Estimation of the individual number entering each development stage in an insect population

A method for estimating the number entering each development stage from data obtained by regular sampling through one generation of an insect population was described. This method is consisted of the following two procedures: The provisional estimates are calculated on the assumption that each stage has a common mortality in a sampling interval. Then these estimates are corrected on another assumption that the mortality is different in each stage but constant during a stage. The result of testing its validity with two laboratory populations of the common cabbage butterfly, Pieris rapae crucivora, showed the availability of the present method.     

Models and estimators linking individual-based and sample-based rarefaction,extrapolation and comparison of assemblages

Aims In ecology and conservation biology, the number of species counted in a biodiversity study is a key metric but is usually a biased underestimate of total species richness because many rare species are not detected. Moreover, comparing species richness among sites or samples is a statistical challenge because the observed number of species is sensitive to the number of individuals counted or the area sampled. For individual-based data, we treat a single, empirical sample of species abundances from an investigator-defined species assemblage or community as a reference point for two estimation objectives under two sampling models: estimating the expected number of species (and its unconditional variance) in a random sample of (i) a smaller number of individuals (multinomial model) or a smaller area sampled (Poisson model) and (ii) a larger number of individuals or a larger area sampled. For sample-based incidence (presence–absence) data, under a Bernoulli product model, we treat a single set of species incidence frequencies as the reference point to estimate richness for smaller and larger numbers of sampling units.Methods The first objective is a problem in interpolation that we address with classical rarefaction (multinomial model) and Coleman rarefaction (Poisson model) for individual-based data and with sample-based rarefaction (Bernoulli product model) for incidence frequencies. The second is a problem in extrapolation that we address with sampling-theoretic predictors for the number of species in a larger sample (multinomial model), a larger area (Poisson model) or a larger number of sampling units (Bernoulli product model), based on an estimate of asymptotic species richness. Although published methods exist for many of these objectives, we bring them together here with some new estimators under a unified statistical and notational framework. This novel integration of mathematically distinct approaches allowed us to link interpolated (rarefaction) curves and extrapolated curves to plot a unified species accumulation curve for empirical examples. We provide new, unconditional variance estimators for classical, individual-based rarefaction and for Coleman rarefaction, long missing from the toolkit of biodiversity measurement. We illustrate these methods with datasets for tropical beetles, tropical trees and tropical ants.Important findings Surprisingly, for all datasets we examined, the interpolation (rarefaction) curve and the extrapolation curve meet smoothly at the reference sample, yielding a single curve. Moreover, curves representing 95% confidence intervals for interpolated and extrapolated richness estimates also meet smoothly, allowing rigorous statistical comparison of samples not only for rarefaction but also for extrapolated richness values. The confidence intervals widen as the extrapolation moves further beyond the reference sample, but the method gives reasonable results for extrapolations up to about double or triple the original abundance or area of the reference sample. We found that the multinomial and Poisson models produced indistinguishable results, in units of estimated species, for all estimators and datasets. For sample-based abundance data, which allows the comparison of all three models, the Bernoulli product model generally yields lower richness estimates for rarefied data than either the multinomial or the Poisson models because of the ubiquity of non-random spatial distributions in nature.     

The determination of key factors from life table data

Summary A new method is proposed for detecting key factors from life tables for animals whose life-cycle is divided into several stages. This method is based upon an equation that partitions the variance of the number alive at the end of the life-cycle into components associated with variation in the number entering the first stage of the cycle, variation in survival rates, and also density-dependent aspects of survival. It is illustrated by analysing Blank and Ash's (1962) census data for a population of partridges. The conclusions reached are somewhat different from those reached by Blank et al. (1967) when they applied Varley and Gradwell's (1960) type of key factor analysis to the same set of data.     

Minimum required number of specimen records to develop accurate species distribution models

Species distribution models (SDMs) are widely used to predict the occurrence of species. Because SDMs generally use presence‐only data, validation of the predicted distribution and assessing model accuracy is challenging. Model performance depends on both sample size and species’ prevalence, being the fraction of the study area occupied by the species. Here, we present a novel method using simulated species to identify the minimum number of records required to generate accurate SDMs for taxa of different pre‐defined prevalence classes. We quantified model performance as a function of sample size and prevalence and found model performance to increase with increasing sample size under constant prevalence, and to decrease with increasing prevalence under constant sample size. The area under the curve (AUC) is commonly used as a measure of model performance. However, when applied to presence‐only data it is prevalence‐dependent and hence not an accurate performance index. Testing the AUC of an SDM for significant deviation from random performance provides a good alternative. We assessed the minimum number of records required to obtain good model performance for species of different prevalence classes in a virtual study area and in a real African study area. The lower limit depends on the species’ prevalence with absolute minimum sample sizes as low as 3 for narrow‐ranged and 13 for widespread species for our virtual study area which represents an ideal, balanced, orthogonal world. The lower limit of 3, however, is flawed by statistical artefacts related to modelling species with a prevalence below 0.1. In our African study area lower limits are higher, ranging from 14 for narrow‐ranged to 25 for widespread species. We advocate identifying the minimum sample size for any species distribution modelling by applying the novel method presented here, which is applicable to any taxonomic clade or group, study area or climate scenario.     

Note on a method for analyzing stage-frequency data

A new method for analyzing stage-frequency data is proposed which is based on the estimation of rates of transition between one stage and the next highest stage in one unit of time, and a unit time survival rate that is assumed to be constant. Once these estimates are calculated it becomes possible to also estimate the mean durations of stages, stage-specific survival rates, and numbers entering stages. An advantage of the method is that it can be applied with any distribution of entry times to stage 1, and any distribution of numbers in stages when sampling begins. Use of the method is illustrated on data from a copepod population in a Canadian lake.     

Estimation of the ROC Curve under Verification Bias

The ROC (receiver operating characteristic) curve is the most commonly used statistical tool for describing the discriminatory accuracy of a diagnostic test. Classical estimation of the ROC curve relies on data from a simple random sample from the target population. In practice, estimation is often complicated due to not all subjects undergoing a definitive assessment of disease status (verification). Estimation of the ROC curve based on data only from subjects with verified disease status may be badly biased. In this work we investigate the properties of the doubly robust (DR) method for estimating the ROC curve under verification bias originally developed by Rotnitzky, Faraggi and Schisterman (2006) for estimating the area under the ROC curve. The DR method can be applied for continuous scaled tests and allows for a non‐ignorable process of selection to verification. We develop the estimator's asymptotic distribution and examine its finite sample properties via a simulation study. We exemplify the DR procedure for estimation of ROC curves with data collected on patients undergoing electron beam computer tomography, a diagnostic test for calcification of the arteries.     

Revisiting the sigmoidal curve fitting applied to quantitative real-time PCR data

Amplification of a cDNA product by quantitative polymerase chain reaction (qPCR) gives rise to fluorescence sigmoidal curves from which absolute or relative target gene content of the sample is inferred. Besides comparative C(t) methods that require the construction of a reference standard curve, other methods that focus on the analysis of the sole amplification curve have been proposed more recently. Among them, the so-called sigmoidal curve fitting (SCF) method rests on the fitting of an empirical sigmoidal model to the experimental amplification data points, leading to the prediction of the amplification efficiency and to the calculation of the initial copy number in the sample. The implicit assumption of this method is that the sigmoidal model may describe an amplification curve quantitatively even in the portion of the curve where the fluorescence signal is hidden in the noise band. The theoretical basis of the SCF method was revisited here for defining the class of experimental amplification curves for which the method might be relevant. Applying the SCF method to six well-characterized different PCR assays illustrated possible pitfalls leading to biased estimates of the amplification efficiency and, thus, of the target gene content of a sample.     

海南霸王岭热带雨林植被取样技术研究

借助地理信息系统软件的表格操作及邻体分析功能,以海南霸王岭自然保护区的沟谷雨林为例,探讨热带雨林的取样技术。结果表明,用种．面积曲线所获得的热带雨林的最小面积往往过大,而采用重要值．面积曲线所确定的最小面积则为4000m^2;无样地取样采用最近个体法,由种．点数曲线可以确定最少点数为119,而采用重要值．点数曲线,可以确定该雨林取样的最小点数为280。种．个体曲线表明,如果要获取多一倍的物种数,则所需调查的个体数应是原来的4倍。     

On the nature of errors involved in estimating stage-specific survival rates by Southwood's method for a population with overlapping stages

This paper has examined the effect of within-stage mortality on the estimation of stage-specific survival rates bySouthwood's (1978, p. 358) method. As pointed out bySouthwood , both the severity and timing of mortality affect the mean duration of a life stage, and consequently the estimate of the number of individuals entering that stage. Knowledge of the form of the survivorship curve permits correction of the estimate under certain circumstances. The use ofSouthwood's method with two overlapping stages having different rates and patterns of mortality leads to complex errors in the estimation of survival for the first stage. The nature of these errors is examined analytically and via a simulation model.Southwood's method is fairly robust, with moderate differences in mortality rates leading to acceptable errors in estimating survival for the first stage. When both the rate and pattern of mortality in both life stages are the same, then the survival estimate is made without error. Precise estimates of stage-specific survival will not usually be possible withSouthwood's method because of the errors introduced by the very parameters being measured. Direct measurement of mortality rates and survivorship patterns (seeSouthwood , 1978, p. 309) is strongly advised, at least in preliminary work.     

Analysis of serial measurements in medical research.

In medical research data are often collected serially on subjects. The statistical analysis of such data is often inadequate in two ways: it may fail to settle clinically relevant questions and it may be statistically invalid. A commonly used method which compares groups at a series of time points, possibly with t tests, is flawed on both counts. There may, however, be a remedy, which takes the form of a two stage method that uses summary measures. In the first stage a suitable summary of the response in an individual, such as a rate of change or an area under a curve, is identified and calculated for each subject. In the second stage these summary measures are analysed by simple statistical techniques as though they were raw data. The method is statistically valid and likely to be more relevant to the study questions. If this method is borne in mind when the experiment is being planned it should promote studies with enough subjects and sufficient observations at critical times to enable useful conclusions to be drawn. Use of summary measures to analyse serial measurements, though not new, is potentially a useful and simple tool in medical research.     

基于logistic模型的中国自然保护区增长动态分析

中国自然保护区建设已由数量扩张型进入质量效益型的新阶段,运用自然保护区统计年鉴数据,基于logistic模型,借助R语言,对自然保护区发展上限进行了估算。同时,运用高等数据曲线曲率求导方法,对发展阶段进行划分,对持续时长和增长速度进行了测算。结果表明:①面积理论饱和值为15470.00万hm²;②将自然保护区发展历程分为缓慢起步期(1956—1989年)、快速发展期(1990—2008年)和稳定完善期(2009—至今);③目前则处于稳定完善期,面积已渐近饱和值,数量仍在小幅度增加。希望本研究结果能为自然保护区主管部门制定管理政策、规划以及整合组建以国家公园为主体的自然保护地体系提供参考。     

Estimation of the maximum utilization area including home range and peripheral sites

There is increasing evidence that occasional utilization area (peripheral sites), in addition to typical utilization area (home range), is important for wildlife conservation and management. Here we estimated the maximum utilization area (MUA), including both typical and occasional utilization areas, based on asymptotic curves of utilization area plotted against sample size. In previous studies, these curves have conventionally been plots of cumulative utilization area versus sample size, but this cumulative method is sensitive to stochastic effects. We propose a new method based on simulation studies where outcomes of replicated simulations are averaged to reduce stochastic effects. In this averaged method, possible combinations of sample size with the same number of location data replicated from a dataset were averaged and applied to the curves of utilization area. The cumulative method resulted in a large variation of MUA estimates, depending on the start date as well as total sample size of the dataset. In the averaged method, MUA estimates were robust against changes in the start date and total sample size. The large variation of MUA estimates arose because location data on any day including the start date are affected by unpredictable effects associated with animal activity and environmental conditions. In the averaged method, replicates of sample size resulted in a reduction of temporal stochasticity, suggesting that the method stably provides reliable estimates for MUA.     

A New Class of Completely Self‐Designing Clinical Trials

A flexible method is proposed for group sequentially performed clinical trials which allows for an adaptive, data‐driven sample size reassessment at each stage. By also adaptively assigning different weights to the several stages the total number of study parts can be steered to an intended early or late end of the trial in dependence on all information available prior to a stage. Although at each stage the null hypothesis is tested on rejection, the full level‐α‐test is preserved at the end of the study. The proposed method is not restricted to normally distributed responses. The discussed adaptive designing is a useful tool provided that a priori information about parameters involved in the trial are not available or subject to uncertainty. The presented learning algorithm enables the complete self‐designing of a study.     

A multiple regression method for analysing stage-frequency data

A linear regression method that allows survival rates to vary from stage to stage is described for the analysis of stage-frequency data. It has advantages over previously suggested methods since the calculations are not iterative, and it is not necessary to have independent estimates of stage durations, numbers entering stages, or the rate of entry to stage 1. Simulation is proposed to determine standard errors for estimates of population parameters, and to assess the goodness of fit of models.     

A simple method to estimate insect mortality from field census data: A modification of the Kiritani-Nakasuji-Manly method

Various methods have been proposed to estimate demographic parameters such as mortality from field census data. Simple methods proposed earlier are applicable only for limited situations. For example, the Kiritani-Nakasuji-Manly method is applicable only if individuals are observable until their death. Improved methods proposed later are not subject to such limitations, but are not so widely used in the field of applied entomology, probably because of the complexity of the calculations involved. In this paper, I propose an intermediate method that requires only a pocket calculator, considering the practical convenience for field scientists. This method, which is a modification of the Kiritani-Nakasuji-Manly method, gives an estimate of the number of individuals entering a stage from the frequency of two stages when the stage duration is known.     

Area under the free-response ROC curve (FROC) and a related summary index

Summary .  Free-response assessment of diagnostic systems continues to gain acceptance in areas related to the detection, localization, and classification of one or more "abnormalities" within a subject. A free-response receiver operating characteristic (FROC) curve is a tool for characterizing the performance of a free-response system at all decision thresholds simultaneously. Although the importance of a single index summarizing the entire curve over all decision thresholds is well recognized in ROC analysis (e.g., area under the ROC curve), currently there is no widely accepted summary of a system being evaluated under the FROC paradigm. In this article, we propose a new index of the free-response performance at all decision thresholds simultaneously, and develop a nonparametric method for its analysis. Algebraically, the proposed summary index is the area under the empirical FROC curve penalized for the number of erroneous marks, rewarded for the fraction of detected abnormalities, and adjusted for the effect of the target size (or "acceptance radius"). Geometrically, the proposed index can be interpreted as a measure of average performance superiority over an artificial "guessing" free-response process and it represents an analogy to the area between the ROC curve and the "guessing" or diagonal line. We derive the ideal bootstrap estimator of the variance, which can be used for a resampling-free construction of asymptotic bootstrap confidence intervals and for sample size estimation using standard expressions. The proposed procedure is free from any parametric assumptions and does not require an assumption of independence of observations within a subject. We provide an example with a dataset sampled from a diagnostic imaging study and conduct simulations that demonstrate the appropriateness of the developed procedure for the considered sample sizes and ranges of parameters.     

Spiral Plate Method for Bacterial Determination

A method is described for determining the number of bacteria in a solution by the use of a machine which deposits a known volume of sample on a rotating agar plate in an ever decreasing amount in the form of an Archimedes spiral. After the sample is incubated, different colony densities are apparent on the surface of the plate. A modified counting grid is described which relates area of the plate of volume of sample. By counting an appropriate area of the plate, the number of bacteria in the sample is estimated. This method was compared to the pour plate procedure with the use of pure and mixed cultures in water and milk. The results did not demonstrate a significant difference in variance between duplicates at the α = 0.01 level when concentrations of 600 to 12 × 10⁵ bacteria per ml were used, but the spiral plate method gave counts that were higher than counts obtained by the pour plate method. The time and materials required for this method are substantially less than those required for the conventional aerobic pour plate procedure.     

海南岛热带山地雨林林分生物量估测方法比较分析

本文通过对海南岛热带山地雨林林分生物量估测方法的比较分析,表明材积转换法不适宜估算海南岛热带山地雨林林分生物量,其结果与皆伐法相比较一般偏高20％—40％;而用实测资料建立的生物量回归模型,对原始林林分有较好的估测结果,除树枝和树叶生物量外,树干、树皮及地上部分生物量的回归模型值,与皆伐法的结果比较,相对误差一般在±10％以内,为允许误差范围,而对热带山地雨林的更新林生物量的估测则效果较差,应建立相应的估测模型。平均木法有工作量小的优点,且误差也在16％以下,但要注意取样的树种多样性和取样强度,在实际中应当慎用。另外本文对测定热带山地雨林生物量(原始林)的所需面积大小问题作了研究,提出了生物量-面积曲线的概念,确定其最小调查面积为2500m~2以上。     

The glycolyzer: Automated glycan annotation software for high performance mass spectrometry and its application to ovarian cancer glycan biomarker discovery

Human serum glycomics is a promising method for finding cancer biomarkers but often lacks the tools for streamlined data analysis. The Glycolyzer software incorporates a suite of analytic tools capable of identifying informative glycan peaks out of raw mass spectrometry data. As a demonstration of its utility, the program was used to identify putative biomarkers for epithelial ovarian cancer from a human serum sample set. A randomized, blocked, and blinded experimental design was used on a discovery set consisting of 46 cases and 48 controls. Retrosynthetic glycan libraries were used for data analysis and several significant candidate glycan biomarkers were discovered via hypothesis testing. The significant glycans were attributed to a glycan family based on glycan composition relationships and incorporated into a linear classifier motif test. The motif test was then applied to the discovery set to evaluate the disease state discrimination performance. The test provided strongly predictive results based on receiver operator characteristic curve analysis. The area under the receiver operator characteristic curve was 0.93. Using the Glycolyzer software, we were able to identify a set of glycan biomarkers that highly discriminate between cases and controls, and are ready to be formally validated in subsequent studies.     

A Model for Adjusting for Nonignorable Verification Bias in Estimation of the ROC Curve and Its Area with Likelihood‐Based Approach

Summary In estimation of the ROC curve, when the true disease status is subject to nonignorable missingness, the observed likelihood involves the missing mechanism given by a selection model. In this article, we proposed a likelihood‐based approach to estimate the ROC curve and the area under the ROC curve when the verification bias is nonignorable. We specified a parametric disease model in order to make the nonignorable selection model identifiable. With the estimated verification and disease probabilities, we constructed four types of empirical estimates of the ROC curve and its area based on imputation and reweighting methods. In practice, a reasonably large sample size is required to estimate the nonignorable selection model in our settings. Simulation studies showed that all four estimators of ROC area performed well, and imputation estimators were generally more efficient than the other estimators proposed. We applied the proposed method to a data set from research in Alzheimer's disease.