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A method for estimating sperm whale abundance in an acoustic line-transect survey with a two-element hydrophone is described. The analysis starts from the point where a set of click trains have been identified by an analyst. Using likelihood methods, a description is given of the estimation from each click train of (i) whale positions from the bearing patterns of click trains, (ii) most likely numbers of whales in aggregations and (iii) a radial detection function based on the times of detected clicks and the estimated position. The method uses the complete set of allowable arrangements of these click trains into different numbers of whales. The number of arrangements is potentially very large yet can be computed because many click train combinations are not permissible, e.g. overlapping click trains cannot be from the same whale. It is suggested that the method could work well over perpendicular distances where the detection function is near-certain i.e. a strip transect survey. The method is applied to survey data from the western Mediterranean. Simulations based on the estimated radial detection function support a strip width of 5km. Some shortcomings and areas for further development are discussed.
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