP and mechanisms by which the IGP leads to coexistence of species and occurrence of alternative states. Intermediate predation is shown to lead to persistence of the predator, while extremely big predation can lead to extinction of one/both species and extremely small predation can lead to extinction of the predator. Numerical computations confirm and extend our results. While empirical observations typically exhibit coexistence of IG predator and IG prey, theoretical analysis in this work demonstrates exact conditions under which this coexistence can occur.