A new class of models of landscape changes for non-continue landscapes and their underlying discrete dynamics

In a landscape, linear elements are highly connected, dividing the landscape into component cells or units, and therefore contrasting with the traditional focus on characteristics within a patch or a matrix (Cantwell and Forman, 1993). "Linear elements, such as roads, are major movement conduits and sources of pollution and energy consumption, and many animals tend to avoid crossing event narrow roads" wrote Cantwell and Forman (1993). However, most of landscape modellings are based on raster and cannot easily handle linear elements, leading to a need for new modelling tools able to handle linears and put in equation the landscape pattern dynamics.

Linear dynamics exhibit both state transition (composition changes) and topology transformation (geometrical changes) simultaneously, which can be seen through the framework of Dynamical System with a Dynamical Structure (DS2) (Giavitto et al., 2008). We hypothesize that graph rewriting system can be integrated in such a complex dynamical system (Sayama, 2009), and that 8 productions (rewriting rules) are enough to handle all line layer changes. We defined one composition production (rotation) and 7 configuration productions (union, division, appearance, disappearance, erosion, dilation and no production).

In this study, we (1) implemented attributes and geometrical transformations of linears in the DYPAL platform (DYnamic Patchy Landscape model), where the shapes of linear elements are based on the polygons' sides of a patchy landscape. Simultaneously, we (2) developed a mathematical formalism to describe these linear manipulations. The formal graph grammar (string-regulated rewriting based on topological alphabet) allows taking into account both geometric (primal) graph representing the "real" landscape and the topological (dual) graph allowing to manipulate the landscape modules (elements). Finally, from this mathematical formalism, we (3) studied graph properties represented by basic indices: number of nodes, number of edges, number of connected components, average degree. We demonstrated some properties on the convergences of these indices in both geometric and topological (dual) graph.

Speaker

Virgile Baudrot, University of Montpellier II, France
Organisers

Department of Ecology, French Institute of Pondicherry.

Venue

Nehru conference hall, French Institute of Pondicherry, 11, Saint Louis Street, Pondicherry - 605 001.