Estimating Animal Abundance Research Articles

Estimating Animal Abundance: Review III

The literature describing methods for estimating animal abundance and related parameters continues to grow. This paper reviews recent developments in the subject over the past seven years and updates two previous reviews.

Estimation in independent observer line transect surveys for clustered populations.

This paper introduces a framework for animal abundance estimation in independent observer line transect surveys of clustered populations. The framework generalizes an approach given in Chen (1999, Environmental and Ecological Statistics 6, in press) to accommodate heterogeneity in detection caused by cluster size and other covariates. Both parametric and nonparametric estimators for the local effective search widths, given the covariates, can be derived from the framework. A nonparametric estimator based on conditional kernel density estimation is proposed and studied owing to its flexibility in modeling the detection functions. A real data set on harbor porpoise in the North Sea is analyzed.

An assessment of distance sampling techniques for estimating animal abundance

Line transects have been widely applied for the estimation of animal abundance because they are regarded as simple, economical, and relatively precise. The recent development of automated techniques for the estimation of animal density from distance sampling data allows greater potential for field biologists and wildlife managers to become involved in the analytical summary of their research. An assessment was made of the ability of program DISTANCE to produce unbiased estimates of density in spite of potential sources of error from the estimation of transect and population density. Populations were simulated to investigate the robustness of program DISTANCE to changes in the density, distribution, and detection of animals across sampling areas and transects. It is concluded that if distance sampling data is collected reliably from a random sample of possible primary sampling units (PSUs) it can be expected that estimates of density will be presented accurately and with correct estimates of variance. If the proportion of the study area surveyed by transects is large however, then the presence of large between PSU variation will cause the variance estimates from program DISTANCE to be a sizeable overestimate.

Measurement Errors in Line Transect Surveys

SUMMARY An important assumption used in the analysis of line transect data for animal abundance estimation is that the perpendicular sighting distances of detected animals to transect lines are measured accurately. However, in many line transect surveys, the sighting distances are likely to be subject to measurement errors. In this paper, we investigate the effect of measurement errors on animal abundance estimation and show that measurement errors cause systematic bias, which cannot be reduced by simply increasing the survey effort. Estimators that correct for measurement errors using the method of moments by assuming an exponential power series detection function and knowledge of only a few moments of the error distribution are proposed.

A Sample Coverage Approach to Multiple-System Estimation with Application to Census Undercount

Abstract The concept of “sample coverage” used in animal abundance estimation is modified to evaluate the undercount of a census. Lack of independence between the census and its postenumeration survey leads to correlation bias for the standard estimator of population size. An additional recapture sample (besides the census and postenumeration survey) can be used to estimate the correlation bias due to two types of dependences. This work expresses the correlation bias for the three-sample model as a function of expected sample coverage and measures of dependence between lists. A nonparametric population size estimator that incorporates the correlation bias is proposed. A simulation study investigates the performance of the proposed procedure. Data from a 1988 dress rehearsal study for the 1990 census conducted by the U.S. Bureau of the Census are used to illustrate the proposed three-system estimation procedure and to compare the resulting estimates with those given by Darroch, Fienberg, Glonek, and Junker and Zaslavsky and Wolfgang.

A Sample Coverage Approach to Multiple-System Estimation with Application to Census Undercount

The concept of “sample coverage” used in animal abundance estimation is modified to evaluate the undercount of a census. Lack of independence between the census and its postenumeration survey leads to correlation bias for the standard estimator of population size. An additional recapture sample (besides the census and postenumeration survey) can be used to estimate the correlation bias due to two types of dependences. This work expresses the correlation bias for the three-sample model as a function of expected sample coverage and measures of dependence between lists. A nonparametric population size estimator that incorporates the correlation bias is proposed. A simulation study investigates the performance of the proposed procedure. Data from a 1988 dress rehearsal study for the 1990 census conducted by the U.S. Bureau of the Census are used to illustrate the proposed three-system estimation procedure and to compare the resulting estimates with those given by Darroch, Fienberg, Glonek, and Junker and Zaslavsky and Wolfgang.

Use of the stratified-Petersen estimator in fisheries management: estimating the number of pink salmon (Oncorhynchus gorbuscha) spawners in the Fraser River

The simple-Petersen estimator is a well-known mark-recapture method to estimate animal abundance. Two key assumptions are equal catchability in both samples and complete mixing of tagged and untagged animals. If these are violated, severe bias can occur. The stratified-Petersen estimator can be used to account for some of the heterogeneity in catchability or mixing. In this paper, we first review recent developments in the stratified-Petersen experiment for fisheries audiences and demonstrate some of the practical problems that can occur that have not been discussed in the theoretical literature. Second, we present a case study to estimate the gross escapement of Fraser River pink salmon (Oncorhynchus gorbuscha) in 1991. The motivation for this study is a discrepancy of over 5 million fish between the estimates as derived by the Pacific Salmon Commission (PSC) (7.5 million fish based on a hydroacoustic method) and the Department of Fisheries and Oceans (DFO), Canada (13.0 million fish based on a mark-recapture method). One hypothesis put forward was that the discrepancy may be due to the use of a pooled-Petersen estimator when there is differential migration over time. The stratified-Petersen model suggests that little of this discrepancy can be explained by differential migration.

Genetic tagging of humpback whales.

The ability to recognize individual animals has substantially increased our knowledge of the biology and behaviour of many taxa. However, not all species lend themselves to this approach, either because of insufficient phenotypic variation or because tag attachment is not feasible. The use of genetic markers ('tags') represents a viable alternative to traditional methods of individual recognition, as they are permanent and exist in all individuals. We tested the use of genetic markers as the primary means of identifying individuals in a study of humpback whales in the North Atlantic Ocean. Analysis of six microsatellite loci among 3,060 skin samples collected throughout this ocean allowed the unequivocal identification of individuals. Analysis of 692 'recaptures', identified by their genotype, revealed individual local and migratory movements of up to 10,000 km, limited exchange among summer feeding grounds, and mixing in winter breeding areas, and also allowed the first estimates of animal abundance based solely on genotypic data. Our study demonstrates that genetic tagging is not only feasible, but generates data (for example, on sex) that can be valuable when interpreting the results of tagging experiments.

Catch-Effort Estimation of Population Parameters under the Robust Design

Catch-effort models, as well as models for many other animal abundance estimation techniques, are distinctly divided in their application to either closed or open populations. Pollock (1982, Journal of Wildlife Management 46, 752-757) first attempted combining open-population and closed-population models in the capture-recapture literature and constructed what is now known as the robust design. In light of the advantages of the capture-recapture robust design, a similar sampling scheme is of interest in the catch-effort estimation framework. Here a description of the robust design for catch-effort methods is provided, complete with explicit maximum likelihood estimators for a range of open models. The presence of mortality and recruitment are handled in the model development sequentially. Monte Carlo simulations were used to evaluate the performance of maximum likelihood estimators under the robust design in comparison with a previously defined regression estimator. The robust design provided for greater model flexibility and in almost all circumstances produced maximum likelihood estimators that were superior to those estimated by regression methods. The advantages of the robust design are discussed for a variety of modeling scenarios.

Bayesian Estimation of Animal Abundance for Line Transect Sampling

This paper develops a Bayesian model for estimating the density of a closed animal population from data obtained by the line transect method. The detection function is assumed to be half-normal and the data are neither grouped nor truncated. A Bayes estimator is constructed with respect to a gamma prior density and two loss functions: relative squared error and absolute squared error. The Bayes estimator is compared with the maximum likelihood estimator as well as the Fourier series estimator using two data sets.

Estimation of Animal Abundance When Capture Probabilities Are Low and Heterogeneous

Obtaining reliable estimates of abundance or relative abundance under conditions of low numbers of captures and recaptures is crucial to properly assess population status of species that are of management concern; however, these characteristics make estimation difficult. We applied the commonly used jackknife (Burnham and Overton 1978, 1979) and moment (Chao 1988) estimators of abundance to capture-recapture data from northern flying squirrel (Glaucomys sabrinus) populations that had low (p ≅ 0.10), heterogeneous, capture probabilities and low densities (approx 2 squirrels/ha). The jackknife estimator selection procedure, higher-order jackknife estimators, and moment estimator were sensitive to the number of trapping occasions. These estimators tended to have low precision. Comparisons of estimators suggested specific, lower-order jackknife estimators performed well. Monte Carlo simulations corroborated results from field data. The moment estimator tended to have low bias, but the high root mean square error made the estimator less reliable than lower-order jackknife estimators. First- and second-order jackknife estimators tended to be the most reliable (low bias and precise) estimators when the number of trapping occasions (t) was ≥ 12. However, confidence interval coverage (% replications in which the constructed confidence interval included true N) was low with the first-order jackknife estimator, reflecting the negative bias of the variance estimator. We improved confidence interval coverage by an ad hoc adjustment to the variance estimator; coverage with the adjusted estimator approached the nominal 90% level at t ≥ 12. Reliable estimates of abundance can be achieved under conditions often encountered in field studies (small N and low, heterogeneous, capture probabilities) with lower-order jackknife estimators, a modification of the variance estimator for the first-order jackknife estimator, and ≥ 12 trapping occasions

Quantifying the Effects of Unequal Catchabilities on Jolly-Seber Estimators Via Sample Coverage

Using the concept of sample coverage, we derive an approximation of the bias in the Jolly-Seber population size estimators due to heterogeneity of capture probabilities. The resulting bias is expressed as a function of sample coverage, average capture probability, and the coefficient of variation of individual capture probabilities. The effect of unequal catchabilities on the Jolly-Seber survival rate estimators is also briefly discussed. We propose new population size estimators which incorporate the heterogeneity of capture probabilities. A simulation study investigates the performance of the approximation formulas of biases and the proposed estimation procedure. A real data set of male black-kneed capsids discussed in Jolly (Biometrika 52, 225-247, 1965), Seber (The Estimation of Animal Abundance, 1982), and Burnham (In Estimation of Analysis of Insect Populations, pp. 416-435, 1989) illustrates the method.

An Improved Removal Method for Estimating Animal Abundance

The problem of estimating animal populations from the numbers in successive catches has been addressed by many authors. Most have assumed asymptotic normality of maximum likelihood estimates to construct confidence intervals. This assumption can be shown to fail in many common practical situations. We construct intervals based on the profile likelihood ratio and show, by stimulation, that their true confidence is much closer to the nominal value than that of previous methods.

Application of Computed Tomography to Morphological Study of Emperor and Adélie Penguins

POLLOCK, K. H., AND W. L. CoRNELIus. 1988. A distribution-free nest survival model. Biometrics 44: 397-404. RAo, C. R. 1965. On discrete distributions arising out of methods of ascertainment. Sankhya, Series A 27:311-324. RAO, C. R. 1973. Linear statistical inference and its applications, 2nd ed. John Wiley and Sons, New York. SEBER, G. A. F. 1982. The estimation of animal abundance, 2nd ed. Macmillan, New York.

Automobile theft: Estimating the size of the criminal population

Animal abundance estimation procedures including a new method of Zelterman are applied in the criminological context of auto theft in the Australian Capital Territory. Using goodness-of-fit statistics and comparing the estimates with known clearance rates, it is estimated that during 1987 about 39% of offenders were charged with at least one count of auto theft. The results also indicate the extent of overrepresentation of juveniles in court statistics compared with their relative participation rate in auto theft.

Estimating Animal Abundance with Capture Frequency Data

I describe a new method for estimating the number of animals in a closed population with capture-recapture data under a heterogeneity model. The model is applied to capture frequency records of striped skunk (Mephitis mephitis), eastern chipmunk (Tamias striatus), eastern cottontail (Sylvilagus floridanus), and taxicab populations. I also report the results of a Monte Carlo simulation to assess the relative merits of the proposed moment estimator and the jackknife estimator. If many individuals are caught more than twice, the jackknife estimator is superior to the proposed moment estimator. However, when the mean capture probability is small, so that most captured animals are caught only 1-2 times in the samples, the moment estimator is usually less biased than the jackknife estimator. The mean coverage probability of the confidence interval associated with the moment estimator is also closer to the nominal level than that of the

A Review of Estimating Animal Abundance

During the past 5 years there have been a number of important developments in the estimation of animal abundance and related parameters such as survival rates. Many of the new techniques need to be more widely publicized as they supplant previous methods. The aim of this paper is to review this literature and suggest further avenues for research.

Long Laying Intervals: A Possible Mechanism and Its Implications

Survival of Manx Shearwaters (Puffinus puffinus). Ibis 115: 535-548. POST, P. W. 1967. Manx, Audubon's, and Little shearwaters in the northwestern North Atlantic. Bird-Banding 38: 278-305. ORIANS, G. H. 1958. A capture-recapture analysis of a shearwater population. J. Anim. Ecol. 27: 7184. RYDER, J. P. 1980. The influence of age on the breeding biology of colonial nesting seabirds. Pp. 153168 in Behavior of marine animals. Vol. 4, Marine birds (J. Burger, B. Olla, and H. Winn, Eds.). New York, Plenum Press. SEBER, G. A. F. 1982. The estimation of animal abundance. New York, Macmillan. STOREY, A. E. 1984. Function of Manx Shearwater calls in mate attraction. Behaviour 89: 73-89. TUCK, L. M. 1971. The occurrence of Greenland and European birds in Newfoundland. Bird-Banding 42: 184-209. WHITE, F. N., G. A. BARTHOLOMEW, & J. L. KINNEY. 1978. Physiological and ecological correlates of tunnel nesting in the European Bee-eater, Merops apiaster. Physiol. Zool. 51: 140-154.

Evaluation of Mark-Recapture for Estimating Striped Skunk Abundance

The mark-recapture method for estimating striped skunk (Mephitis mephitis) abundance was evaluated by systematically livetrapping a radio-equipped population on a 31.4-km2 study area in North Dakota during late April of 1977 and 1978. The study population was 10 females and 13 males in 1977 and 20 females and 8 males in 1978. Skunks were almost exclusively nocturnal. Males traveled greater nightly distances than females (3.3 vs. 2.6 km, P < 0.05) and had larger home ranges (308 vs. 242 ha) although not significantly so. Increased windchill reduced night-time activity. The population was demographically but not geographically closed. Frequency of capture was positively correlated with time skunks spent on the study area. Little variation in capture probabilities was found among trap-nights. Skunks exhibited neither trap-proneness nor shyness. Capture rates in 1977 were higher for males than for females; the reverse occurred in 1978. Variation in individual capture rates was indicated among males in 1977 and among females in 1978. Ten estimators produced generally similar results, but all underestimated true population size. Underestimation was a function of the number of untrapped skunks, primarily those that spent limited time on the study area. The jackknife method produced the best estimates of skunk abundance. J. WILDL MANAGE. 49(2):332-340 The estimation of animal abundance is often difficult. Mark-recapture is used commonly to estimate the abundance of secretive mammals, including striped skunks (Verts 1967, Bailey 1971, Lynch 1972). Although there are many estimators available (Cormack 1968, 1979; Otis et al. 1978; Pollock 1981; Seber 1982), there are few data on their application to populations of known size. This paper assesses the applicability of several estimators with data for populations of striped skunks of known size in 2 years and discusses aspects of skunk biology that influence capture probability. Although captures in this study are fewer than desired for most markrecapture evaluations, the approach represents a practical application of the mark-recapture method. W. B. Bicknell and J. L. Piehl provided field assistance. Radiotelemetry equipment was obtained from the James Ford Bell Mus., Cedar Creek Natl. Hist. Area, Univ. of Minnesota, St. Paul. D. R. Anderson and G. C. White provided the CAPTURE computer program. Appreciation is extended to D. W. Sparling, who verified J. Wildl. Manage. 49(2):1985 STRIPED SKUNK MARK-RECAPTURE * Greenwood et al. 333 some of the calculations and reviewed the manuscript, and to D. R. Anderson, K. P. Burnham, R. M. Cormack, L. L. Eberhardt, D. L. Otis, K. H. Pollock, and G. C. White, who provided constructive comments on the manu-

The Estimation of Animal Abundance and Related Parameters.

The author, one of the world's leading experts in the study of animal populations, explains in detail the methods developed by ecologists for estimating animal numbers and related parameters such as mortality and birth rates.