Modeling and formal analysis of meta-ecosystems with dynamic structure using graph transformation

Abstract

The dynamics of meta-ecosystems are of crucial importance and, therefore, in theoretical ecology, various model-based approaches are employed to analyze their internal effects and to derive predictions on their future behavior and interactions. However, existing model-based approaches are limited in their support for the modeling of space structure dynamics of meta-ecosystems growing and shrinking in size over time due to intrinsic and extrinsic process as well as neighboring opportunities.In this paper, we employ the formal technique of Graph Transformation (GT) to qualitatively model the space structure dynamics and ecological dynamics of meta-ecosystems. In such GTSs, states of meta-ecosystems are given by graphs and evolutions from one state to the next are derived by applying GT rules describing local modifications of graphs. As a case study, we introduce GTSs capturing the space structure dynamics and ecological dynamics of three different savanna meta-ecosystems, which vary in their space structure dynamics. We then consider several qualitative analysis technique for GTSs such as for the existence of structural stabilities and apply them in our case study. We conclude that GTSs provide a complementary avenue to that of existing approaches to rigorously model and analyze qualitative ecological phenomena with adequate support for capturing not only ecological effects but also various forms of space structure dynamics.