Horvitz–Thompson whale abundance estimation adjusting for uncertain recapture, temporal availability variation, and intermittent effort

Abstract

A Horvitz-Thompson-type estimator is introduced to estimate total abundance of the Bering-Chukchi-Beaufort Seas population of bowhead whales using combined visual and acoustic location data. The estimator divides sightings counts by three correction factors that are themselves estimated from various portions of the data. The first correction models how detection probabilities depend on covariates like offshore distance and visibility. The second correction adjusts for availability using the acoustic location data to estimate a time-varying smooth function of the probability that animals pass within visual range of the observation stations. The third correction accounts for whales passing during periods when one or both sighting stations were temporarily closed down. We derive an asymptotically unbiased estimator of abundance incorporating all these components and a corresponding variance estimate. Correcting the count of 4011 observed whales yields a 2011 abundance estimate of 16,820 with a 95% confidence interval of (15,176, 18,643) and an estimated annual rate of population increase of 3.7% (2.9%, 4.6%). These results are indicative of very low conservation risk for this population under the current low levels of aboriginal hunting permitted by the International Whaling Commission. Although few other capture-recapture surveys will confront exactly the same set of challenges addressed here, many studies face one or more issues that could be resolved by adapting portions of our approach or relevant underlying concepts thereof. Moreover, the generic estimator we derive represents an improved way to handle random correction factors rather than assuming fixed values.

Time series sightability modeling of animal populations

“…Sightability models require an initial investment to develop a model of detection using marked individuals, but are more cost-efficient since the model can then be applied to detection-only surveys in subsequent years, assuming the relationship between covariates and detection probabilities is consistent over time. Hence, the sightability model approach is popular for monitoring many wildlife species, such as moose [ 8 , 9 , 11 , 15 ], elk ( Cervus elaphus ) [ 25 , 26 ], mountain goats ( Oreamnos americanus ) [ 27 , 28 ], desert bighorn sheep [ 6 ], and bowhead whales [ 7 ].…”

“…In other words, sightability models were developed to account for situations where animals might be distributed on the landscape differently from year to year, or even seasonally, by directly relating visibility bias to covariates that are measured at the time of the surveys. The mHT estimator has been applied to many wildlife species in various geographies, including desert bighorn sheep ( Ovis canadensis ) in southwestern Arizona, USA [ 6 ], bowhead whales ( Balaena mysticetus ) in the Bering-Chukchi-Beaufort Seas [ 7 ], and moose ( Alces alces ) in Minnesota, Wyoming, Washington, Alaska, USA and Alberta, Canada [ 8 – 13 ]. In northeastern Minnesota, the Minnesota Department of Natural Resources (DNR) has used a sightability model, fit to detection/non-detection data collected from radiocollared moose between 2004 and 2007, to adjust for detection probabilities for moose groups during subsequent annual operational surveys (i.e., detection-only data) between 2005 and 2017 (see for example DelGiudice [ 13 ]).…”

Future Directions in Eubalaena spp.: Comparative Research to Inform Conservation

“…The 'right' whale to kill, these species are large baleen whales that tend to float when dead and yielded long baleen plates (known as whalebone historically), and much valuable oil that was used in industries from cosmetics to commercial lubricant (Allen, 1916;International Whaling Commission [IWC], 2001). The family (Balaenidae) also includes a fourth member, the bowhead whale (Balaena mysticetus), which was also heavily exploited but the Pacific population has had a major recovery and numbers more than the combined populations of the other three species (Givens et al, 2016). Exploitation of right whales began in earnest in the eastern North Atlantic with Basque shore and Basque pelagic whaling as early as 1000 AD (Reeves and Smith, 2006).…”

Prevalence and Abundance of Cyamid “Whale Lice” (<i>Cyamus ceti</i>) on Subsistence Harvested Bowhead Whales (<i>Balaena mysticetus</i>)

“…A mechanistic explanation for these trends likely involves many factors. One consideration is that the current growth rate of the BCB bowhead population (Givens et al, 2016) makes it plausible that their age distribution is shifting over time toward greater numbers of younger whales. Another possibility concerns the implications of a Barrow Whaling Captains' Association decision to open the fall whaling season later in the year, when air temperatures are cooler and smaller migrating bowheads are more abundant, thereby decreasing the chance of harvesting large bowheads.…”

“…Although the Bering-Chukchi-Beaufort Seas (BCB) population of bowheads is currently large and increasing (Givens et al, 2016), its remote Arctic home range means that these whales are a difficult species to monitor, and little is known about their cyamid ectoparasites. Bowheads are legally hunted by Native Alaskans, and postmortem examinations of subsistence harvested bowhead whales have been conducted for more than 40 years in cooperation with the Alaska Eskimo Whaling Commission and village whaling captains' associations.…”