SEQUENTIAL SAMPLING DESIGNS TO ESTIMATE ABUNDANCE IN RARE POPULATIONS 

                   Mary C. Christman
         Department of Mathematics and Statistics
                  American University
                    Washington, D.C.

Consider a finite population composed of two subgroups,
those with the character of interest and those without, where the
elements in the population displaying the character are very rare and
highly clustered. Of interest is estimating the total of a second variable,
Y say, whose value is related to the characteristic.  Throughout, it is
assumed that the variable has a negligible value for those elements
without the characteristic.

We suppose that the subpopulation with the characteristic are not
identified until they are sampled.  Hence, sampling designs which rely on
prior knowledge of the population structure cannot be used.  As a
consequence, many small or zero Y-values likely will be observed in order
to obtain a reasonable number of samples with the character of  
interest. In fact, there is a positive probability under fixed sample size
designs of obtaining zero estimates.
    
We consider estimators based on inverse sampling designs in which
samples are taken sequentially until some Redefined number of elements
with the characteristic are observed. The stopping rules are based on
controlling the number of clusters sampled from the population.   An
example using a dataset on the geographic distribution of Bluewinged
Teal in Florida is given.