Nil pi P2

This is because the observers must reconcile the lists after sampling in order to obtain the yii frequency. For example, it is common for observers to sketch a map of the area sampled, and then reconcile the maps after sampling. Independence of observations is crucial, and this typically might be a practical field limitation. For example, if an observer is more likely to detect an individual as a result of another observer's detection (e.g., the former detects it as a result of the latter's scribbling on paper and intense focus on a bush 50 m away from the point of observation). A variation has been proposed (Nichols et al., 2000) in which the observations are dependent. One observer serves as a checker, records the first observer's data, and adds birds to the list that the first observer missed. During the survey, the observers switch roles to yield identifiability of both observer's detection probabilities. This protocol seems more practical in many field situations.

Note that the objective of these multiple observer methods is to induce dependence in the observed counts via the multinomial observation structure. An alternative approach to data collection with multiple observers is to obtain simultaneous independent counts resulting in data without the reconciled count yii. For these data, the hierarchical models described in Royle (2004c) are appropriate. We address such models (in part) in Chapter 8. We expect that this type of multiple observer protocol should be more widely useful than existing multiple observer methods.

5.5.3 Example: Aerial Waterfowl Survey

Here we consider counts of mallard ducks (Anas platyrhynchos) collected by the U.S. Fish and Wildlife Service during the 2005 annual waterfowl population survey in the northeastern United States and eastern Canada (Koneff et al., 2008). Sample units in this fixed-wing survey are 18 mile linear segments (Smith, 1995), and 121 such segments were sampled using two observers (front seat, back seat) with detection probabilities pi, and p2, respectively. A total of 162 groups (or clusters) of birds were observed. The detection history frequencies of each group size, aggregated over all 121 segments, are given in Table 5.4. The segments are 18 miles long and 0.25 miles wide, so the total sampled area is 544.5 mi2. The main focus of this study was to assess the efficacy of the aerial surveys, as characterized by the detection probability parameter. Longer term, parties seek an operational approach to adjust observed counts for imperfect sampling, or differential efficacy of platforms (e.g., helicopters vs. fixed-wing aircraft). In this type of survey, we might also wonder whether the size of the group affects its detectability. We note that the data used here deviate slightly from Koneff et al. (2008), and they also consider slightly different models.

For now, we ignore the group size (but see Chapter 6), and focus attention on the pooled counts (pooling all group sizes). The R instructions for obtaining the

Table 5.4. Mallard double-observer detection history frequencies from 121 aerial segments. In the detection history (x,y) position x represents the pilot and y represents the backseat observer.

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