Small Fish Community Structure in Ozark Streams: Improvements in the Statistical Analysis of Presenceabsence Data

Abstract

Matthews's (1982) statistical tests for nonrandom species occurrence and abundance patterns among small fish (minnow) communities in Ozark streams are improved. The data for such tests are standardized as a binary presence-absence matrix. Because the presence-absence matrix is a single, small, unreplicated record of species occurrences, the sampling of sites and species for probabilistic colonization models should occur without replacement, rather than with replacement, of sites and species to the original data set. We discuss the effect of differences in sampling design (i.e., sampling with and without replacement) and sample size upon the calculation of three different probabilistic expectations: (1) the number of sample sites co-occupied by pairs of species; (2) the number of sites occupied by a given number of species, and (3) the number of sample sites shared by a given number of species. In all three cases, methods (either direct or by computer simulation) are available which sample without replacement. Unfortunately, independence problems beset the first and third analyses. All these tests also often require larger sample sizes than may be possible, given real-world constraints of community composition. In the first and third cases, simulation methods may be used where sample sizes are small, but these methods are subject to currently unquantifiable type II error and hidden incorporation of the same biotic effectors they