A contingency table approach based on nearest neighbour relations for testing self and mixed correspondence

Nearest neighbour methods are employed for drawing inferences about spatial patterns of points from two or more classes. We introduce a new pattern called correspondence which is motivated by (spatial) niche/habitat specificity and segregation, and define an associated contingency table called a correspondence contingency table, and examine the relation of correspondence with the motivating patterns (namely, segregation and niche specificity). We propose tests based on the correspondence contingency table for testing self and mixed correspondence and determine the appropriate null hypotheses and the underlying conditions appropriate for these tests. We compare finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and illustrate the methods on two artificial data sets and one real-life ecological data set.