David L. Borchers

Density Estimation by Spatially Explicit Capture–Recapture: Likelihood-Based Methods

Population density is a key ecological variable, and it has recently been shown how captures on an array of traps over several closely-spaced time intervals may be modelled to provide estimates of population density (Borchers and Efford 2007). Specifics of the model depend on the properties of the traps (more generally ‘detectors’). We provide a concise description of the newly developed likelihood-based methods and extend them to include ‘proximity detectors’ that do not restrict the movements of animals after detection. This class of detector includes passive DNA sampling and camera traps. The probability model for spatial detection histories comprises a submodel for the distribution of home-range centres (e.g. 2-D Poisson) and a detection submodel (e.g. halfnormal function of distance between a range centre and a trap). The model may be fitted by maximising either the full likelihood or the likelihood conditional on the number of animals observed. A wide variety of other effects on detection probability may be included in the likelihood using covariates or mixture models, and differences in density between sites or between times may also be modelled. We apply the method to data on stoats Mustela erminea in a New Zealand beech forest identified by microsatellite DNA from hair samples. The method assumes that multiple individuals may be recorded at a detector on one occasion. Formal extension to ‘single-catch’ traps is difficult, but in our simulations the ‘multi-catch’ model yielded nearly unbiased estimates of density for moderate levels of trap saturation (≤ 86% traps occupied), even when animals were clustered or the traps spanned a gradient in density.

Mark-Recapture Models for Line Transect Surveys

SUMMARY One of the key assumptions of conventional line transect (LT) theory is that all animals in the observers path are detected. When this assumption fails, simultaneous survey by two independent observers can be used to estimate detection probabilities and abundance. Models are developed for such surveys for both grouped and ungrouped perpendicular distance data. The models unify and generalize existing line transect and mark-recapture models. They provide a general framework for the estimation of abundance from LT surveys in which detection of animals on the trackline is not certain and/or the probability of detection depends on perpendicular distance and additional covariates. Existing LT models in the literature are obtained as special cases of the general models. We use data from a shipboard line transect survey of Antarctic minke whales to illustrate use of

Estimating the Encounter Rate Variance in Distance Sampling

The dominant source of variance in line transect sampling is usually the encounter rate variance. Systematic survey designs are often used to reduce the true variability among different realizations of the design, but estimating the variance is difficult and estimators typically approximate the variance by treating the design as a simple random sample of lines. We explore the properties of different encounter rate variance estimators under random and systematic designs. We show that a design-based variance estimator improves upon the model-based estimator of Buckland et al. (2001, Introduction to Distance Sampling. Oxford: Oxford University Press, p. 79) when transects are positioned at random. However, if populations exhibit strong spatial trends, both estimators can have substantial positive bias under systematic designs. We show that poststratification is effective in reducing this bias.

Point Transect Sampling Along Linear Features

Distance sampling is a widely used methodology for assessing animal abundance. A key requirement of distance sampling is that samplers (lines or points) are placed according to a randomized design, which ensures that samplers are positioned independently of animals. Often samplers are placed along linear features such as roads, so that bias is expected if animals are not uniformly distributed with respect to distance from the linear feature. We present an approach for analyzing distance data from a survey when the samplers are points placed along a linear feature. Based on results from a simulation study and from a survey of Irish hares in Northern Ireland conducted from roads, we conclude that large bias may result if the position of samplers is not randomized, and analysis methods fail to account for nonuniformity.

A non-technical overview of spatially explicit capture–recapture models

Most capture–recapture studies are inherently spatial in nature, with capture probabilities depending on the location of traps relative to animals. The spatial component of the studies has until recently, however, not been incorporated in statistical capture–recapture models. This paper reviews capture–recapture models that do include an explicit spatial component. This is done in a non-technical way, omitting much of the algebraic detail and focussing on the model formulation rather than on the estimation methods (which include inverse prediction, maximum likelihood and Bayesian methods). One can view spatially explicit capture–recapture (SECR) models as an endpoint of a series of spatial sampling models, starting with circular plot survey models and moving through conventional distance sampling models, with and without measurement errors, through mark–recapture distance sampling (MRDS) models. This paper attempts a synthesis of these models in what I hope is a style accessible to non-specialists, placing SECR models in the context of other spatial sampling models.

Increasing abundance of bowhead whales in West Greenland

In April 2006, a dedicated survey of bowhead whales (Balaena mysticetus) was conducted on the former whaling ground in West Greenland to determine the current wintering population abundance. This effort included a double platform aerial survey design, satellite tracking of the movements of nine whales, and estimation of high-resolution surface time from 14 whales instrumented with time–depth recorders. Bowhead whales were estimated to spend an average of 24% (cv=0.03) of the time at or above 2 m depth, the maximum depth at which they can be seen on the trackline. This resulted in a fully corrected abundance estimate of 1229 (95% CI: 495–2939) bowhead whales when the availability factor was applied and sightings missed by observers were corrected. This surprisingly large population estimate is puzzling given that the change in abundance cannot be explained by a recent or rapid growth in population size. One possible explanation is that the population, which demonstrates high age and sex segregation, has recently attained a certain threshold size elsewhere, and a higher abundance of mature females appears on the winter and spring feeding ground in West Greenland. This in combination with the latest severe reduction in sea ice facilitating access to coastal areas might explain the surprising increase in bowhead whale abundance in West Greenland.

Double-observer line transect methods : levels of independence

Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark-recapture data. Like conventional mark-recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark-recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark-recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters.

The influence of animal mobility on the assumption of uniform distances in aerial line-transect surveys

Line-transect distance sampling is a widely used method for estimating animal density from aerial surveys. Analysis of line-transect distance data usually relies on a requirement that the statistical distribution of distances of animal groups from the transect line is uniform. We show that this requirement is satisfied by the survey design if all other assumptions of distance sampling hold, but it can be violated by consistent survey problems such as responsive movement of the animals towards or away from the observer. We hypothesise that problems with the uniform requirement are unlikely to be encountered for immobile taxa, but might become substantial for species of high mobility. We test evidence for non-uniformity using double-observer distance data from two aerial surveys of five species with a spectrum of mobility capabilities and tendencies. No clear evidence against uniformity was found for crabeater seals or emperor penguins on the pack-ice in East Antarctica, while minor non-uniformity consistent with responsive movement up to 30 m was found for Adelie penguins. Strong evidence of either non-uniformity or a failure of the capture-recapture validating method was found for eastern grey kangaroos and red kangaroos in Queensland.

Using Hidden Markov Models to Deal with Availability Bias on Line Transect Surveys

We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary state-dependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence.

Abundance of narwhals (Monodon monoceros) on the hunting grounds in Greenland

Abstract Narwhals (Monodon monoceros L.) occur in the Atlantic sector of the Arctic where for centuries they have been subject to subsistence hunting by Inuit in Greenland and Canada. Scientific advice on the sustainable levels of removals from narwhal populations provides the basis for quotas implemented in both Greenland and Canada. The scientific advice relies heavily on extensive aerial surveys that are the only feasible way to acquire data on narwhal densities and abundance throughout their range. In some areas lack of information on abundance, in combination with high exploitation levels, has caused conservation concerns leading to restrictions on the international trade in narwhal tusks. Narwhals also are regarded as highly sensitive to habitat disturbance caused by global warming. This study analyzed data from aerial sighting surveys covering four major narwhal hunting grounds in Greenland. The surveys were conducted as double observer experiments with 2 independent observation platforms, 1 at the front and 1 at the rear of the survey plane. The sighting data were analyzed using mark–recapture distance sampling techniques that allow for correction for whales that were missed by the observers. The surveys also were corrected for animals that were submerged during the passage of the survey plane, using diving and submergence data from satellite-linked time–depth recorders deployed on 2 free-ranging narwhals. The abundance of narwhals on the wintering ground in West Greenland in 2006 was 7,819 (95% confidence interval [CI]: 4,358–14,029). The abundances of narwhals in Inglefield Bredning and Melville Bay, northwest Greenland in 2007 were 8,368 (95% CI: 5,209–13,442) and 6,024 (95% CI: 1,403–25,860), respectively. The abundance of narwhals in East Greenland in 2008 was 6,444 (95% CI: 2,505–16,575). These surveys provide the first estimates of narwhal abundance from important hunting areas in East and West Greenland and provide larger and more complete estimates from previously surveyed hunting grounds in Inglefield Bredning. The estimates can be used for setting catch limits for the narwhal harvest in West and East Greenland and as a baseline for examining the effects of climate change on narwhal abundance.