Applying Graph Theory to Conservation Ecology
Graph theory allows us to understand connections across undetermined distances, allowing ecologists to visualize landscape connectivity- a particularly important application in the field of conservation ecology. In a 2000 study, researchers leveraged graph theory to understand habitat connectivity for species with different abilities to disperse across habitats. This allowed the researchers to understand the role of each patch of land in terms of its ability to function as a habitat for Mink and Warblers in the context of other tracts of land within the Alligator River National Wildlife Refuge in North Carolina, an wetland region.
The analysis involved using geospatial data to parameterize tracts of land- if the land included “bottomland hardwood swamp or oak gum cypress swamp, and riverine, lacustrine, or palustrine forested wetland”, it was defined as habitat. Considering edges between these habitat zones lets us approach a key result from a new perspective- animals rarely travel from point A to point B based on euclidean distance. Instead, they travel so as to maximize their presence within habitats suitable for camouflage or rest- thus, using graph theory helps us approach the issue of understanding the distance covered by animals when traveling between points- it is dependent on the path length between habitat nodes.
To understand how important each node is as a habitat, the approach of ‘node removal’ can be used. This corresponds to habitat destruction. Two parameters are then useful in understanding the role of a specific node- the node’s Traversability T and the node’s area-dispersal flux F. The flux “measures a node’s influence to a landscape-level metapopulation”, and the traversability of a node is defined by the ‘diameter’ of the largest component in a graph induced by the removal of the node- this corresponds to the rate at which risk can be distributed across a range, or the ability of a species to evade a localized disaster event. By calculating the flux associated with each node, linked to its dispersal potential, we can understand the role of each region for a species with a specific dispersion rate.
Intuitively, we would believe that species with a larger dispersive range would be able to form edges between habitats that are further apart. Thus, the study shows that as their habitat is reduced, species with a larger range can essentially view a landscape as a single habitat for a dispersed population, whereas species with a lower range (such as the warblers) treat the landscape as host to several small populations.
How is this relevant to the species themselves? The study shows us that the Mink and Warblers “perceived this landscape differently, as a function of their dispersal capabilities”. By parametrizing the landscape into habitat nodes, we can also prioritize the value of each node in terms of its utility for species- for instant, I would speculate that a local bridge would be of relatively higher value in terms of increasing genetic diversity as opposed to a node with many edges.
Although understanding landscapes in terms of their ecological flux and their importance to species remains a challenge, this study shows us that a graph-theoretic representation allows us to conduct an assessment of importance without requiring population data of the species over a long period of time, and thus exhibits demonstrated utility at a range of scales.
1.Bunn, A., Urban, D., & Keitt, T. (2000). Landscape connectivity: A conservation application of graph theory. Journal of Environmental Management, 59(4), 265-278. doi:10.1006/jema.2000.0373
The study used can be downloaded at:
http://www.sciencedirect.com/science/article/pii/S0301479700903736