George A. F. Seber

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.

Detectability in Conventional and Adaptive Sampling

In this paper a simple but very general method is given for estimating a population total with any sampling design when objects in sampled units are observed with imperfect detectability--a problem characteristic of many surveys of natural and human populations. In the most general case, the method consists of dividing the value of the variable of interest associated with each detected object by the detection probability for that object and then proceeding to use the estimation method that would ordinarily be used under the design if there were no detectability problems. Examples illustrating the method include simple random sampling, conventional unequal probability sampling, and adaptive cluster sampling.

THE REMOVAL METHOD FOR TWO AND THREE SAMPLES

SUMMARY Morans remnoval method for estimating the size N of an animal population is discussed for the case of two samples and a new confidence interval for N is proposed. This new interval is found to be more satisfactory than the usual method when N < 200. The effect of a variable catchability in the population on the usual maximum likelihood estimate N is also considered. It is found that Rq and the usual estimate of the variance of N are both fairly insensitive to such variations. This robustness of N is also demonstrated for the case of three samples. L. INTRODUCTION Coinsider a closed animal population, i.e. a population in which immigration, emigration, birth, death, etc. are absent (or at least negligible for the period of investigation). Let N be the size of this population and suppose that k consecutive random samples of size yi (i = 1, 2, * *, k) are removed from the population. If p(= 1 - q), the probability of capture in a sample, is the same for each animal and remains constant from sample to sample, then the joint probability function of y, , y2 ,. * * , Yk is given by

TWO-STAGE ADAPTIVE CLUSTER SAMPLING

Adaptive cluster sampling is a powerful method for parameter estimation when a population is highly clumped with clumps widely separated. Unfortunately, its use has been somewhat limited until now because of the lack of a suitable theory for using a pilot survey to design an experiment with a given efficiency or expected cost. A two-stage sampling procedure using an initial sample of primary units that fills this role is described. As adaptive cluster sampling amounts to sampling clusters of secondary units, two schemes are possible depending on whether the clusters are allowed to overlap primary unit boundaries or not. For each of these schemes, there are two types of unbiased estimators available based, respectively, on modifications of the well-known Horvitz-Thompson and Hansen-Hurwitz estimators. Questions of cost and efficiency are discussed. A demonstration example is given.

An Adaptive Procedure for Sampling Animal Populations

SUMMARY We consider an adaptive stratified sampling procedure for animal populations in which the sample size in a given stratum or primary unit depends on the observations obtained in previous strata or primary units. This method provides a more efficient way of sampling sparse but highly clustered populations. Two sampling approaches are considered. The first is a design unbiased strategy as the estimate of population density is unbiased through design-induced factors such as the random selection of sites in each stratum. The second is called a model unbiased strategy as the density estimate is unbiased under the model assumed for the spatial distribution of the population. The theory is demonstrated by reference to sampling from a shrimp population.

Theory & Methods: A New Proof of Murthy's Estimator which Applies to Sequential Sampling

Murthys estimator has been used for constructing an unbiased estimator of a population total or mean from a sample of fixed size when there is unequal probability sampling without replacement. Traditionally, the estimator is derived by constructing an unordered version of Rajs ordered unbiased estimator. This paper presents an elementary proof of Murthys estimator which applies the Rao–Blackwell theorem to a very simple estimator. This proof includes any sequential sampling scheme, thus extending the usefulness of Murthys estimator. We demonstrate this extension by deriving unbiased estimators for inverse sampling.

The Estimation of Animal Abundance and Related Parameters

The author, one of the worlds 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.

Comparing two proportions from the same survey

Abstract Seber and Scott discussed the problem of comparing two proportions from the same survey and noted that the frequent occurrence of this situation in newspapers and magazines warrants its inclusion in introductory statistics courses. A related problem in which the two proportions overlap also warrants the same attention.

Difference of Proportions from the Same Survey

Abstract The problem of estimating the difference between two proportions for the same sample survey occurs often in practice and should be considered in introductory statistics courses.

ESTIMATING SURVIVAL RATES FROM BIRD-BAND RETURNS

Survival rates of birds can be estimated by releasing a group of banded birds at the beginning of each year for, say, s years and then recovering the bands from the dead birds for, say, t years. If the birds are banded as nestlings, then the younger birds tend to have a lower suaival rate than the adult birds and the methods used for estimation in this situation generally assume that the survival rate is age- dependent. However, adult birds tend to have a constant survival rate except when there are considerable fluctuations in the climatic conditions and similar factors from year to year. Thus, if only adult birds are banded, another approach to the problem of estimation is to assume that the survival rate depends on the calendar year and not on age the so-called time-dependent survival. A number of methods used in the past for estimating survival rates for both the age- and time-dependent models are discussed. It is shown both algebraically and by means of worked examples, that unless t is much greater than s, so that virtually all the birds are dead by the end of the experiment, all the methods discussed here tend to underestimate the true rates. The methods of Lack ( 1943 ) and Haldane ( 1953, 195S ), based on a constant survival rate are discussed and Haldanes method is generalized to the case when t 7& s. A regression method applica- ble to this situation is also discussed briefly. AGE-SPECIFIC SURVIVAL