# Nearest neighbours point pattern analysis

This module tests for clustering or overdispersion of points given as two-dimensional coordinate values. The procedure assumes that elements are small compared to their distances, that the domain is predominantly convex, and *n*>50. Two columns of x/y positions are required. Applications of this module include spatial ecology (are trees clustered), morphology (are trilobite tubercles overdispersed), and geology (distribution of e.g. volcanoes, earthquakes, hot springs).

The calculation of point distribution statistics using nearest neighbour analysis follows Davis (1986) with modifications. The area is estimated either by the smallest enclosing rectangle or using the convex hull, which is the smallest convex polygon enclosing the points. Both are inappropriate for points in very concave domains. Two different edge effect adjustment methods are available: wrap-around ("torus") and Donnelly's correction. Wrap-around edge detection is only appropriate for rectangular domains.

The null hypothesis is a random Poisson process, giving a modified exponential nearest neighbour distribution. The probability that the distribution is Poisson is presented, together with the *R* value. Clustered points give *R*<1, Poisson patterns give *R*~1, while overdispersed points give *R*>1.

The expected (theoretical) distribution under the null hypothesis is plotted as a continuous curve together with the histogram of observed distances.

The orientations (0-180 degrees) and lengths of lines between nearest neighbours, are also included. The orientations can be subjected to directional analysis, for example.

#### References

Clark, P.J. & Evans, F.C. 1954. Distance to nearest neighbor as a measure of spatial relationships in populations. *Ecology* 35:445-453.

Davis, J.C. 1986. *Statistics and Data Analysis in Geology*. John Wiley & Sons.

Hammer, Ř. 2009. New methods for the statistical analysis of point alignments. *Computers & Geosciences* 35:659-666.