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Modeling and Formal Analysis of Meta-Ecosystems with Dynamic Structure using Graph Transformation
(2022)
The dynamics of ecosystems is of crucial importance. Various model-based approaches exist to understand and analyze their internal effects. In this paper, we model the space structure dynamics and ecological dynamics of meta-ecosystems using the formal technique of Graph Transformation (short GT). We build GT models to describe how a meta-ecosystem (modeled as a graph) can evolve over time (modeled by GT rules) and to analyze these GT models with respect to qualitative properties such as the existence of structural stabilities. As a case study, we build three GT models describing the space structure dynamics and ecological dynamics of three different savanna meta-ecosystems. The first GT model considers a savanna meta-ecosystem that is limited in space to two ecosystem patches, whereas the other two GT models consider two savanna meta-ecosystems that are unlimited in the number of ecosystem patches and only differ in one GT rule describing how the space structure of the meta-ecosystem grows. In the first two GT models, the space structure dynamics and ecological dynamics of the meta-ecosystem shows two main structural stabilities: the first one based on grassland-savanna-woodland transitions and the second one based on grassland-desert transitions. The transition between these two structural stabilities is driven by high-intensity fires affecting the tree components. In the third GT model, the GT rule for savanna regeneration induces desertification and therefore a collapse of the meta-ecosystem. We believe that GT models provide a complementary avenue to that of existing approaches to rigorously study ecological phenomena.
The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) with its land and vegetation height data product (ATL08), and Global Ecosystem Dynamics Investigation (GEDI) with its terrain elevation and height metrics data product (GEDI Level 2A) missions have great potential to globally map ground and canopy heights. Canopy height is a key factor in estimating above-ground biomass and its seasonal changes; these satellite missions can also improve estimated above-ground carbon stocks. This study presents a novel Sparse Vegetation Detection Algorithm (SVDA) which uses ICESat-2 (ATL03, geolocated photons) data to map tree and vegetation heights in a sparsely vegetated savanna ecosystem. The SVDA consists of three main steps: First, noise photons are filtered using the signal confidence flag from ATL03 data and local point statistics. Second, we classify ground photons based on photon height percentiles. Third, tree and grass photons are classified based on the number of neighbors. We validated tree heights with field measurements (n = 55), finding a root-mean-square error (RMSE) of 1.82 m using SVDA, GEDI Level 2A (Geolocated Elevation and Height Metrics product): 1.33 m, and ATL08: 5.59 m. Our results indicate that the SVDA is effective in identifying canopy photons in savanna ecosystems, where ATL08 performs poorly. We further identify seasonal vegetation height changes with an emphasis on vegetation below 3 m; widespread height changes in this class from two wet-dry cycles show maximum seasonal changes of 1 m, possibly related to seasonal grass-height differences. Our study shows the difficulties of vegetation measurements in savanna ecosystems but provides the first estimates of seasonal biomass changes.