A first test of a new modelling approach to estimate food consumption in particle-feeding fish

Models for estimating food consumption in fish by analysing changes in stomach fullness over time are invariably based on a stomach evacuation rate obtained when the fish is fasting, on the assumption that this rate also applies to when the fish is feeding. However, this often is not the case in fish that feed on small particles. A new modelling approach was therefore tested, which is based not only on stomach fullness but also on gut contents. To eliminate errors arising from assimilation in the gut, titanium(IV) oxide (TiO₂) was used as an indigestible marker. When applied to a dataset obtained from tilapia given several equal doses of pelleted feed over a 2.5‐h period, the new approach gave a closer true consumption estimate than a conventional model. The evacuation rate proved to be a more sensitive parameter than the ingestion rate, but the former was no longer required by the new approach for estimating ingestion, thus liberating the food consumption estimate from any errors and dependencies inherent in the evacuation rate. The new approach assumes that the digesta of previous feedings can be distinguished from those of the feeding phase being analysed and therefore needs further refinement for those cases when this does not apply. Suggestions for such refinements are also given. This new approach is expected to be equally suitable for estimating consumption in stomachless fish.     

A method for determining the dielectric constant and the conductivity of membrane-bounded particles of biological relevance

Numerical assessment is made regarding Pauly and Schwan's theory which describes the dielectric behaviour of a suspension of “shell spheres” as a model of biological membrane-bounded particles. The results indicate that approximate expressions of the theory may give rise to serious errors when applied to particles smaller than about 1 Μm in diameter. With a view to performing analysis according to a general expression of the theory, some of the characteristic responses of dielectric parameters upon changes in phase parameters are examined with particular reference to some numerical ranges of biological interest. On this basis a simplified and systematic procedure is proposed for estimating the phase parameters of particles whose shell phase can be regarded as non-conductive. As the application of the procedure proposed, a set of dielectric data of a synaptosome suspension is analyzed, so that the following three phase parameters are successfully determined: membrane capacitance (or shell phase dielectric constant), internal phase conductivity and internal phase dielectric constant. Some limitations of the procedure are discussed for the cases of conducting shells and small particles.     

A method for determining the dielectric constant and the conductivity of membrane-bounded particles of biological relevance.

Numerical assessment is made regarding Pauly and Schwan's theory which describes the dielectric behavior of a suspension of "shell spheres" as a model of biological membrane-bounded particles. The results indicate that approximate expressions of the theory may give rise to serious errors when applied to particles smaller than about 1 mum in diameter. With a view to performing analysis according to a general expression of the theory, some of the characteristic responses of dielectric parameters upon changes in phase parameters are examined with particular reference to some numerical ranges of biological interest. On this basis a simplified and systematic procedure is proposed for estimating the phase parameters of particles whose shell phase can be regarded as non-conductive. As the application of the procedure proposed, a set of dielectric data of a synaptosome suspension is analyzed, so that the following three phase parameters are successfully determined: membrane capacitance (or shell phase dielectric constant), interval phase conductivity and internal phase dielectric constant. Some limitations of the procedure are discussed for the cases of conducting shells and small particles.     

Moment estimation of population diversity and genetic distance from data on recessive markers

A moment-based method for estimating a measure of population diversity, theta or Wright's FST, is given for dominant markers such as amplified fragment length polymorphisms (AFLPs) or RAPDs in noninbred populations. Basic assumptions are that there is random mating, Hardy-Weinberg equilibrium, linkage equilibrium, no mutation from common ancestor and equally distant populations. It is based on the variances between and within populations of genotype frequencies, whereas previously moment methods for dominant markers have been indirect in that they have been based on first estimating allele frequencies and then using the variances of those frequencies. The use of genotype frequencies directly appears to be more robust. Approximate sampling errors of the estimates are given. Methods are extended to estimate genetic distances and their sampling errors. The AFLP data from samples of breeds of pig are used for illustration.     

Integrated stereological and biochemical studies on hepatocytic membranes. II. Correction of section thickness effect on volume and surface density estimates

The basic stereological formulas for estimating volume (Vv) and surface (Sv) densities are strictly valid only for true infinitely thin sections; the use of "ultrathin" sections of finite thickness T introduces systematic errors, mostly in the sense of overestimation of the parameters. These errors depend on the size and shape of the structural elements and on T. Correction factors for this effect of T are derived by considering model structures that simulate the shape and arrangement of subcellular organelles: (a) spherical vesicles, (b) disks as models for rough endoplasmic reticulum (RER) cisternae, (c) cylindrical tublules as models for smooth endoplasmic reticulum (SER) tubules, microvilli, etc. For vesicles, a model of discrete convex spherical particles is assumed; the correction factors consider loss of caps due to grazing sections and size distribution of the vesicles. The disk and tubule models are used in connection with the new integral geometric formulas of R.E. Miles which consider random aggregates of "inter-penetrating" particles so that the resultant structure is non- convex and thus approximates in nature the networks characteristic of endoplasmic reticulum (ER). Some practical examples relative to liver cells show that the errors due to section thickness may be of the order of 20-40% or more. Computation formulas as well as graphs are given for the determination of the correction factors for Vv and Sv.     

An ab initio algorithm for low-resolution 3-D reconstructions from cryoelectron microscopy images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

Measurement error and estimates of population extinction risk

It is common to estimate the extinction probability for a vulnerable population using methods that are based on the mean and variance of the long‐term population growth rate. The numerical values of these two parameters are estimated from time series of population censuses. However, the proportion of a population that is registered at each census is typically not constant but will vary among years because of stochastic factors such as weather conditions at the time of sampling. Here, we analyse how such sampling errors influence estimates of extinction risk and find sampling errors to produce two opposite effects. Measurement errors lead to an exaggerated overall variance, but also introduce negative autocorrelations in the time series (which means that estimates of annual growth rates tend to alternate in size). If time series data are treated properly these two effects exactly counter balance. We advocate routinely incorporating a measure of among year correlations in estimating population extinction risk.     

Automatic particle selection from electron micrographs using machine learning techniques

The 3D reconstruction of biological specimens using Electron Microscopy is currently capable of achieving subnanometer resolution. Unfortunately, this goal requires gathering tens of thousands of projection images that are frequently selected manually from micrographs. In this paper we introduce a new automatic particle selection that learns from the user which particles are of interest. The training phase is semi-supervised so that the user can correct the algorithm during picking and specifically identify incorrectly picked particles. By treating such errors specially, the algorithm attempts to minimize the number of false positives. We show that our algorithm is able to produce datasets with fewer wrongly selected particles than previously reported methods. Another advantage is that we avoid the need for an initial reference volume from which to generate picking projections by instead learning which particles to pick from the user. This package has been made publicly available in the open-source package Xmipp.     

The calculation of errors and the choice of sampling times in the determination of irreversible disposal rates in vivo by isotope experiments

In well-known methods of estimating rates of irreversible disposal (utilization) in vivo the rates are calculated from the areas to infinity under specific radioactivity-time (S-t) or quantity-of-label-time (q-t) curves obtained by measurements on samples of plasma after intravenous injection of labelled substrate. The errors in the calculated rates are mostly those of the estimates of the areas. These errors are of two kinds: random, caused by the variances of the values of S or q, and systematic, caused by differences between the curves used to interpolate between these values and the true curves. A rigorous method is given for calculating the random errors from the variances of the values of S or q, and is applied to choosing the best times to sample the plasma from small animals from which few plasma samples can be taken. A procedure for estimating systematic errors is also given. Programs in BASIC language to carry out the calculations are deposited as Supplementary Publication SUP 50058 (5 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms given in Biochem. J. (1975) 145, 5.     

Effects of genotyping errors on parentage exclusion analysis

Genetic markers are widely used to determine the parentage of individuals in studies of mating systems, reproductive success, dispersals, quantitative genetic parameters and in the management of conservation populations. These markers are, however, imperfect for parentage analyses because of the presence of genotyping errors and undetectable alleles, which may cause incompatible genotypes (mismatches) between parents and offspring and thus result in false exclusions of true parentage. Highly polymorphic markers widely used in parentage analyses, such as microsatellites, are especially prone to genotyping errors. In this investigation, I derived the probabilities of excluding a random (related) individual from parentage and the probabilities of Mendelian-inconsistent errors (mismatches) and Mendelian-consistent errors (which do not cause mismatches) in parent-offspring dyads, when a marker having null alleles, allelic dropouts and false alleles is used in a parentage analysis. These probabilities are useful in evaluating the impact of various types of genotyping errors on the information content of a set of markers in and thus the power of a parentage analysis, in determining the threshold number of genetic mismatches that is appropriate for a parentage exclusion analysis and in estimating the rates of genotyping errors and frequencies of null alleles from observed mismatches between known parent-offspring dyads. These applications are demonstrated by numerical examples using both hypothetical and empirical data sets and discussed in the context of practical parentage exclusion analyses.     

Fermentation data analysis and state estimation in the presence of incomplete mass balance

A method is developed for identifying measurement errors and estimating fermentation states in the presence of unidentified reactant or product. Unlike conventional approaches using elemental balances, this method employs an empirically determined basis, which can tolerate unidentified reaction species. The essence of this approach is derived from the concept of reaction subspace and the technique of singular value decomposition. It is shown that the subspace determined via singular value decomposition of multiple experimental data provides an empirical basis for identifying measurement errors. The same approach is applied to fermentation state estimation. Via the formulation of the reaction subspace, the sensitivity of state estimates to measurement errors is quantified in terms of a dimensionless quantity, maximum error gain (MEG). It is shown that using the empirically determined subspace, one can circumvent the problem of unidentified reaction species, meanwhile reducing the sensitivity of the estimates.     

Joint Estimation of Diagnostic Accuracy Measures for Paired Organs – Application in Ophthalmology

Diagnostic studies in ophthalmology frequently involve binocular data where pairs of eyes are evaluated, through some diagnostic procedure, for the presence of certain diseases or pathologies. The simplest approach of estimating measures of diagnostic accuracy, such as sensitivity and specificity, treats eyes as independent, consequently yielding incorrect estimates, especially of the standard errors. Approaches that account for the inter‐eye correlation include regression methods using generalized estimating equations and likelihood techniques based on various correlated binomial models. The paper proposes a simple alternative statistical methodology of jointly estimating measures of diagnostic accuracy for binocular tests based on a flexible model for correlated binary data. Moments' estimation of model parameters is outlined and asymptotic inference is discussed. The resulting estimates are straightforward and easy to obtain, requiring no special statistical software but only elementary calculations. Results of simulations indicate that large‐sample and bootstrap confidence intervals based on the estimates have relatively good coverage properties when the model is correctly specified. The computation of the estimates and their standard errors are illustrated with data from a study on diabetic retinopathy.     

Measuring the precision of genetic parameters by a simulation technique

Summary Approximate standard errors of genetic parameter estimates were obtained using a simulation technique and approximation formulae for a simple statistical model. The similarity of the corresponding estimates of standard errors from the two methods indicated that the simulation technique may be useful for estimating the precision of genetic parameter estimates for complex models or unbalanced population structures where approxi mation formulae do not apply. The method of generating simulation populations in the computer is outlined, and a technique of setting approximate confidence limits to heritability estimates is described.     

An ab Initio Algorithm for Low-Resolution 3-D Reconstructions from Cryoelectron Microscopy Images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

Maximum-likelihood estimation of allelic dropout and false allele error rates from microsatellite genotypes in the absence of reference data

The importance of quantifying and accounting for stochastic genotyping errors when analyzing microsatellite data is increasingly being recognized. This awareness is motivating the development of data analysis methods that not only take errors into consideration but also recognize the difference between two distinct classes of error, allelic dropout and false alleles. Currently methods to estimate rates of allelic dropout and false alleles depend upon the availability of error-free reference genotypes or reliable pedigree data, which are often not available. We have developed a maximum-likelihood-based method for estimating these error rates from a single replication of a sample of genotypes. Simulations show it to be both accurate and robust to modest violations of its underlying assumptions. We have applied the method to estimating error rates in two microsatellite data sets. It is implemented in a computer program, Pedant, which estimates allelic dropout and false allele error rates with 95% confidence regions from microsatellite genotype data and performs power analysis. Pedant is freely available at http://www.stats.gla.ac.uk/ approximately paulj/pedant.html.     

Varying coefficient model with unknown within-subject covariance for analysis of tumor growth curves

SUMMARY: In this article we develop a nonparametric estimation procedure for the varying coefficient model when the within-subject covariance is unknown. Extending the idea of iterative reweighted least squares to the functional setting, we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients. Smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood. The covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a Kullback-Leibler criterion. Empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors.     

Estimation of the size of bilayer liposome by optical density and refractive index

A simple method for estimating a mean particles size in a suspension is suggested on the basis of an empirical correlation of a liposome size found by the optical shift method and on optic properties of the suspension. For liposome size characteristics only two parameters: optical density and refraction index increment are measured.     

Estimating surface area of sponges and gorgonians as indicators of habitat availability on Caribbean coral reefs

A rapid method to estimate the three-dimensional (3D) surface area (SA) of marine gorgonians and sponges from field measurements of colony height, diameter, and morphology was developed as an indicator of habitat availability for fish and invertebrates. Colony characteristics for sponges and gorgonians were compiled from field measurements, expert judgment, and taxonomic literature, and employed to generate 3D images using computer-aided design software. The images were used to test various statistical models and geometric surrogates that best estimated SA using only height and diameter measurements. A morphological classification system was devised using shapes and relative proportions of sponges and gorgonians which are commonly found in shallow waters (<25 m depth) of the Central Western Atlantic Ocean. Regression models (linear, quadratic, or cubic) were found to be more robust than geometric surrogates, exhibiting greater accuracy at range extremes. Statistical models explained over 90% of the variation in SA and forecast errors of less than 20%. The best models for estimating SA are presented for eight sponge and nine gorgonian morphologies. Application of these methods with existing estimators for stony corals SA can be used as an indicator of structural habitat availability, which is an important ecosystem service of coral reefs.     

Capture-recapture, epidemiology, and list mismatches: two lists

In recent years, capture-recapture methods for closed populations have been extensively applied to epidemiology. For example, suppose we have several incomplete lists of diabetics and we wish to estimate the total number of diabetics by estimating the number missing from all the lists. A major problem is that the information about individuals on the lists may have been given incorrectly or the information may have been typed incorrectly so that some list matches are missed. Using the concept of tag loss borrowed from animal population studies, we consider methods for estimating both the probabilities of making list errors and the population size for just two independent lists. The effect of heterogeneity on the errors is examined. The methods are applied to a large data set of diabetic persons consisting of a list obtained from a survey and a list obtained from doctors' records. It was found that the error rates were high and that ignoring the errors led to a gross overestimate of the total number of diabetic persons.     

Estimating haplotype frequencies and standard errors for multiple single nucleotide polymorphisms

Estimating haplotype frequencies becomes increasingly important in the mapping of complex disease genes, as millions of single nucleotide polymorphisms (SNPs) are being identified and genotyped. When genotypes at multiple SNP loci are gathered from unrelated individuals, haplotype frequencies can be accurately estimated using expectation-maximization (EM) algorithms (Excoffier and Slatkin, 1995; Hawley and Kidd, 1995; Long et al., 1995), with standard errors estimated using bootstraps. However, because the number of possible haplotypes increases exponentially with the number of SNPs, handling data with a large number of SNPs poses a computational challenge for the EM methods and for other haplotype inference methods. To solve this problem, Niu and colleagues, in their Bayesian haplotype inference paper (Niu et al., 2002), introduced a computational algorithm called progressive ligation (PL). But their Bayesian method has a limitation on the number of subjects (no more than 100 subjects in the current implementation of the method). In this paper, we propose a new method in which we use the same likelihood formulation as in Excoffier and Slatkin's EM algorithm and apply the estimating equation idea and the PL computational algorithm with some modifications. Our proposed method can handle data sets with large number of SNPs as well as large numbers of subjects. Simultaneously, our method estimates standard errors efficiently, using the sandwich-estimate from the estimating equation, rather than the bootstrap method. Additionally, our method admits missing data and produces valid estimates of parameters and their standard errors under the assumption that the missing genotypes are missing at random in the sense defined by Rubin (1976).