Accurate Recognition of Spatial Patterns Arising in Spatio-Temporal Dynamics of Invasive Species

Accurate identification of spatial patterns remains a challenging problem in many ecological applications. One example is a problem of biological invasion where distinguishing between patchy spatial density pattern and continuous front spatial density pattern is important for monitoring and control of the invasive species. In this paper we address the problem of pattern recognition in biological invasion in terms of a biologically meaningful mathematical model consisting of two coupled integro-difference equations. The model allows for generating topologically different spatial structures and we employ several topological characteristics of spatial pattern to investigate various spatial density distributions. It is argued that, among the other topological quantities, the number of objects in the visual image of a spatial distribution gives us the most reliable conclusion about spatial pattern when it is required to distinguish between continuous and discontinuous (patchy) spatial structures. Furthermore, sensitivity of the pattern classification above to the definition of a monitoring protocol is discussed in the paper. Two basic properties of the monitoring protocol (i.e. the threshold density value and the number of sampling locations) are investigated and it is demonstrated how their variation affects correct reconstruction of spatial density pattern.