Estimating the proportions of closely related species: Performance of the two-phase ratio estimator

In many ecological field contexts, accurately classifying closely related species based on phenotypic characteristics may be difficult. In such cases, definitive classification of species may require expensive genetic analysis of tissues or extensive quantitative measurements. If inexpensive phenotype-based species classifications are highly correlated with expensive but definitive classifications, however, then estimating the proportion of a target species in a mixed species complex using a two-phase ratio estimator may prove cost-efficient. In two-phase ratio estimation, a first-phase sample is randomly selected, and phenotype is used to classify all individuals in the sample. A smaller, second-phase sample is then randomly selected from the first-phase sample, and a definitive method is used to classify the individuals in this subsample. Net relative efficiency (i.e., cost-effectiveness) of the optimally allocated two-phase ratio estimator of a proportion depends on the relative costs of classification at the first and second phases, on the phenotypic classification accuracy for the target species (sensitivity) and nontarget species (specificity), and on the magnitude of the target species proportion. Results are presented that allow assessment of the circumstances in which this two-phase estimation approach can be recommended over an equal-cost single-phase approach based only on expensive but definitive classification. An illustrative application of these methods is provided using an example of two closely related, sympatric, anadromous salmonid species: steelhead (Oncorhynchus mykiss) and coastal cutthroat trout (O. clarki clarki).