An Application of Spatio-temporal Modeling to Finite Population Abundance Prediction

Spatio-temporal models can be used to analyze data collected at various spatial locations throughout multiple time points. However, even with a finite number of spatial locations, there may be a lack of resources to collect data from every spatial location at every time point. We develop a spatio-temporal finite-population block kriging (ST-FPBK) method to predict a quantity of interest, such as a mean or total, across a finite number of spatial locations. This ST-FPBK predictor incorporates an appropriate variance reduction for sampling from a finite population. Through an application to moose surveys in the east-central region of Alaska, we show that the predictor has a substantially smaller standard error compared to a predictor from the purely spatial model that is currently used to analyze moose surveys in the region. We also show how the model can be used to forecast a prediction for abundance in a time point for which spatial locations have not yet been surveyed. A separate simulation study shows that the spatio-temporal predictor is unbiased and that prediction intervals from the ST-FPBK predictor attain appropriate coverage. For ecological monitoring surveys completed with some regularity through time, use of ST-FPBK could improve precision. We also give an R package that ecologists and resource managers could use to incorporate data from past surveys in predicting a quantity from a current survey.