Sampling to Detect Rare Species

Often a sampling program has the objective of detecting the presence of one or more species. One night wish to obtain a species list for the habitat, or to detect the presence of a rare and possibly endangered species. How can the sampling effort necessary for the detection of a rare species can be determined? The Poisson and the negative binomial are two possible spatial distributions that could be assumed. The Poisson assumption leads to the simple relationship n = -(1/m)log @b, where n is the number of quadrats needed to detect the presence of a species having density m, with a chance @b (the Type 2 error probability) that the species will not be collected in any of the n quadrats. Even if the animals are not randomly distributed the Poisson distribution will be adequate if the mean density is very low (i.e., the species is rare, which we arbitrarily define as a true mean density of <0.1 individuals per sample unit), and the spatial distribution is not highly aggregated. Otherwise a more complicated relationship based on the negative binomial distribution would have to be used. Published sampling distributions of 37 unionid mollusc species over river miles (distance measured along the path of the river; 1 mile = 1.609347 km) in two southern Appalachian rivers were evaluated to determine the appropriateness of the simple Poisson-based formula for estimation of necessary sample size to detect species presence. For each of 273 species x river mile combinations we estimated the mean, the variance, and the negative binomial parameter k, and then estimated "necessary n" from both the Poisson- and the negative-binomial-based formulae. We defined "Poisson adequacy" to be the proportion that the Poisson estimate is of the negative binomial estimate of necessary sample size, and stated the requirement that it be >0.95. Only 8 of the 273 cases represented rare species that failed this requirement. Thus we conclude that a Poisson-based estimate of necessary sample size will generally be adequate and appropriate.