Potential applications of randomised graph sampling to invasive species surveillance and monitoring.

Many invasive plants and animals disperse preferentially through linear networks in the landscape, including road networks, riparian corridors, and power transmission lines. Unless the network of interest is small, or the budget for surveillance is large, it may be necessary to draw inferences from a sample rather than a complete census on the network. Desired features of a surveillance system to detect and quantify invasion include: (1) the ability to make unbiased statements about the spatial extent of invasion, the abundance of the invading organism, and the degree of impact; (2) the ability to quantify the uncertainty associated with those statements; (3) the ability to sample by moving within the network in a reasonable fashion, and with little wasted non-measurement time; and (4) the ability to incorporate auxiliary information (such as remotely sensed data, ecological models, or expert opinion) to direct sampling where it will be most fruitful. Randomised graph sampling (RGS) has all of these attributes. The network of interest (such as a road network) is recomposed into a graph, consisting of vertices (such as road intersections) and edges (such as road segments connecting nodes). The vertices and edges are used to construct paths representing reasonable sampling routes through the network; these paths are then sampled, potentially with unequal probability. Randomised graph sampling is unbiased, and the incorporation of auxiliary information can dramatically reduce sample variances. We illustrate RGS using simplified examples, and a survey of Polygonum cuspidatum (Siebold & Zucc.) within a high-priority conservation region in southern Maine, USA.