Estimation of Finite and Closed Population Size: An Inverse Sampling Approach with Unequal Recapture Probability

Based on capture-mark-recapture sampling methods the problem of estimating unknown population size was considered. The sampling started with the assumption that at the beginning of the experiment all the individuals were unmarked, and the unmarked individuals caught in each sample will be marked and returned to the original population before the next sample is drawn. It is also assumed that the population is closed by birth, death, emigration and immigration. Using a general inverse sampling approach, the unknown population size N is estimated by a maximum likelihood estimator (MLE), and a simple form for approximate MLE is obtained. The probability function for S (the minimum number of samples required to be drawn to have L (L ≥ 1) samples, each of which contains at least one marked individual) and the form for E[S] are also obtained. In addition, corrections and improvements of some previous works in this field are given.     

On the Estimation of Relative Risks and Longevities of a Class of Cancer Patients Based on Randomly Censored Data

An attempt has been made to measure the relative risks and longevities of a group of cancer patients using a Weibull model whose parameters are function of covariatcs (viz treatment and condition of the patient). The methodology is Cox's Partial Likelihood and the Maximum Likelihood techniques for randomly censored data. The data consists of the records of 134 patients under a clinical trial in the treatment of Carcinoma of the Oro Pharynx as quoted by Kalbfleisch and Prentice (1980).     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

A novel method for estimating the number of species within a region

Ecologists are often required to estimate the number of species in a region or designated area. A number of diversity indices are available for this purpose and are based on sampling the area using quadrats or other means, and estimating the total number of species from these samples. In this paper, a novel theory and method for estimating the number of species is developed. The theory involves the use of the Laplace method for approximating asymptotic integrals. The method is shown to be successful by testing random simulated datasets. In addition, several real survey datasets are tested, including forests that contain a large number (tens to hundreds) of tree species, and an aquatic system with a large number of fish species. The method is shown to give accurate results, and in almost all cases found to be superior to existing tools for estimating diversity.     

Analyzing Multiple‐Probe Microarray: Estimation and Application of Gene Expression Indexes

Summary Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re‐examined this problem using a new profile likelihood‐based transformation estimation approach that is more statistically elegant and computationally efficient. We demonstrate the applicability of the proposed method using a benchmark Affymetrix U95A spiked‐in experiment. Moreover, We introduced a new multivariate expression index and used the empirical study to shows its promise in terms of improving model fitting and power of detecting differential expression over the commonly used univariate expression index. As the other important content of the work, we discussed two generally encountered practical issues in application of gene expression index: normalization and summary statistic used for detecting differential expression. Our empirical study shows somewhat different findings from the MAQC project ( MAQC, 2006 ).     

On a Problem of Allocation of Sample Size in Stratified Random Sampling

In this paper we shall consider the problem of judging how good an actual compromise allocation is compared to Neyman's optimum allocation for the case of stratified random sampling by obtaining a bound to the ratio of the corresponding variances. A solution to a more general version of the problem considered by COCHRAN (1977) and RAO (1983) has been obtained and the results have been empirically demonstrated.     

Estimation of the position and effect of a lethal factor locus on a molecular marker linkage map

In the mapping of DNA markers the distortion of segregation of marker genotypes is often observed, which may be caused by a lethal factor acting in filial generations derived from distant crosses. A method is presented for estimating the recombination values between a lethal factor locus and neighboring molecular markers, and the relative viability or fertilization ability of gametes or zygotes affected by the lethal factor in an F₂ population using the maximum likelihood method and the expectation conditional maximization (ECM) algorithm. Three selection models of gamete or zygote were considered, and the most likely one was determined by goodness of fit of the observed frequency of the phenotypes to the expected ones under the models. The method was applied to segregation data of molecular markers of an F₂ population consisting of 144 individuals derived from a cross between an Indica and a Japonica rice variety. The presence of a lethal factor locus (L) located on chromosome III that caused partial gametic selection in both the male and female sides was suggested. The locus L was tightly linked to RFLP marker number 23 of the RFLP linkage map of Saito et al. (1991a), and the fertilization chance of a male or female gamete possessing the lethal factor was, on average, 41.5% of that of the normal gamete.     

Point and Interval Estimation of the Population Size Using a Zero‐Truncated Negative Binomial Regression Model

This paper presents the zero‐truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero‐truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz–Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero‐truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simultaneous estimation of mortality and dispersal rates of an artificially released population

Mark-recapture methods cannot estimate both mortality and dispersal rates of a wild population simultaneously. However, when an artificially cultured population is released into an area, the initial population size and the initial population distribution are usually known. If artificially cultured individuals are released with marks or distinguished from wild individuals or if no wild individual exists in the study area, we can estimate both the mortality and dispersal rates of the artificial population. The numbers of dispersed and dead individuals are estimated from the dispersal rate from the diffusion model and the total decreasing rate estimated from a mark-recapture data. We can estimate both the time-dependent and time-independent dispersal rates from the data. We choose the best fit model that has the smallest value of Akaike's Information Criteria. We also consider ‘concentric circles approximation” of spatial distribution, in which the cumulative and frequency distributions are analytically obtained.     

A model for the secondary structure of beta-lactamases

The effects of the quaternary agent meproadifen on ACh-activated channel currents were studied on myoballs cultured from hind limb muscles of neonatal rats. Meproadifen (0.02-0.1 microM) combined with ACh (0.1-0.3 microM) in the patch pipette caused an increase, followed by a decrease, in the frequency of channel openings. At concentrations greater than 0.2 microM the initial phase was not detected and a rapid and marked reduction in the opening frequency was observed. Meproadifen (up to 2.5 microM) produced no change in the duration or conductance of the open state of ACh-activated channels. In addition, this agent induced the appearance of events with a marked increase in the 'noise' during the opening phase. The lack of effect under inside-out patch conditions suggested that meproadifen binds to a site located at the external portion of the nicotinic macromolecule and has no access to it through the cell membrane. This study indicated that non-competitive antagonists such as meproadifen can facilitate receptor activation and desensitization.     

Population structure of the boll weevil in cotton fields and subtropical forests of South America: a bayesian approach

The main goal of this contribution is to investigate the genetic structure of boll weevil populations from South America (Argentina and Brazil) and to make further comparisons with a putative source population from USA. Samples were collected in a Paranaense forest under reserve protection, cotton fields and non-cultivated areas. Data from anonymous molecular markers were analysed using both traditional methods of population genetics and Bayesian approaches. Results help to support a previous hypothesis on the presence of two lineages of boll weevil populations in South America: one with characteristics of recent invaders and the other with characteristics of ancient populations. The sample from Urugua-í Provincial Park (Misiones, Argentina) shows the highest percentage of polymorphic loci, the highest values of mean heterozigosity, and the largest number of population-specific alleles, all being typical features of ancient populations. Furthermore, the Urugua-í sample shows two gene pools occurring in sympatry, probably as a consequence of a secondary contact. The remaining samples reveal not only lower percentages of polymorphic loci and heterozygosity values, but also an almost negligible presence of specific alleles. Bayesian methods also suggest the occasional migration of some individuals of ancient lineages from their natural habitats in fragments of the Paranaense forest into cotton fields, and vice versa.     

On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty

Summary .   We consider the estimation of the size of a closed population, often of interest for wild animal populations, using a capture–recapture study. The estimate of the total population size can be very sensitive to the choice of model used to fit to the data. We consider a Bayesian approach, in which we consider all eight plausible models initially described by Otis et al. (1978, Wildlife Monographs 62, 1–135) within a single framework, including models containing an individual heterogeneity component. We show how we are able to obtain a model-averaged estimate of the total population, incorporating both parameter and model uncertainty. To illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known, before considering a real example relating to a population of dolphins off northeast Scotland.     

Estimation of individual genetic effects from binary observations on relatives applied to a family history of respiratory illnesses and chronic lung disease of newborns

This paper considers methods for estimating the relationship between a binary response Y and the genetic effects responsible for a second binary trait Z. The responses Y are observed only for target individuals, and the responses Z are observed only for the relatives of these targets. The analysis consists of two parts. The first part concerns the analysis of the family data Z and the second part estimates the relation between the genetic effects and Y. For the family data, a generalized linear mixed model with a logit link and Gaussian genetic (random) effects is used. Estimates of the variances of the genetic effects are obtained by using a pseudo-profile log-likelihood method. Estimation of the log likelihood involves averaging over n-dimensional normal distributions, which is done by importance sampling. The methods used in the second part are straightforward. The methods are applied to a data set containing chronic lung disease (CLDN) responses of newborns and asthma (AS), allergy (AL), chronic bronchitis (CB) and eczema (EC) responses observed for the relatives of these newborns. The clinical question is whether genetic effects of AS, AL, CB, and EC have an effect on the risk for CLDN. It can be concluded that for AS, AL, CB, and EC, the influence of genetic effects is significant. However, these genetic predispositions have no significant effect on CLDN.     

Population viscosity can promote the evolution of altruistic sterile helpers and eusociality

Because it increases relatedness between interacting individuals, population viscosity has been proposed to favour the evolution of altruistic helping. However, because it increases local competition between relatives, population viscosity may also act as a brake for the evolution of helping behaviours. In simple models, the kin selected fecundity benefits of helping are exactly cancelled out by the cost of increased competition between relatives when helping occurs after dispersal. This result has lead to the widespread view, especially among people working with social organisms, that special conditions are required for the evolution of altruism. Here, we re-examine this result by constructing a simple population genetic model where we analyse whether the evolution of a sterile worker caste (i.e. an extreme case of altruism) can be selected for by limited dispersal. We show that a sterile worker caste can be selected for even under the simplest life-cycle assumptions. This has relevant consequences for our understanding of the evolution of altruism in social organisms, as many social insects are characterized by limited dispersal and significant genetic population structure.     

kakusan: a computer program to automate the selection of a nucleotide substitution model and the configuration of a mixed model on multilocus data

The application of different substitution models to each gene (a.k.a. mixed model) should be considered in model‐based phylogenetic analysis of multigene sequences. However, a single molecular evolution model is still usually applied. There are no computer programs able to conduct model selection for multiple loci at the same time, though several recently developed types of software for phylogenetic inference can handle mixed model. Here, I have developed computer software named ‘kakusan’ that enables us to solve the above problems. Major running steps are briefly described, and an analysis of results with kakusan is compared to that obtained with other program.