Estimating Population Size with Correlated Sampling Unit Estimates

Finite population sampling theory is useful in estimating total population size (abundance) from abundance estimates of each sampled unit (quadrat). We develop estimators that allow correlated quadrat abundance estimates, even for quadrats in different sampling strata. Correlated quadrat abundance estimates based on mark-recapture or distance sampling methods occur when data are pooled across quadrats to estimate, for example, capture probability parameters or sighting functions. When only minimal information is available from each quadrat, pooling of data across quadrats may be necessary to efficiently estimate capture probabilities or sighting functions. We further include information from a quadrat-based auxiliary variable to more precisely estimate total population size via a ratio estimator. We also provide variance estimators for the difference between or the ratio of 2 abundance estimates, taken at different times. We present an example based on estimating the number of Mexican spotted owls (Strix occidentalis lucida) in the Upper Gila Mountains Recovery Unit, Arizona and New Mexico, USA. Owl abundance for each quadrat was estimated with a Huggins 4-pass mark-resight population estimator, but with initial capture and resighting probabilities modeled in common across all sample quadrats. Pooling mark-resight data across quadrats was necessary because few owls were marked on individual quadrats to estimate quadrat-specific capture probabilities. Model-based estimates of owl abundance for each quadrat necessitated variance estimation procedures that take into account correlated quadrat estimates. An auxiliary variable relating to topographic roughness of sampled quadrats provided a useful covariate for a ratio estimator.