Intraguild Predation in Periodic Habitats

Fragmentation of natural landscapes is an ongoing process, mainly led by human activities, such as urban growth, roadway construction and farming. This phenomena may lead to many changes in the dynamics of populations that live in such landscapes, posing new challenges to our understanding of population persistence and diversity therein. One of the first approaches on how we may treat such problems mathematically was given by Shigesada in 1986, where a single population invading an infinite unidimensional habitat, composed of two types of patches layed on the real line alternately, is considered. Along that, theoretical aspects of how populations behave on the borders between different types of patches were developed, unraveling new classes of realistic boundary conditions for spatial ecology models, giving us new results and insights in this field. In this work we consider an Intraguild Predation (IGP) model, a community module composed of two consumers of a shared resource, with a predation relation between such consumers, usually referred as IG-Prey and IG-Predator. First we deal with invasions of both IG-Prey and IG-Predator in an homogeneous landscape, with either the resource established alone or together with the other consumer. Then, using Cobbold and Yurk's homogenization technique, we formulate and investigate the problem in a periodic habitat, composed of two types of patches where IGP relations are present, but allowed to have different parameters, such as less resource consumption, enhanced mortality or reduced resource productivity in one of the patches. Our results show that coexistence between IG-Prey and IG-Predator is possible within a range of resource productivity in homogeneous landscapes, being such range determined via analysis of the minimal speeds of invasion. In heterogeneous landscapes, with IGP being viable on both patches, we find that the necessary conditions for coexistence may be relaxed given certain movement behavior of both consumers and resource alike, whilst some configurations restrict such condition. We also explore how the ranges of coexistence in terms of resource productivity change with the sizes of the two habitat types considered, finding that such regions are also diminished or enlarged, depending on the movement behavior of the IGP populations.