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deep-diving animals that use echolocation to find prey–but compared with beaked whales their echolocation clicks are much louder, so that “trains” of clicks from the same individ- ual can often be detected on multiple hydrophones from the AUTEC range. This means it is possible, with some effort, to localize individuals, or at least groups of individuals (see Baggenstoss, 2011, for details), and to estimate the number of individuals within a diving group as the number of overlap- ping (direct path) click trains.
Ward et al. (in press 2012) began by quickly screening the data to exclude long stretches of time when sperm whales were not present. For the remaining times, a systematic random sam- ple of 50 10-minute periods were taken and subjected to more detailed analysis, where the number of animals diving and click- ing within the study area was estimated. They assumed that all clicking animals in the sample periods were counted without error. Given this, the density estimator can be written
(4)
where n is the total number of animals counted within the
study area a during the k=50 10-minute periods, 𝑝𝑛𝑝 is the pro-
portion of the 42-day period for which sperm whales were not
present in the quick screening, and 𝑝ˆ is the average probabili- 𝑣
ty of a whale vocalizing in a 10-minute period. This last multi- plier was estimated from independent DTAG data—not from the same time or place, and so has similar limitations to those we discussed before.
Distance sampling—North Pacific right whales in the Bering Sea
It is quite rare to have a dense enough network of sensors over the area we wish to monitor that we can be certain to detect all animals vocalizing (or related cues such as group dives or vocalizations). Hence, it is almost always necessary to include an estimate of detection probability as a multipli- er. The question then becomes how to estimate this probabil- ity. The answer depends on what data can be gathered about the detections. If it is possible to estimate the horizontal dis- tance from a sensor to each detection then the distance sam- pling approach mentioned earlier may be possible. This relies on us assuming that the sensors are distributed randomly with respect to the animals—in this case the pattern of detected distances tells us about the change in detectability with distance. If we further assume that all animals at zero distance can be detected then we can estimate absolute detectability, and hence the average detection probability (See Fig. 4).
An example of this approach is Marques et al. (2011), who obtained preliminary density estimates for North Pacific right whales Eubalaena japonica in the Bering sea from their calls—i.e., using a cue-count approach. This species is con- sidered one of the world’s most endangered, having been sub- ject to catastrophic whaling in the past, and estimates from intensive visual and genetic surveys put the population size in the tens.
In their paper, Marques et al. (2011) took advantage of special propagation conditions caused by the shallow water
and amenable substrate. That meant that distances to detect- ed calls could be obtained by analyzing the received calls and comparing them to a model of modal dispersal in a shallow water waveguide (see Munger et al., 2011, for details). They used standard distance sampling methods to obtain an esti- mate of the probability of detecting a call, p, and then calcu- lated density using Eq. 2. Other multipliers required were the false positive rate, in this case assumed to be zero, and the call rate, which was obtained from a separate survey that had been undertaken where groups of whales of known size were followed and call rates measured.
A significant limitation of this work was that only three sampling locations were available, straining the assumption that hydrophones were located at random with respect to the animals and also making extrapolation from local density in the region of the hydrophones to density in some larger area of interest merely speculation. Despite this, when they mul- tiplied the density estimate by the area of Bering Sea shelf thought to contain right whales at the times of year sur- veyed, they obtained estimates comparable with the much more expensive ship-based surveys (25 whales, with 95% CI 13-47). This suggests that, if the sampling was expanded to a larger number of randomly-selected sites (20-30 ideally) then reliable inferences could be made for this important species.
Spatially explicit capture recapture (SECR)—minke whales off Hawaii
Another method of estimating detection probability is possible if animal vocalizations are detected on multiple hydrophones, and if the same call detected on multiple hydrophones can be accurately matched. If the hydrophones are close enough together and vocalizations frequent enough that animals can be localized and tracked, then the complete count methods described previously can be used. But in many cases only occasional calls are heard, and perhaps only on 1, 2, or 3 hydrophones, so that localization is generally not possible. Nevertheless, the pattern of detection and non- detection on the hydrophones gives us an indication both of where the sound comes from, but also the probability of it being detected (see Fig. 5). The method makes use of this information is called spatially explicit capture recapture (SECR).
Martin et al. (in press 2012) used this approach to esti- mate the call density for minke whales using 12 days of data from 14 bottom-mounted hydrophones located at another Navy testing range, the Pacific Missile Range Facility (PMRF) off Kauai, Hawaii. Minke whales are known to occur season- ally in this area, but are extremely visually cryptic; on the other hand their calls, called “boings,” are readily detected. Matching (“associating”) boings across hydrophones was done semi-manually, using timing and frequency informa- tion, on a subset of the data, and the association information was used in an SECR analysis to estimate the detection prob- ability multiplier. This was then used to estimate a boing den- sity for the whole dataset. Unfortunately, a reliable estimate of boing rate (i.e., the cue rate multiplier) was not available, so once again only a preliminary estimate of animal density
40 Acoustics Today, July 2012