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Breeding Population Inventories and Measures of Recruitment

IV. Sampling

C. Sample Design and Error

A complete discussion of sampling is beyond the scope of this chapter and is covered in detail in a number of statistical texts (e.g., Cochran 1977), but certain aspects of sample design are especially important in waterfowl investigations. Jolly (1969a) described three sampling methods that are appropriate for inventories of breeding ducks and for estimating recruitment: (1) equal-size sample units, (2) unequal-size units using ratio methods, and (3) equal- or unequal-size units, selecting with probability proportional to size. He presents procedures for estimating total animals in the area sampled and the variances of these estimates. Unfortunately, some waterfowl surveys suffer from a lack of statistical design, and for that reason none of these three methods is appropriate. Method 1 is probably the most common method used in waterfowl inventories, especially where plots are studied by ground methods. Method 2 is also frequently used especially for transect surveys where transect lengths vary. Transect lengths frequently vary in surveys designed for aircraft counts. Method 3 is the least common of the methods even though, as Jolly points out, it is probably the simplest and most useful method available.

Jolly (1969b) defined error in a count from any sampling unit as the sum of bias and random error. If the survey is properly designed, an estimate of sample variance is available, and estimation procedures are appropriate, then it is possible to determine the sample size needed for a required degree of precision or to relate sampling intensity to cost.

Unfortunately, estimation of bias in the counts is far more complex and in some cases may not even be possible. Progress has been made in estimating the bias associated with inability to count birds from aircraft and development of air-ground correction factors. Other factors, including the effect of observers, weather, and habitat, have been studied (Diem and Lu 1960), but methods for improving accuracy have not been developed.

Perhaps more important are biases that are introduced by biological interpretation required to convert the social groups of ducks observed to estimates of breeding birds as discussed earlier. The effect of bias may not be important where interest is in determining trends in population, but when estimates of actual population size are required, as in evaluation of population dynamics, bias must be estimated. Confidence limits based on improperly defined sample units or from units having measurement errors can be highly misleading, because statistical assumptions have not been met. The actual count from each sample unit is often treated as though it were made without error. In addition, if sample transects are often broken into segments, the segments should not be treated as independent sample units.

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