Multi-stage sampling for large scale natural resources surveys: a case study of rice and waterfowl

Large-scale sample surveys to estimate abundance and distribution of organisms and their habitats are increasingly important in ecological studies. Multi-stage sampling (MSS) is especially suited to large-scale surveys because of the natural clustering of resources. To illustrate an application, we: (1) designed a stratified MSS to estimate late autumn abundance (kg/ha) of rice seeds in harvested fields as food for waterfowl wintering in the Mississippi Alluvial Valley (MAV); (2) investigated options for improving the MSS design; and (3) compared statistical and cost efficiency of MSS to simulated simple random sampling (SRS). During 2000-2002, we sampled 25-35 landowners per year, 1 or 2 fields per landowner per year, and measured seed mass in 10 soil cores collected within each field. Analysis of variance components and costs for each stage of the survey design indicated that collecting 10 soil cores per field was near the optimum of 11-15, whereas sampling >1 field per landowner provided few benefits because data from fields within landowners were highly correlated. Coefficients of variation (CV) of annual estimates of rice abundance ranged from 0.23 to 0.31 and were limited by variation among landowners and the number of landowners sampled. Design effects representing the statistical efficiency of MSS relative to SRS ranged from 3.2 to 9.0, and simulations indicated SRS would cost, on average, 1.4 times more than MSS because clustering of sample units in MSS decreased travel costs. We recommend MSS as a potential sampling strategy for large-scale natural resource surveys and specifically for future surveys of the availability of rice as food for waterfowl in the MAV and similar areas.