Testing association between species abundance and a continuous variable with Kolmogorov-Smirnov statistics

Association of species abundance with a continuous environmental variable is frequently tested with regression or correlation analyses. However, because these methods ignore the range and frequency distribution of levels of the variable occurring in the study area, they may generate misleading results. We give examples to illustrate the argument. A better approach to test the association between species abundance and a continuous variable should compare levels of the variable in the study area to levels of the variable occurring in sites occupied by the species. If a particular species abundance is not associated with a given continuous variable, then the frequency distribution of levels of this variable measured where individuals of the species occur should mirror the frequency distribution of levels of the variable measured over the study area. We explain how to use the one- and two-sample Kolmogorov-Smirnov statistics to compare the cumulative relative frequencies of levels of the variable where individuals are present with points in the study area. We discuss the statistics, assumptions, limitations, and advantages of these tests.