Landscape graphs: Ecological modeling with graph theory to detect configurations common to diverse landscapes

In view of the bewildering diversity of landscapes and possible patterns therein, our objectives were to see if a useful modeling method for directly comparing land mosaics could be developed based on graph theory, and whether basic spatial patterns could be identified that are common to diverse landscapes. The models developed were based on the spatial configuration of and interactions between landscape elements (ecosystems, land uses or ecotopes). Nodes represented landscape elements and linkages represented common boundaries between elements. Corridors, corridor intersections, and the matrix were successfully incorporated in the models. Twenty-five landscape graphs were constructed from aerial photographs chosen solely to represent a breadth of climates, land uses and human population densities. Seven distinctive clusters of nodes and linkages were identified and common, three of which, in the forms of a ‘spider’, ‘necklace’ and ‘graph cell,’ were in >90% of the graphs. These represented respectively the following ‘configurations’ of patches, corridors and matrix: (1) a matrix area surrounding or adjoining many patches; (2) a corridor bisecting a heterogeneous area; and (3) a unit in a network of intersecting corridors. The models also indicated that the connectivity or number of linkages for several common elements, such as fields and house clearings, was relatively constant across diverse landscapes, and that linear shaped elements such as roads and rivers were the most connected. Several additional uses of this graph modeling, including compatibility with systems dynamics models, are pinpointed. Thus the method is useful in allowing simple direct comparisons of any scale and any landscape to help identify patterns and principles. A focus on the common and uncommon configurations should enhance our understanding of fluxes across landscapes, and consequently the quality of land planning and management.