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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. [ABSTRACT FROM AUTHOR]

We compare two Monte Carlo (MC) procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of state–space models for animal populations. The procedures were applied to both simulated and real pup count data for the British grey seal metapopulation, as well as to simulated data for a Chinook salmon population. The MCMC implementation was based on tailor-made proposal distributions combined with analytical integration of some of the states and parameters. SIS was implemented in a more generic fashion. For the same computing time MCMC tended to yield posterior distributions with less MC variation across different runs of the algorithm than the SIS implementation with the exception in the seal model of some states and one of the parameters that mixed quite slowly. The efficiency of the SIS sampler greatly increased by analytically integrating out unknown parameters in the observation model. We consider that a careful implementation of MCMC for cases where data are informative relative to the priors sets the gold standard, but that SIS samplers are a viable alternative that can be programmed more quickly. Our SIS implementation is particularly competitive in situations where the data are relatively uninformative; in other cases, SIS may require substantially more computer power than an efficient implementation of MCMC to achieve the same level of MC error. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

(2001, Biometrics 57, 1130–1137) consider an approach to line transect sampling using a separate calibration study to estimate the detection function g. They present a simulation study contrasting their results with poor results from a traditional estimator, labeled the “Buckland” estimator and referenced to (1993, Distance Sampling: Estimating Abundance of Biological populations). The poor results from the “Buckland” estimator can be explained by the following observations: (i) the estimator is designated for untruncated distance data, but was applied by Melville and Welsh to truncated distance data; (ii) distance data were not pooled across transects, contrary to standard practice; and (iii) bias of the estimator was evaluated with respect to a fixed rather than a randomized grid of transect lines. We elaborate on the points above and show that the traditional methods perform to expectation when applied correctly. We also emphasize that the estimator labeled the “Buckland” estimator by Melville and Welsh is not an estimator recommended by Buckland et al. for practical survey applications. [ABSTRACT FROM AUTHOR]

An implicit assumption of standard line transect methodology is that detection probabilities depend solely on the perpendicular distance of detected objects to the transect line. Heterogeneity In detection probabilities is commonly minimized using stratification, but this may be precluded by small sample sizes. We develop a general methodology which allows the effects of multiple covariates to be directly incorporated into the estimation procedure using a conditional likelihood approach. Small sample size properties of estimators are examined via simulations. As an example the method is applied to eastern tropical Pacific dolphin sightings data. [ABSTRACT FROM AUTHOR]

A new use of the Robbins-Monro search process to generate Monte Carlo confidence intervals for a single-parameter density function is described. When the optimal value of a 'step length constant' is known asymptotically the process gives exact confidence intervals and is fully efficient. We modify the process for the case where the optimal step length constant is unknown and find that it has low bias and typically achieves an efficiency above 75% for 90% and 95% confidence intervals and above 65% for 99% intervals. Multiple-sample mark-recapture data are used to illustrate the method. [ABSTRACT FROM AUTHOR]

A robust procedure is developed for estimating density functions from data. It requires the existence of a parametric function, called the key function, to give a first approximation to the density and then improves the fit using polynomial adjustments. When the key function is the normal density, Hermite polynomials may be used; similarly, Laguerre polynomials might be preferred if the key is negative exponential. However, adequacy of fit is little affected by choice of polynomials, and it is more straightforward to use simple polynomials whatever the form of the key. Short examples illustrate the wide applicability of the technique. The methodology was developed to allow valid analysis of migration count data for the California grey whale, and this example is considered in detail. [ABSTRACT FROM AUTHOR]