Associated LAH Numbers,Factorial Series Distributions and Unbiased Estimation of a Size Parameter

A finite population consists of kN individuals of N different categories with k individuals each. It is required to estimate the unknown parameter N, the number of different classes in the population. A sequential sampling scheme is considered in which individuals are sampled until a preassigned number of repetitions of already observed categories occur in the sample. Corresponding fixed sample size schemes were considered by Charalambides (1981). The sequential sampling scheme has the advantage of always allowing unbiased estimation of the size parameter N. It is shown that relative to Charalambides' fixed sample size scheme only minor adjustments are required to account for the sequential scheme. In particular, MVU estimators of parametric functions are expressible in terms of the C-numbers introduced by Charalambides.     

Establishing Baseline Indices for the Quality of the Biodiversity of Restored Habitats Using a Standardized Sampling Process

The need for standardized biodiversity assessment methods to enable biodiversity quality to be measured is outlined. A general approach to sampling is suggested. The results of the use of this sampling process are given for two case studies of different taxonomic groups. The data assessment is made easier by the use of a bespoke computer program. Examples of the program output are presented. The advantage of this standardized measurement of biodiversity compared to species lists and the use of indicator species are outlined in the case studies macrofungi and butterflies. It was shown that the biodiversity quality of sites can be compared by the use of a range of measured biodiversity indices in a way that allows sites to be compared through time or between sites/treatments. In one case (butterflies), data that have been collected systematically in a recording scheme have been analyzed retrospectively and yielded valuable information on changes in biodiversity quality. The uses of this method in establishing baselines in restoration ecology are discussed. The importance of restoration ecology in the conservation of biodiversity could be underlined by the use of the methods presented in this article.     

MAXIMUM LIKELIHOOD APPROACH TO CLUSTERING

在各种各样应用研究的模型中,经常会遇到所研究的总体是由两个或多个具不同性质的亚总体混合而成的。因此混合分布,特别是混合正态分布可以广泛应用于这些模型。混向总体的分解问题是相当重要和有用的。对于当观测资料不知属于两个可能的总体的哪一个时的分类问题,本文研究了通常使用的基于极大似然估计的两种聚类方法。文中给出了基于在混合抽样和分离抽样这两种不同的抽并方式下的模拟结果对比,并阐述了这两种方法的基本假设及其有关性质。文中使用了基于抗血友病因子(AHF)话性和似抗血友病(AHF-like)抗原为变量以判别妇女是正常还是血友病 A 基因携带者的实际资料,分帮了这两种方法的基本区别。     

Sequential sampling: a novel method in farm animal welfare assessment

Lameness in dairy cows is an important welfare issue. As part of a welfare assessment, herd level lameness prevalence can be estimated from scoring a sample of animals, where higher levels of accuracy are associated with larger sample sizes. As the financial cost is related to the number of cows sampled, smaller samples are preferred. Sequential sampling schemes have been used for informing decision making in clinical trials. Sequential sampling involves taking samples in stages, where sampling can stop early depending on the estimated lameness prevalence. When welfare assessment is used for a pass/fail decision, a similar approach could be applied to reduce the overall sample size. The sampling schemes proposed here apply the principles of sequential sampling within a diagnostic testing framework. This study develops three sequential sampling schemes of increasing complexity to classify 80 fully assessed UK dairy farms, each with known lameness prevalence. Using the Welfare Quality herd-size-based sampling scheme, the first ‘basic’ scheme involves two sampling events. At the first sampling event half the Welfare Quality sample size is drawn, and then depending on the outcome, sampling either stops or is continued and the same number of animals is sampled again. In the second ‘cautious’ scheme, an adaptation is made to ensure that correctly classifying a farm as ‘bad’ is done with greater certainty. The third scheme is the only scheme to go beyond lameness as a binary measure and investigates the potential for increasing accuracy by incorporating the number of severely lame cows into the decision. The three schemes are evaluated with respect to accuracy and average sample size by running 100 000 simulations for each scheme, and a comparison is made with the fixed size Welfare Quality herd-size-based sampling scheme. All three schemes performed almost as well as the fixed size scheme but with much smaller average sample sizes. For the third scheme, an overall association between lameness prevalence and the proportion of lame cows that were severely lame on a farm was found. However, as this association was found to not be consistent across all farms, the sampling scheme did not prove to be as useful as expected. The preferred scheme was therefore the ‘cautious’ scheme for which a sampling protocol has also been developed.     

Proportionate spatial sampling and equal‐time sampling of mobile animals: A dilemma for inferring areal dependence

Abstract Patch or island area is one of the most frequently used variables for inference in conservation biology and biogeography, and is often used in ecological applications. Given that all of these disciplines deal with large spatial scales, exhaustive censusing is not often possible, especially when there are large numbers of patches (e.g. for replication and control purposes). Therefore, data for patches or islands are usually collected by sampling. We argue that if area is to be used as an inferential factor, then the objects under study (i.e. the patches) must be characterized on an areal basis. This necessarily means that fixed‐area sampling is inadequate (e.g. a single standard quadrat or transect set within patches irrespective of the patch area) and that some form of area‐proportionate sampling is needed (e.g. a fixed areal proportion of each patch is surveyed by random allocation of standard quadrats across each patch). However, use of area‐proportionate sampling is not usually dissociated from the increased temporal intensity of sampling that arises from using this approach. The dilemma we see is deciding how much of the area‐specificity of variables such as species richness, rare‐species indices or probabilities of occurrence of individual species is related to the area‐proportionate survey protocol and how much is due to the temporal intensity of surveys. We undertook a study in which we balanced temporal and spatial effects by increasing the time spent surveying smaller patches of vegetation to account for the area‐ratio difference. The estimated species richness of birds of the box–ironbark system of central Victoria, Australia, was found to depend strongly upon area when area‐proportionate sampling alone was performed. When time‐balancing was imposed upon area‐proportionate sampling, the differences between smaller (10‐ha) and larger (40‐ha) areas were much reduced or effectively disappeared. We show that species found in the additional surveys used to conduct the time‐balancing were significantly less abundant than species recorded in area‐proportionate sampling. This effect is probably most severe for mobile animals, but may emerge in other forms of sampling.     

Pair Rank Set Sampling

Ranked set sampling (RSS) as suggested by McIntyre (1952) may be modified to introduced a new sampling method called pair rank set sampling (PRSS), which might be used in some area of application instead of the RSS to increase the efficiency of the estimators relative to the simple random sampling (SRS) method. Estimators of the population mean are considered. An example using real data is presented to illustrate computations.     

General ranked set sampling with cost considerations

Nahhas, Wolfe, and Chen (2002, Biometrics58, 964-971) considered optimal set size for ranked set sampling (RSS) with fixed operational costs. This framework can be very useful in practice to determine whether RSS is beneficial and to obtain the optimal set size that minimizes the variance of the population estimator for a fixed total cost. In this article, we propose a scheme of general RSS in which more than one observation can be taken from each ranked set. This is shown to be more cost-effective in some cases when the cost of ranking is not so small. We demonstrate using the example in Nahhas, Wolfe, and Chen (2002, Biometrics58, 964-971), by taking two or more observations from one set even with the optimal set size from the RSS design can be more beneficial.     

The organization of interphase chromatin in drosophilidae

Cytological evidence is presented which shows that for Drosophila virilis and Samoaia leonensis at least, each satellite DNA is condensed into a distinct heterochromatic mass during interphase. This is seen as just one example of a general phenomenon in which chromatin containing a particular DNA sequence binds to other chromatin containing the same sequence. It is proposed that DNA sequence specific proteins can account for this phenomenon.     

The effect of sampling density and study area size on landscape genetics inferences for the Mississippi slimy salamander (Plethodon mississippi)

In landscape genetics, it is largely unknown how choices regarding sampling density and study area size impact inferences upon which habitat features impede vs. facilitate gene flow. While it is recommended that sampling locations be spaced no further apart than the average individual''s dispersal distance, for low‐mobility species, this could lead to a challenging number of sampling locations, or an unrepresentative study area. We assessed the effects of sampling density and study area size on landscape genetic inferences for a dispersal‐limited amphibian, Plethodon mississippi, via analysis of nested datasets. Microsatellite‐based genetic distances among individuals were divided into three datasets representing sparse sampling across a large study area, dense sampling across a small study area, or sparse sampling across the same small study area. These datasets were a proxy for gene flow (i.e., the response variable) in maximum‐likelihood population effects models that assessed the nature and strength of their relationship with each of five land‐use classes (i.e., potential predictor variables). Comparisons of outcomes were based on the rank order of effect, sign of effect (i.e., gene flow resistance vs. facilitation), spatial scale of effect, and functional relationship with gene flow. The best‐fit model for each dataset had the same sign of effect for hardwood forests, manmade structures, and pine forests, indicating the impacts of these land‐use classes on dispersal and gene flow in P. mississippi are robust to sampling scheme. Contrasting sampling densities led to a different inferred functional relationship between agricultural areas and gene flow. Study area size appeared to influence the scale of effect of manmade structures and the sign of effect of pine forests. Our findings provided evidence for an influence of sampling density, study area size, and sampling effort upon inferences. Accordingly, we recommend iterative subsampling of empirical datasets and continued investigation into the sensitivities of landscape genetic analyses using simulations.     

Statistics of natural populations. III. Sequential sampling plans for the estimation of gene frequencies

In previous work several models have been developed for genetic surveys of natural populations. Parents of unknown genotype are collected from a natural population, polymorphic at a single genetic locus. From each of these N cryptic parents a number of offspring are identified for their genotype. Our problem is to select an efficient offspring sampling plan for estimating the frequency of an allele in the cryptic adult population based on the N family profiles of juvenile genotypes. A criterion called the information per unit cost of observation is introduced to evaluate sequential sampling plans, in which the number of offspring per family examined is random. Some simple, practical schemes for stopping the sampling of offspring from a collected parent are introduced; one example is stopping when: (i) the offspring are definitive about the parental genotype(s) for the first time; (ii) a fixed number of one genotype only is seen; or (iii) a fixed maximum feasible number of offspring have been genotyped. This sampling scheme is recommended. For each sampling scheme, the best linear unbiased estimator and the sequential maximum likelihood estimator of the allele frequency are characterized. From the moments of these estimators, it is then possible to tabulate efficient sequential sampling plans, which are better (in the sense of information per unit cost), just as simple, and less costly than corresponding fixed sampling plans in use.     

Effects of cluster sampling on epidemiologic analysis in population-based case-control studies

We consider population-based case-control designs in which controls are selected by one of three cluster sampling plans from the entire population at risk. The effects of cluster sampling on classical epidemiologic procedures are investigated, and appropriately modified procedures are developed. In particular, modified procedures for testing the homogeneity of odds ratios across strata, and for estimating and testing a common odds ratio are presented. Simulations that use the data from the 1970 Health Interview Survey as a population suggest that classical procedures may be fairly robust in the presence of cluster sampling. A more extreme example based on a mixed multinomial model clearly demonstrates that the classical Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748) and Woolf-Haldane tests of no exposure effect may have sizes exceeding nominal levels and confidence intervals with less than nominal coverage under an alternative hypothesis. Classical estimates of odds ratios may also be biased with non-self-weighting cluster samples. The modified procedures we propose remedy these defects.     

Fast egg collection method greatly improves randomness of egg sampling in Drosophila melanogaster

When obtaining samples for population genetic studies, it is essential that the sampling is random. For Drosophila, one of the crucial steps in sampling experimental flies is the collection of eggs. Here an egg collection method is presented, which randomizes the eggs in a water column and diminishes environmental variance. This method was compared with a traditional egg collection method where eggs are collected directly from the medium. Within each method the observed and expected standard deviations of egg-to-adult viability were compared, whereby the difference in the randomness of the samples between the two methods was assessed. The method presented here was superior to the traditional method. Only 14% of the samples had a standard deviation higher than expected, as compared with 58% in the traditional method. To reduce bias in the estimation of the variance and the mean of a trait and to obtain a representative collection of genotypes, the method presented here is strongly recommended when collecting eggs from Drosophila.     

A comparison of diversity estimators applied to a database of host–parasite associations

Understanding the drivers of biodiversity is important for forecasting changes in the distribution of life on earth. However, most studies of biodiversity are limited by uneven sampling effort, with some regions or taxa better sampled than others. Numerous methods have been developed to account for differences in sampling effort, but most methods were developed for systematic surveys in which all study units are sampled using the same design and assemblages are sampled randomly. Databases compiled from multiple sources, such as from the literature, often violate these assumptions because they are composed of studies that vary widely in their goals and methods. Here, we compared the performance of several popular methods for estimating parasite diversity based on a large and widely used parasite database, the Global Mammal Parasite Database (GMPD). We created artificial datasets of host–parasite interactions based on the structure of the GMPD, then used these datasets to evaluate which methods best control for differential sampling effort. We evaluated the precision and bias of seven methods, including species accumulation and nonparametric diversity estimators, compared to analyzing the raw data without controlling for sampling variation. We find that nonparametric estimators, and particularly the Chao2 and second-order jackknife estimators, perform better than other methods. However, these estimators still perform poorly relative to systematic sampling, and effect sizes should be interpreted with caution because they tend to be lower than actual effect sizes. Overall, these estimators are more effective in comparative studies than for producing true estimates of diversity. We make recommendations for future sampling strategies and statistical methods that would improve estimates of global parasite diversity.     

Proportional hazards regression for cancer studies

Summary.   There has been some recent work in the statistical literature for modeling the relationship between the size of cancers and probability of detecting metastasis, i.e., aggressive disease. Methods for assessing covariate effects in these studies are limited. In this article, we formulate the problem as assessing covariate effects on a right-censored variable subject to two types of sampling bias. The first is the length-biased sampling that is inherent in screening studies; the second is the two-phase design in which a fraction of tumors are measured. We construct estimation procedures for the proportional hazards model that account for these two sampling issues. In addition, a Nelson–Aalen type estimator is proposed as a summary statistic. Asymptotic results for the regression methodology are provided. The methods are illustrated by application to data from an observational cancer study as well as to simulated data.     

油松毛虫(Dendrolimus labulaeformis)幼虫抽样技术的研究

本文在测定油松毛虫幼虫静态格局和动态格局的条件下,全面而系统地进行了株抽样、轮抽样和“枝”抽样的研究。根据幼虫在各轮垂直分布的特征和喜食二年生针叶的特性,建立回归模型,从轮抽样发展到“枝”抽样,通过检验,预报精度在91—98％之间。轮抽样比株抽样平均提高效率6倍,“枝”抽样比轮抽样又平均提高1.5倍。如费用以每株0.20元计,轮抽样比株抽样每株平均减少0.16元,“枝”抽样每株又减少0.032元。     

Problem of the structural and functional organization of the immature motor center

A hypothetical structural and functional scheme of organization of the immature spinal motor center is proposed, based on our own studies carried out on rat pups of the first month of postnatal development as well as on the analysis of data from literature. Taking into account peculiarities of functioning of various chains of the segmental reflex apparatus (high excitability of the motor center, heterochrony in the development of interneurons of the spinal cord dorsal horns as well as of excitatory and inhibitory mechanisms, possibility of generation of rhythmic activity by one of the half-centers of the motor generator regardless of the activity of the other one) and the mechanisms of its cholinergic and catecholaminergic regulation, age-related changes are considered, which are connected with the organization of interrelations of elements both within the motor center and from the descending regulatory systems.     

A probabilistic model for designing and assessing the performance of eDNA sampling protocols

Environmental DNA (eDNA) sampling, the detection of species‐specific genetic material in water samples, is an emerging tool for monitoring aquatic invasive species. Optimizing eDNA sampling protocols can be challenging because there is imperfect understanding of how each step of the protocol influences its sensitivity. This paper develops a probabilistic model that characterizes each step of an eDNA sampling protocol to evaluate the protocol's overall detection sensitivity for one sample. The model is then applied to analyse how changes over time made to the eDNA sampling protocol to detect bighead (BH) and silver carp (SC) eDNA have influenced its sensitivity, and hence interpretation of the results. The model shows that changes to the protocol have caused the sensitivity of the protocol to fluctuate. A more efficient extraction method in 2013, new species‐specific markers with a qPCR assay in 2014, and a more efficient capture method in 2015 have improved the sensitivity, while switching to a larger elution volume in 2013 and a smaller sample volume in 2015 have reduced the sensitivity. Overall, the sensitivity of the current protocol is higher for BH eDNA detection and SC eDNA detection compared to the original protocol used from 2009 to 2012. The paper shows how this model of eDNA sampling can be used to evaluate the effect of proposed changes in an eDNA sampling and analysis protocol on the sensitivity of that protocol to help researchers optimize their design.     

Glass wool filters for concentrating waterborne viruses and agricultural zoonotic pathogens

The key first step in evaluating pathogen levels in suspected contaminated water is concentration. Concentration methods tend to be specific for a particular pathogen group, for example US Environmental Protection Agency Method 1623 for Giardia and Cryptosporidium, which means multiple methods are required if the sampling program is targeting more than one pathogen group. Another drawback of current methods is the equipment can be complicated and expensive, for example the VIRADEL method with the 1MDS cartridge filter for concentrating viruses. In this article we describe how to construct glass wool filters for concentrating waterborne pathogens. After filter elution, the concentrate is amenable to a second concentration step, such as centrifugation, followed by pathogen detection and enumeration by cultural or molecular methods. The filters have several advantages. Construction is easy and the filters can be built to any size for meeting specific sampling requirements. The filter parts are inexpensive, making it possible to collect a large number of samples without severely impacting a project budget. Large sample volumes (100s to 1,000s L) can be concentrated depending on the rate of clogging from sample turbidity. The filters are highly portable and with minimal equipment, such as a pump and flow meter, they can be implemented in the field for sampling finished drinking water, surface water, groundwater, and agricultural runoff. Lastly, glass wool filtration is effective for concentrating a variety of pathogen types so only one method is necessary. Here we report on filter effectiveness in concentrating waterborne human enterovirus, Salmonella enterica, Cryptosporidium parvum, and avian influenza virus.     

On a supplemented case-control design

The supplemented case-control design consists of a case-control sample and of an additional sample of disease-free subjects who arise from a given stratum of one of the measured exposures in the case-control study. The supplemental data might, for example, arise from a population survey conducted independently of the case-control study. This design improves precision of estimates of main effects and especially of joint exposures, particularly when joint exposures are uncommon and the prevalence of one of the exposures is low. We first present a pseudo-likelihood estimator (PLE) that is easy to compute. We further adapt two-phase design methods to find maximum likelihood estimates (MLEs) for the log odds ratios for this design and derive asymptotic variance estimators that appropriately account for the differences in sampling schemes of this design from that of the traditional two-phase design. As an illustration of our design we present a study that was conducted to assess the influence to joint exposure of hepatitis-B virus (HBV) and hepatitis-C virus (HCV) infection on the risk of hepatocellular carcinoma in data from Qidong County, Jiangsu Province, China.