NEAREST-NEIGHBOR ANALYSIS AND KARST GEOMORPHOLOGY: AN INTRODUCTION TO SPATIAL STATISTICS

This poster outlines an exercise I use in an upper-division geomorphology course to introduce students to nearest-neighbor analysis, a basic technique in spatial statistics. Nearest-neighbor analysis is a method of comparing the observed average distance between points and their nearest neighbor to the expected average nearest-neighbor distance in a random pattern of points. The pattern of points on a map or 2-D graph can be classified into three categories: CLUSTERED, RANDOM, REGULAR. Nearest-neighbor analysis provides an objective method for distinguishing among these possible spatial distributions. The technique also produces a population statistic, the nearest-neighbor index, which can be compared from area to area.

Geoscience applications include the analysis of the spatial distribution of karst sinkholes, drumlins, volcanic centers, cirques, river-basin outlets, fossils on bedding planes, and crystals in polished slabs. The technique is also useful in characterizing the distribution of data points or sample locations. In general, nearest-neighbor analysis can be applied to any geoscience phenomenon or feature whose spatial distribution can be categorized as a point pattern. The basic distance data can come from topographic maps, aerial photographs, or field measurements.

The exercise presented in this poster applies this technique to the study of karst landforms on topographic maps, specifically the spatial distribution of sinkholes, and draws heavily on the karst studies of McConnell and Horn (1972) and Williams (1972). The procedures and formulae used are those outlined by Davis (1973). Students are commonly surprised at how common a random distribution of sinkholes is within karst areas. Of course, if a point pattern is found to be non-random, that is clustered or regular, then other possible geologic controls need to be investigated – fracture patterns for example.

The advantages of introducing nearest-neighbor analysis in an undergraduate lab is that: (1) it reinforces important concepts related to data collection (e.g significant figures), map use (e.g. scale and the UTM grid), and basic statistics (e.g. hypothesis testing); (2) the necessary calculations are easily handled by most students; and (3) once learned, the technique can be widely applied in geoscience problem-solving.