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Johnson et al. (1987) developed a mallard productivity model. That model and habitat data from a large sample (n=422) of 10.4-km² plots and nest-survival estimates in those habitats (Klett et al. 1988) were used by Cowardin et al. (1988) to simulate results from various management scenarios. These plots and the data files from them were used as the basis for the remote-sensing-based system. From 1982 to 1986, preliminary compilation of data and tests of proposed techniques were conducted in the Arrowwood Waterfowl Management District. The study included breeding-pair counts on 10.4-km² plots and building of baseline regression equations for estimating duck numbers from pond data. These regressions were specific to areas and years when data were available. They were later modified to account for annual and regional variations. We also assessed the adequacy of the regression equations for estimating duck numbers and evaluated video cameras.

Sample Universe

The remote-sensing-based system was applied in the prairie pothole region of the United States in Minnesota, North Dakota, South Dakota, and Montana. This area of glacial landscape is bounded on the east by forest land in Minnesota, on the south and west by the limit of glaciation in the Dakotas and Montana, and on the north by the Canadian border (Fig. 1). We approximated the boundaries by transferring boundaries presented by Hammond (1965) and Mann (1974) to 1:500,000 U.S. Geological Survey (USGS) maps with the constraint that boundaries must follow townships, which were used as a basis for stratifying sampling units.

Sample Design

The sampling units for habitat data were 10.4-km² plots. The plot size was chosen to approximate the homerange size of a breeding mallard pair (Cowardin et al. 1988). By 1990, the sample of 335 plots in 1987 was increased to 443 plots (Table 1).

1. A low landownership stratum contained 15.5 km² or less of easements and 0 km² of land owned by the service.
2. A moderate landownership stratum contained greater than 15.5 km² of easements and less than 2.6 km² of land owned by the service.
3. A high landownership stratum contained 2.6 km² or more of land owned by the service.

We randomly drew 10.4-km² plots from each landownership stratum to obtain a sample with higher sampling fraction in areas with high service landownership or easement because these areas were most desirable for simulations of management. At that time, recent color-infrared aerial photographs of only 422 of the selected 500 plots were available. The photographs were taken in May of a wet year. The final sample had sampling fractions of 0.0045 in the low, 0.0100 in the moderate, and 0.0824 in the high service landownership strata. Although considered sufficiently representative for model simulations, the sample was no longer strictly random because of the plots without photographs (Cowardin et al. l988).

We used the existing 422 sample plots as the basis for the remote-sensing-based system because of the large prior expenditure for mapping and digitizing data from those plots. This decision created three problems. First, the remote-sensing-based system required estimates by wetland management districts that were not considered in the original sample selection. Second, the method of stratification resulted in some plots without service landownership in the high or moderate landownership strata because townships were assigned to strata and the rules did not apply to the plots. Third, when the wetland-management-district boundaries were placed over the existing sample, some waterfowl management districts contained few sample plots and some strata inside waterfowl management districts were not represented.

We restratified the sample to overcome the first two problems by estimating landownership in each 10.4-km² cell of the sample universe and by assigning each plot to a wetland management district. This procedure allowed us to calculate weights for each stratum and thus obtain unbiased estimates of each parameter in each waterfowl management district. The restratification was accomplished by mapping and digitizing all landownership classes in the entire sample universe on 1:250,000 USGS maps and by then overlaying a grid of all 10.4-km² plots. Where wetland-management district boundaries lay along rivers, the areas were divided into irregularly shaped plots of approximately 10.4 km² . This grid was digitized, and the digital data were merged with the landownership map by The Map Overlay and Statistical System (Pywell and Niedzweadk 1980) to produce a file with the landownership of each 10.4-km² cell in the universe. Based on these data, all plots in the universe were assigned to strata by the following rules:

1. A refuge stratum included any plot that contained any national wildlife refuge land regardless of other landownership in the plot.
2. A waterfowl-production-area stratum included any plot not classified as a refuge that included 64.8 ha or more of waterfowl production area.
3. An easement stratum included any plot not classified as refuge or waterfowl production area and 64.8 ha or more of service easement.
4. A private stratum included any plot not in the previous three strata.

To overcome the third problem, we added additional plots inside waterfowl management districts that had insufficient sample size. We required at least two sample plots in each landownership in each wetland management district. The sample contained few plots from the refuge stratum. Refuges are often larger than 10.4-km² plots, and the plot size is not well suited to obtaining a representative sample. Therefore, for this report, we collapsed refuge (stratum 1) and waterfowl production area (stratum 2) into a single stratum called service.

Sample Wetland Basins

Approximately 200 wetland basins were selected from all plots in each wetland management district as sites for conducting breeding-pair counts. Sample size was determined according to the amount of time available for conducting pair counts rather than by statistical estimation of sample size required for a given degree of precision. The purpose of the pair counts was to adjust baseline regressions for annual and geographic variation in pair density. Therefore, we used an optimum allocation for a stratified random sample and treated the wetland-basin classes as strata to obtain a sample throughout the range of wetland-basin sizes and to avoid oversampling of small basins that are often dry and, therefore, provide no information about duck density. Although the technique is intended for minimizing the variance of a stratified mean, given the individual strata variances (see Neyman allocation in Cochran 1977), it also had the desired effect of reducing the sample of temporary wetlands basins, which had a smaller variance than the more permanent wetland-basin classes. Strata variances were estimated from a regression model by obtaining estimates of the number of mallard pairs in each wetland basin in each plot. The area of each wetland basin was obtained from special maps prepared by the National Wetland Inventory. All wetland basins were assumed to contain ponds. Variances of the number of mallard pairs among wetland basins within each wetland-basin class in each wetland management district were then calculated.