Nonparametric Estimation of Population Density for Line Transect Sampling Using FOURIER Series

A nonparametric, robust density estimation method is explored for the analysis of right-angle distances from a transect line to the objects sighted. The method is based on the FOURIER series expansion of a probability density function over an interval. With only mild assumptions, a general population density estimator of wide applicability is obtained.     

Estimating Effective Population Size and Mutation Rate from Sequence Data Using Metropolis-Hastings Sampling

We present a new way to make a maximum likelihood estimate of the parameter 4N(e)μ (effective population size times mutation rate per site, or θ) based on a population sample of molecular sequences. We use a Metropolis-Hastings Markov chain Monte Carlo method to sample genealogies in proportion to the product of their likelihood with respect to the data and their prior probability with respect to a coalescent distribution. A specific value of θ must be chosen to generate the coalescent distribution, but the resulting trees can be used to evaluate the likelihood at other values of θ, generating a likelihood curve. This procedure concentrates sampling on those genealogies that contribute most of the likelihood, allowing estimation of meaningful likelihood curves based on relatively small samples. The method can potentially be extended to cases involving varying population size, recombination, and migration.     

Estimating Competition in Cladocerans Using Data on Dynamics of Clutch Size and Population Density

Negative correlations between clutch size and population density are proposed to be considered as indices of intra- and interspecific competition in cladocerans if they are revealed while analyzing population dynamics and clutch size and time lags are taken into account. The proper correlation analysis of summer populations of Diaphanosoma brachyurum, Bosmina coregoni, Daphnia cucullata and D. galeata from mesotrophic Lake Glubokoye (Moscow Region) in 1975, 1978, and 1979 indicates the important role of competition of both types for the community studied. High niche overlap in food and space in the four populations was also observed.     

Line Transect Sampling in Small Regions

This article develops an approach to estimating population abundance from line transect surveys that uses a calibration survey to estimate the detection function, which is then employed as a weight function in constructing the abundance estimate. Nonparametric methods of estimating the detection function via local regression and via a kernel density estimator are considered. The proposed methods are evaluated using a set of Western Australian plant data and weed enumeration data.     

Some Mathematical Models for Line Transect Sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we extend that mathematical framework to several different sampling models, and a number of interesting discrete probability distributions emerge.     

Line Transect Sampling in Small and Large Regions

Melville and Welsh (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 Buckland et al. (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.     

Estimating the Population Mean Using Extreme Ranked Set Sampling

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean. ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.     

Line Transect Sampling of Primates: Can Animal-to-Observer Distance Methods Work?

Line transect sampling is widely used for estimating abundance of primate populations. Researchers commonly use animal-to-observer distances (AODs) in analysis, in preference to perpendicular distances from the line, which is in marked contrast with standard practice for other applications of line transect sampling. We formalize the mathematical shortcomings of approaches based on AODs, and show that they are likely to give strongly biased estimates of density. We review papers that claim good performance for the method, and explore this performance through simulations. These confirm strong bias in estimates of density using AODs. We conclude that AOD methods are conceptually flawed, and that they cannot in general provide valid estimates of density.     

Estimating Size and Trend of the North Interlake Woodland Caribou Population Using Fecal-DNA and Capture-Recapture Models

A critical step in recovery efforts for endangered and threatened species is the monitoring of population demographic parameters. As part of these efforts, we evaluated the use of fecal-DNA based capture–recapture methods to estimate population sizes and population rate of change for the North Interlake woodland caribou herd (Rangifer tarandus caribou), Manitoba, Canada. This herd is part of the boreal population of woodland caribou, listed as threatened under the federal Species at Risk Act (2003) and the provincial Manitoba Endangered Species Act (2006). Between 2004 and 2009 (9 surveys), we collected 1,080 fecal samples and identified 180 unique genotypes (102 females and 78 males). We used a robust design survey plan with 2 surveys in most years and analysed the data with Program MARK to estimate encounter rates (p), apparent survival rates (φ), rates of population change (λ), and population sizes (N). We estimated these demographic parameters for males and females and for 2 genetic clusters within the North Interlake. The population size estimates were larger for the Lower than the Upper North Interlake area and the proportion of males was lower in the Lower (33%) than the Upper North Interlake (49%). Population rate of change for the entire North Interlake area (2005–2009) using the robust design Pradel model was significantly <1.0 (λ = 0.90, 95% CI: 0.82–0.99) and varied between sex and area with the highest being for males in Lower North Interlake (λ = 0.98, 95% CI: 0.83–1.13) and the lowest being for females in Upper North Interlake (λ = 0.83, 95% CI: 0.69–0.97). The additivity of λ between sex and area is supported on the log scale and translates into males having a λ that is 0.09 greater than females and independent of sex, Lower North Interlake having a λ that is 0.06 greater than Upper North Interlake. Population estimates paralleled these declining trends, which correspond to trends observed in other fragmented populations of woodland caribou along the southern part of their range. The results of this study clearly demonstrate the applicability and success of non-invasive genetic sampling in monitoring populations of woodland caribou. © 2012 The Wildlife Society.     

On Estimating a Population Proportion via Ranked Set Sampling

This paper explores the use of the rank set sampling (RSS) protocol as it pertains to the estimation of a population proportion. The maximum likelihood estimator (MLE) and the sample proportion, both based on the RSS data, are discussed and their corresponding asymptotic distributions are derived. Based on these results the MLE is found to be uniformly more efficient than the sample proportion. Nevertheless, both estimators are more efficient than the simple random sample proportion. The greatest gains in efficiency are obtained at the center of the parameter space. Finally, these results remain valid in the presence of judgment error. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Point Transect Sampling Along Linear Features

Summary 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.     

Sampling Methods for Estimating Breeding Population and Hunting Mortality of Game Birds

In this paper we will summarize some of the important sampling and non-sampling errors with special reference to the mail surveys on migratory game birds and aerial surveys on breeding birds in North America. Where possible, methods for controlling the errors will be indicated.     

Estimating Population Size for Continuous-Time Capture-Recapture Models Via Sample Coverage

An estimation procedure using the idea of sample coverage is proposed to estimate population size for capture-recapture experiments in continuous time. The capture rates (intensity) are allowed to vary by time and individuals (heterogeneity). Only capture frequency history are sufficient for estimating population size while capture times and sequential orders of animals caught are irrelevant for the analysis. An example is given for illustration. The performance of the proposed estimation procedure is also investigated by simulation.     

Asian Elephants in China: Estimating Population Size and Evaluating Habitat Suitability

We monitored the last remaining Asian elephant populations in China over the past decade. Using DNA tools and repeat genotyping, we estimated the population sizes from 654 dung samples collected from various areas. Combined with morphological individual identifications from over 6,300 elephant photographs taken in the wild, we estimated that the total Asian elephant population size in China is between 221 and 245. Population genetic structure and diversity were examined using a 556-bp fragment of mitochondrial DNA, and 24 unique haplotypes were detected from DNA analysis of 178 individuals. A phylogenetic analysis revealed two highly divergent clades of Asian elephants, α and β, present in Chinese populations. Four populations (Mengla, Shangyong, Mengyang, and Pu’Er) carried mtDNA from the α clade, and only one population (Nangunhe) carried mtDNA belonging to the β clade. Moreover, high genetic divergence was observed between the Nangunhe population and the other four populations; however, genetic diversity among the five populations was low, possibly due to limited gene flow because of habitat fragmentation. The expansion of rubber plantations, crop cultivation, and villages along rivers and roads had caused extensive degradation of natural forest in these areas. This had resulted in the loss and fragmentation of elephant habitats and had formed artificial barriers that inhibited elephant migration. Using Geographic Information System, Global Positioning System, and Remote Sensing technology, we found that the area occupied by rubber plantations, tea farms, and urban settlements had dramatically increased over the past 40 years, resulting in the loss and fragmentation of elephant habitats and forming artificial barriers that inhibit elephant migration. The restoration of ecological corridors to facilitate gene exchange among isolated elephant populations and the establishment of cross-boundary protected areas between China and Laos to secure their natural habitats are critical for the survival of Asian elephants in this region.     

Estimating the Population Size and Genetic Diversity of Amur Tigers in Northeast China

Over the past century, the endangered Amur tiger (Panthera tigris altaica) has experienced a severe contraction in demography and geographic range because of habitat loss, poaching, and prey depletion. In its historical home in Northeast China, there appears to be a single tiger population that includes tigers in Southwest Primorye and Northeast China; however, the current demographic status of this population is uncertain. Information on the abundance, distribution and genetic diversity of this population for assessing the efficacy of conservation interventions are scarce. We used noninvasive genetic detection data from scats, capture-recapture models and an accumulation curve method to estimate the abundance of Amur tigers in Northeast China. We identified 11 individual tigers (6 females and 5 males) using 10 microsatellite loci in three nature reserves between April 2013 and May 2015. These tigers are confined primarily to a Hunchun Nature Reserve along the border with Russia, with an estimated population abundance of 9–11 tigers during the winter of 2014–2015. They showed a low level of genetic diversity. The mean number of alleles per locus was 2.60 and expected and observed heterozygosity were 0.42 and 0.49, respectively. We also documented long-distance dispersal (~270 km) of a male Amur tiger to Huangnihe Nature Reserve from the border, suggesting that the expansion of neighboring Russian populations may eventually help sustain Chinese populations. However, the small and isolated population recorded by this study demonstrate that there is an urgent need for more intensive regional management to create a tiger-permeable landscape and increased genetic connectivity with other populations.     

A Remark on the Line Transect Method

This paper gives a re-formulation of a model for the line transect method in terms of the theory of stationary point processes. The well-known formulae for this method are shown to be valid also under very general assumptions.