Jeffrey L. Laake

Distance software: design and analysis of distance sampling surveys for estimating population size

Summary 1. Distance sampling is a widely used technique for estimating the size or density of biological populations. Many distance sampling designs and most analyses use the software Distance. 2. We briefly review distance sampling and its assumptions, outline the history, structure and capabilities of Distance, and provide hints on its use. 3. Good survey design is a crucial prerequisite for obtaining reliable results. Distance has a survey design engine, with a built‐in geographic information system, that allows properties of different proposed designs to be examined via simulation, and survey plans to be generated. 4. A first step in analysis of distance sampling data is modelling the probability of detection. Distance contains three increasingly sophisticated analysis engines for this: conventional distance sampling, which models detection probability as a function of distance from the transect and assumes all objects at zero distance are detected; multiple‐covariate distance sampling, which allows covariates in addition to distance; and mark–recapture distance sampling, which relaxes the assumption of certain detection at zero distance. 5. All three engines allow estimation of density or abundance, stratified if required, with associated measures of precision calculated either analytically or via the bootstrap. 6. Advanced analysis topics covered include the use of multipliers to allow analysis of indirect surveys (such as dung or nest surveys), the density surface modelling analysis engine for spatial and habitat modelling, and information about accessing the analysis engines directly from other software. 7. Synthesis and applications. Distance sampling is a key method for producing abundance and density estimates in challenging field conditions. The theory underlying the methods continues to expand to cope with realistic estimation situations. In step with theoretical developments, state‐of‐the‐art software that implements these methods is described that makes the methods accessible to practising ecologists.

Guidelines for Line Transect Sampling of Biological Populations

Practical field procedures for conducting line transect surveys to estimate the size or density of biological populations are presented and discussed. Assumptions required for valid line transect surveys are specified. We emphasize that it is crucial to conduct observations along straight transects and obtain accurate measurements of distances and sighting angles. It is most important to conduct the survey in such a way as to maximize the probability that all objects on the centerline are found.

Trends and status of harbor seals in Washington State: 1978-1999

In the first half of the 20th century, harbor seal (Phoca vitulina richardsi) numbers were severely reduced in Washington state by a state-financed population control program. Seal numbers began to recover after the cessation of bounties in 1960 and passage of the Marine Mammal Protection Act (MMPA) in 1972. From 1978 to 1999, aerial surveys were flown at midday low tides during pupping season to determine the distribution and abundance of harbor seals in Washington. We used exponential and generalized logistic models to examine population trends and size relative to maximum net productivity level (MNPL) and carrying capacity (K). Observed harbor seal abundance has increased 3-fold since 1978, and estimated abundance has increased 7 to 10-fold since 1970. Under National Marine Fisheries Service (NMFS) management, Washington harbor seals are divided into 2 stocks: coastal and inland waters. The observed population size for 1999 is very close to the predicted Kfor both stocks. The current management philosophy for marine mammals that assumes a density-dependent response in population growth with MNPL > K/2 is supported by growth of harbor seal stocks in Washington waters.

Probability of detecting harbor porpoise from aerial surveys : Estimating g(0)

Harbor porpoise (Phocoena phocoena), and most other cetaceans, spend a significant proportion of time submerged, and are undetectable from the air. Abundance estimates based on line transect sampling may be severely biased by assuming that all porpoise near the line are detected [g(0) = 1]. By tracking groups of harbor porpoise from land, we estimated the proportion of time harbor porpoise spent at the surface and the probability that aerial observers detected groups within 200 m of the transect line. Two teams on land, equipped with electronic theodolites, tracked harbor porpoise while surveys were conducted from an aircraft equipped with side-bubble windows and a belly window. During 7 days, 33 hours of observation were made in a high-density area for harbor porpoise near Orcas Island, Washington. We monitored 7 different harbor porpoise groups from 15 to 66 minutes each. The average proportion of time at or near the surface was 0.231 (SE = 0.032). From a selected sample of 164 land-based sightings of harbor porpoise groups, 50 (30.5%) were observed from the aircraft. For our aerial line transect surveys of harbor porpoise conducted by experienced observers, g(0) = 0.292 (SE = 0.107). However, for the inexperienced observers, g(0) was 0.079 (SE = 0.046), which demonstrates the importance of experience and training.

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.

A Model-Based Approach for Making Ecological Inference from Distance Sampling Data

We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaikes information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.

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.

Visibility bias in aerial survey: mark–recapture, line-transect or both?

Mark-recapture and line-transect sampling procedures both provide estimators for visibility bias in aerial surveys, and have coexisted in the literature for decades. Mark-recapture estimators of abundance tend to be negatively biased in this context as a result of unmodelled heterogeneity. Line-transect sampling can also be negatively biased if detection probability on the line is less than 1.0. Numerous papers have described hybrid approaches using mark-recapture and line transect methods but there have been some subtle but important differences that may not be apparent to the practitioner. We have used wild horse survey data collected in south-eastern Australia and some imaginary data to highlight these subtle differences. We demonstrate the advantage of using the hybrid approach, which uses the strengths of both mark-recapture and line-transect procedures by fitting a detection function (with p(0) = 1) to the line-transect data to estimate the shape of the detection function, and uses a separate detection function for the mark-recapture data to estimate the intercept (p(0)).

Survival Rates of the California Sea Lion, Zalophus californianus, in Mexico

Abstract California sea lions (Zalophus californianus) in the Gulf of California have declined by 20% over the past 2 decades. The lack of data on life-history parameters for this species has limited the development of demographic models to assess the status of this population. We estimated age- and sex-specific annual survival probabilities for California sea lions using resighting data on 5 pup cohorts from 1981 to 2006. We modeled apparent survival and resighting probability using age-class, sex, and time as potential explanatory variables. Apparent survival rates varied for different age- and sex-classes. Only survival of pups varied by year (from 0.556 to 0.998). Survival was the same for immature males and females (0.90), but differed by sex for young (males = 0.90, females = 0.97) and old (males = 0.75, females = 0.91) adults. Resighting probabilities varied by time, age-class, and sex. Resighting probabilities were higher for females than for males, and lowest for juveniles. The survival estimates presented here provide practical insight into understanding age- and sex-specific survival rates for California sea lions.

marked: an R package for maximum likelihood and Markov Chain Monte Carlo analysis of capture–recapture data

Summary We describe an open-source r package, marked, for analysis of mark–recapture data to estimate survival and animal abundance. Currently, marked is capable of fitting Cormack–Jolly–Seber (CJS) and Jolly–Seber models with maximum likelihood estimation (MLE) and CJS models with Bayesian Markov Chain Monte Carlo methods. The CJS models can be fitted with MLE using optimization code in R or with Automatic Differentiation Model Builder. The latter allows incorporation of random effects. Some package features include: (i) individual-specific time intervals between sampling occasions, (ii) generation of optimization starting values from generalized linear model approximations and (iii) prediction of demographic parameters associated with unique combinations of individual and time-specific covariates. We demonstrate marked with a commonly analysed European dipper (Cinclus cinclus) data set. The package will be most useful to ecologists with large mark–recapture data sets and many individual covariates.