Page 37 - Acoustics Today

The potential for passive acoustic data to be used to make inferences about animal populations has been recog- nized for decades (see, e.g., review by Mellinger et al. 2007). However, these inferences have largely been limited to con- firming presence, or quantifying spatial and temporal pat- terns in relative indices such as vocalizations detected per day. Although useful in many contexts, a fundamental limi- tation of such measures is that they do not account for spatial and temporal variation in the acoustic detectability of ani- mals and hence may not reflect true patterns of density or abundance. We aim, so far as possible, to account for such issues with the methods discussed in this article.
Much of our expertise in this area comes from a three- year research project, DECAF,2 which focused on developing methods for estimating cetacean (whale and dolphin) density from fixed sensors. The examples presented here retain that bias. However the methods can readily be applied to terrestri- al systems, and using mobile sensors, and we return to this at the end of the article. DECAF was a highly collaborative multi-agency, multi-disciplinary project bringing together an international team of statisticians, acousticians, engineers and biologists. We gratefully acknowledge the other team mem- bers: David Moretti, Ronald Morrissey, Nancy DiMarzio and Jessica Ward from the Navy Undersea Warfare Centre in Newport, Rhode Island; David Mellinger and Elizabeth Küsel from Oregon State University, Newport, Oregon; Stephen Martin from the Space and Naval Warfare Systems Centre Pacific, San Diego, California; David Borchers and Catriona Harris from the University of St. Andrews, Scotland; and Peter Tyack of Woods Hole Oceanographic Institution, Woods Hole, Massachusetts (now also at the University of St. Andrews).
Density estimation 101
Imagine the following general scenario. We have made acoustic recordings at a set of random locations throughout the region within which we were interested in estimating ani- mal density. Together, these recordings survey an area a (the union of a set of circles around each recorder with radius large enough that no call from outside these circles can be detected). We have processed the recordings using detection and classification algorithms to produce a count, n, for exam- ple the number of a particular type of call.3 To convert the count into a density, D, we use an equation of the form
(1)
where m represents a set of multipliers that convert count- per-unit-area (i.e., n/a) to animal density, and “hats” over quantities indicate that they are estimates.
In general, the multipliers that make up m do two jobs. First they account for inaccuracies in the detection process, i.e., false positive and false negative detections. The false pos- itive rate is usually easiest to estimate, by hand-validating a sample of detections (assuming that we view a human analyst as the gold standard). False negative rate is often expressed as its complement, the detection probability; it is generally harder to determine, and will be the focus of much of this
article. The second job of multipliers is to convert the object counted (e.g., a call) into the number of animals it represents. The exact nature of these second multipliers depends on the type of object counted. In some cases acoustic processing can yield the number of animals present (e.g., if animals have unique vocalizations or can be otherwise isolated)—hence the count is of animals and no multiplier of this type is need- ed. In other cases, it may be possible to count groups of ani- mals, in which case the required multiplier is mean group size. Most commonly, however, the count is of sounds, such as calls or clicks, and the required multiplier is the sound pro- duction rate. This latter type of surveying is called “cue counting” in the statistical literature (the sound is an acoustic cue), and the multiplier is called the “cue rate.”
Just as important as the estimate itself is a reliable char- acterization of uncertainty in the estimate. Your interpreta- tion of a density estimate of 1 whale per 1,000 km2 would be quite different if we told you that the 95% confidence inter- val was 0.8–1.2 versus 0.2–5.1 whales per 1,000 km2. Quanitifying uncertainty is also fundamental in testing for trends over time, differences between areas, etc. One com- mon way to report uncertainty is as coefficient of variation, CV, which is the standard error of an estimate divided by the estimate, and usually reported in percent. From here, it’s straightforward to calculate quantities like confidence inter- vals (see, e.g., Buckland et al. 2001, p.77). A CV of 10% on a density estimate is very good, corresponding to the kind of 95% confidence interval we gave first, above. A CV of 20% is reasonable, but by the time you get to CVs of 100% the esti- mate is nearly useless (as in the second confidence interval we gave above). The CV on a density estimate can be calcu- lated easily given the CV on each random component mak- ing up the estimate (the n and each multiplier in m, assuming each is statistically independent).4 It is our experience, how- ever, that not enough attention is paid to this—all too often estimates are given without corresponding CVs or confidence intervals, or there is no discussion of how reliable the esti- mates are.
An example—Cue counting beaked whales in the Bahamas
To take a concrete example, Marques et al. (2009) estimat- ed the density of Blainville’s beaked whales (Mesoplodon den- sirostris) at Tongue of the Ocean, Bahamas over a 6-day period in spring 2005. This area contains a US Navy testing range, the Atlantic Undersea Testing and Evaluation Center (AUTEC) which is instrumented with a wide baseline array of 82 bot- tom-mounted hydrophones (see Fig. 1) cabled to shore, mak- ing it an ideal laboratory for bioacoustic studies. Blainville’s beaked whales occur there, and are of particular concern to the Navy because there have been documented strandings of this and related species coincident with Navy exercises (D’Amico et al., 2009). In common with other beaked whale species, they undertake long (~45 minute), deep (600-1200 m) foraging dives, during which they produce high frequency echolocation clicks to locate prey. Running a simple detection and classifi- cation algorithm on the sound recordings over the survey peri- od logged 𝑛 = 2,940,521 echolocation clicks. Marques et al.
36 Acoustics Today, July 2012