The relation between size of motoneurons and their position in the cat spinal cord

Experiments were performed to test whether motoneurons in the plantaris and medial gastrocnemius muscles of the cat are arranged in the spinal cord according to their sizes. It was found that motoneurons are randomly distributed with respect to size in their motor nuclei. Evidence is also presented that motoneuron density in these pools is irregular, and that there is considerable variability of position of medial gastrocnemius and plantaris motor pools from animal to animal.     

Evaluation of DNA pooling for the estimation of microsatellite allele frequencies: a case study using striped bass (Morone saxatilis)

Using striped bass (Morone saxatilis) and six multiplexed microsatellite markers, we evaluated procedures for estimating allele frequencies by pooling DNA from multiple individuals, a method suggested as cost-effective relative to individual genotyping. Using moment-based estimators, we estimated allele frequencies in experimental DNA pools and found that the three primary laboratory steps, DNA quantitation and pooling, PCR amplification, and electrophoresis, accounted for 23, 48, and 29%, respectively, of the technical variance of estimates in pools containing DNA from 2-24 individuals. Exact allele-frequency estimates could be made for pools of sizes 2-8, depending on the locus, by using an integer-valued estimator. Larger pools of size 12 and 24 tended to yield biased estimates; however, replicates of these estimates detected allele frequency differences among pools with different allelic compositions. We also derive an unbiased estimator of Hardy-Weinberg disequilibrium coefficients that uses multiple DNA pools and analyze the cost-efficiency of DNA pooling. DNA pooling yields the most potential cost savings when a large number of loci are employed using a large number of individuals, a situation becoming increasingly common as microsatellite loci are developed in increasing numbers of taxa.     

A Comparison of Nonparametric Error Rate Estimation Methods in Classification Problems

Assessment of the misclassification error rate is of high practical relevance in many biomedical applications. As it is a complex problem, theoretical results on estimator performance are few. The origin of most findings are Monte Carlo simulations, which take place in the “normal setting”: The covariables of two groups have a multivariate normal distribution; The groups differ in location, but have the same covariance matrix and the linear discriminant function LDF is used for prediction. We perform a new simulation to compare existing nonparametric estimators in a more complex situation. The underlying distribution is based on a logistic model with six binary as well as continuous covariables. To study estimator performance for varying true error rates, three prediction rules including nonparametric classification trees and parametric logistic regression and sample sizes ranging from 100‐1,000 are considered. In contrast to most published papers we turn our attention to estimator performance based on simple, even inappropriate prediction rules and relatively large training sets. For the major part, results are in agreement with usual findings. The most strikingly behavior was seen in applying (simple) classification trees for prediction: Since the apparent error rate Êrr.app is biased, linear combinations incorporating Êrr.app underestimate the true error rate even for large sample sizes. The .632+ estimator, which was designed to correct for the overoptimism of Efron's .632 estimator for nonparametric prediction rules, performs best of all such linear combinations. The bootstrap estimator Êrr.B0 and the crossvalidation estimator Êrr.cv, which do not depend on Êrr.app, seem to track the true error rate. Although the disadvantages of both estimators – pessimism of Êrr.B0 and high variability of Êrr.cv – shrink with increased sample sizes, they are still visible. We conclude that for the choice of a particular estimator the asymptotic behavior of the apparent error rate is important. For the assessment of estimator performance the variance of the true error rate is crucial, where in general the stability of prediction procedures is essential for the application of estimators based on resampling methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complete parameter bounds and quasiidentifiability conditions for a class of unidentifiable linear systems

Lack of unique structural identifiability for parameters of dynamic system models is a very common situation with practical experimental schemes, particularly when studying biological systems. However, for well-structured (e.g., multicompartmental) models, it is often possible to localize unidentifiable parameters between finite limits (“interval identifiability”), using the same data base, and under certain conditions these limits nearly coincide. Two new results in this area are presented: (1) The smallest ranges on all unidentifiable rate constants and pool sizes of the most general n-compartment mammillary system are derived, in an easy-to-program algorithmic form, for the common case of input forcing and output measurements in the central pool only. From these results we see why elimination rate constants (“leaks”) are difficult to distinguish from zero, whereas exchange rate constants between pools, and pool sizes, may be bounded very tightly in certain circumstances. (2) The notion of quasiidentifiability, or sufficient identifiability for practical purposes, is introduced to quantify these circumstances. Each of the rate constants between central and peripheral pools, and all pool sizes, are quasiidentifiable if the magnitude of the ratio of the coefficient to the eigenvalue of the slowest mode is very much greater than the largest coefficient in the sum-of-exponentials response function. Also quasiidentifiability is a necessary condition for applicability of noncompartmental analysis to estimate pool sizes and residence times of mammillary systems with “leaky” noncentral pools.     

Assessment of arbovirus vector infection rates using variable size pooling

Pool testing of vector samples for arboviruses is widely used in surveillance programmes. The proportion of infected mosquitoes (Diptera: Culicidae) is often estimated from the minimum infection rate (MIR), based on the assumption of only one infected mosquito per positive pool. This assumption becomes problematic when pool size is large and/or infection rate is high. By relaxing this constraint, maximum likelihood estimation (MLE) is more useful for a wide range of infection levels that may be encountered in the field. We demonstrate the difference between these two estimation approaches using West Nile virus (WNV) surveillance data from vectors collected by gravid traps in Chicago during 2002. MLE of infection rates of Culex mosquitoes was as high as 60 per 1000 at the peak of transmission in August, whereas MIR was less than 30 per 1000. More importantly, we demonstrate roles of various pooling strategies for better estimation of infection rates based on simulation studies with hypothetical mosquito samples of 18 pools. Variable size pooling (with a serial pool sizes of 5, 10, 20, 30, 40 and 50 individuals) performed consistently better than a constant size pooling of 50 individuals. We conclude that variable pool size coupled with MLE is critical for accurate estimates of mosquito infection rates in WNV epidemic seasons.     

A comparison of two bias-corrected covariance estimators for generalized estimating equations

Mancl and DeRouen (2001, Biometrics57, 126-134) and Kauermann and Carroll (2001, JASA96, 1387-1398) proposed alternative bias-corrected covariance estimators for generalized estimating equations parameter estimates of regression models for marginal means. The finite sample properties of these estimators are compared to those of the uncorrected sandwich estimator that underestimates variances in small samples. Although the formula of Mancl and DeRouen generally overestimates variances, it often leads to coverage of 95% confidence intervals near the nominal level even in some situations with as few as 10 clusters. An explanation for these seemingly contradictory results is that the tendency to undercoverage resulting from the substantial variability of sandwich estimators counteracts the impact of overcorrecting the bias. However, these positive results do not generally hold; for small cluster sizes (e.g., <10) their estimator often results in overcoverage, and the bias-corrected covariance estimator of Kauermann and Carroll may be preferred. The methods are illustrated using data from a nested cross-sectional cluster intervention trial on reducing underage drinking.     

Estimating Effective Population Size or Mutation Rate Using the Frequencies of Mutations of Various Classes in a Sample of DNA Sequences

Mutations resulting in segregating sites of a sample of DNA sequences can be classified by size and type and the frequencies of mutations of different sizes and types can be inferred from the sample. A framework for estimating the essential parameter θ = 4Nu utilizing the frequencies of mutations of various sizes and types is developed in this paper, where N is the effective size of a population and μ is mutation rate per sequence per generation. The framework is a combination of coalescent theory, general linear model and Monte-Carlo integration, which leads to two new estimators θ(ξ) and θ(η) as well as a general Watterson''s estimator θ(K) and a general Tajima''s estimator θ(π). The greatest strength of the framework is that it can be used under a variety of population models. The properties of the framework and the four estimators θ(K), θ(π), θ(ξ) and θ(η) are investigated under three important population models: the neutral Wright-Fisher model, the neutral model with recombination and the neutral Wright''s finite-islands model. Under all these models, it is shown that θ(ξ) is the best estimator among the four even when recombination rate or migration rate has to be estimated. Under the neutral Wright-Fisher model, it is shown that the new estimator θ(ξ) has a variance close to a lower bound of variances of all unbiased estimators of θ which suggests that θ(ξ) is a very efficient estimator.     

Empirical Bayes estimation for combinations of multivariate bioassays

This article presents a new empirical Bayes estimator (EBE) and a shrinkage estimator for determining the relative potency from several multivariate bioassays by incorporating prior information on the model parameters based on Jeffreys' rules. The EBE can account for any extra variability among the bioassays, and if this extra variability is 0, then the EBE reduces to the maximum likelihood estimator for combinations of multivariate bioassays. The shrinkage estimator turns out to be a compromise of the prior information and the estimator from each multivariate bioassay, with the weights depending on the prior variance.     

Analysis of multistage pooling studies of biological specimens for estimating disease incidence and prevalence

The testing of pooled samples of biological specimens for the purpose of estimating disease prevalence may be more cost effective than testing individual samples, particularly if the prevalence of disease is low. Multistage pooling studies involve testing pools and then sequentially subdividing and testing the positive pools. A simple estimator of disease prevalence and its variance are derived for general multistage pooling studies and are shown to be natural generalizations of Thompson's (1962) original estimators for single-stage pooling studies. The reduction in variance associated with each additional stage is calibrated. The results are extended to estimating disease incidence rates. The methods are used to estimate HIV incidence rates from a prevalence study of early HIV infection using a PCR assay for HIV RNA.     

Judgement post-stratification for designed experiments

Summary .   In many scientific studies, information that is not easily translated into covariates is ignored in the analysis. However, this type of information may significantly improve inference. In this research, we apply the idea of judgment post-stratification to utilize such information. Specifically, we consider experiments that are conducted under a completely randomized design. Sets of experimental units are formed, and the units in a set are ranked. Estimation is performed conditional on the sets and ranks. We propose a new estimator for a treatment contrast. We improve the new estimator by Rao–Blackwellization. Asymptotic distribution theory and corresponding inferential procedures for both estimators are developed. Simulation studies quantify the superiority of the new estimators and show their desirable properties for small and moderate sample sizes. The impact of the new techniques is illustrated with data from a clinical trial.     

Estimating risk difference in multicenter studies under baseline-risk heterogeneity

In this paper, we consider the case of efficient estimation of the risk difference in a multicenter study allowing for baseline heterogeneity. We consider the optimally weighted estimator for the common risk difference and show that this estimator has considerable bias when the true weights (which are inversely proportional to the variances of the center-specific risk difference estimates) are replaced by their sample estimates. In addition, we propose a new estimator for this situation of the Mantel-Haenszel type that is unbiased and, in addition, has a smaller variance for small sample sizes within the study centers. Simulations illustrate these findings.     

Uniformly minimum variance unbiased estimation of gene diversity

Gene diversity is an important measure of genetic variability in inbred populations. The survival of species in changing environments depends on, among other factors, the genetic variability of the population. In this communication, I have derived the uniformly minimum variance unbiased estimator of gene diversity. The proposed estimator of gene diversity does not assume that the inbreeding coefficient is known. I have also provided the approximate variance of this estimator according to Fisher's method. In addition, I have developed a numerical resampling-based method for obtaining variances and confidence intervals based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. Efficiency in estimation of the gene diversity based on these two estimators is discussed. In accordance with the simulation results, I found that the uniformly minimum variance estimator developed in this report is more accurate for estimation of gene diversity than the maximum likelihood estimator.     

An estimator for pairwise relatedness using molecular markers

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/or small sample sizes.     

Projected climate changes threaten ancient refugia of kelp forests in the North Atlantic

Intraspecific genetic variability is critical for species adaptation and evolution and yet it is generally overlooked in projections of the biological consequences of climate change. We ask whether ongoing climate changes can cause the loss of important gene pools from North Atlantic relict kelp forests that persisted over glacial–interglacial cycles. We use ecological niche modelling to predict genetic diversity hotspots for eight species of large brown algae with different thermal tolerances (Arctic to warm temperate), estimated as regions of persistence throughout the Last Glacial Maximum (20,000 YBP), the warmer Mid‐Holocene (6,000 YBP), and the present. Changes in the genetic diversity within ancient refugia were projected for the future (year 2100) under two contrasting climate change scenarios (RCP2.6 and RCP8.5). Models predicted distributions that matched empirical distributions in cross‐validation, and identified distinct refugia at the low latitude ranges, which largely coincide among species with similar ecological niches. Transferred models into the future projected polewards expansions and substantial range losses in lower latitudes, where richer gene pools are expected (in Nova Scotia and Iberia for cold affinity species and Gibraltar, Alboran, and Morocco for warm‐temperate species). These effects were projected for both scenarios but were intensified under the extreme RCP8.5 scenario, with the complete borealization (circum‐Arctic colonization) of kelp forests, the redistribution of the biogeographical transitional zones of the North Atlantic, and the erosion of global gene pools across all species. As the geographic distribution of genetic variability is unknown for most marine species, our results represent a baseline for identification of locations potentially rich in unique phylogeographic lineages that are also climatic relics in threat of disappearing.     

Arthropods as Bioindicators in Agroecosystems of Jiang Han Plain,Qianjiang City,Hubei China

Using sweeping nets and pitfall traps, arthropods on the soil surface and on vegetation were periodically surveyed in two villages on the Jiang Han Plain from April to September 1994. Statistical analysis of the resulting data delineated groups of bioindicators on vegetation and on the grounds that represent components of formulas for evaluating environmental quality in agroecosystems. These groups are (1) Coccinellidae and Chrysopidae (seasonally migrating predators factor); (2) Braconidae and Chalcidoidea (parasitic insects factor); (3) Araneae and Mantodea on vegetation and Araneae, Carabidae, Opiliones and Nitidulidae on the ground (carnivorous arthropods factor); and (4) Formicidae, Isopoda, and Chilopoda (soil-dwelling arthropods factor). The following resource pools were identified for the different model arthropods: woodlots for Araneae and Mantodea; field margins for Chrysopidae and Coccinellidae; hedgerows for Braconidae and Chalcidoidea; and low-input cropfields on the floodplains for epigeic carnivorous arthropods. Comparison of these insect groups in different rural landscape units demonstrated the importance of a mosaic rural landscape, including woodlots, rationally designed field margins, and cropland, for creating an ecologically favorable agricultural environment.     

Incorporating Estimates of Group Size in Sightability Models for Wildlife

ABSTRACT Sightability models have been used to estimate population size of many wildlife species; however, a limitation of these models is an assumption that groups of animals observed and counted during aerial surveys are enumerated completely. Replacing these unknown counts with maximum observed counts, as is typically done, produces population size estimates that are negatively biased. This bias can be substantial depending on the degree of undercounting occurring. We first investigated a method-of-moments estimator of group sizes. We then defined a population size estimator using the method-of-moments estimator of group sizes in place of maximum counts in the traditional sightability models, thereby correcting for bias associated with undercounting group size. We also provide associated equations for calculating the variance of our estimator. This estimator is an improvement over existing sightability model techniques because it significantly reduces bias, and variance estimates provide near nominal confidence interval coverage. The data needed for this estimator can be easily collected and implemented by wildlife managers with a field crew of only 3 individuals and little additional flight or personnel time beyond the normal requirements for developing sightability models.     

Group Sequential Monitoring with Arbitrary Inspection Times

The classical group sequential test procedures that were proposed by Pocock (1977) and O'Brien and Fleming (1979) rest on the assumption of equal sample sizes between the interim analyses. Regarding this it is well known that for most situations there is not a great amount of additional Type I error if monitoring is performed for unequal sample sizes between the stages. In some cases, however, problems can arise resulting in an unacceptable liberal behavior of the test procedure. In this article worst case scenarios in sample size imbalancements between the inspection times are considered. Exact critical values for the Pocock and the O'Brien and Fleming group sequential designs are derived for arbitrary and for varying but bounded sample sizes. The approach represents a reasonable alternative to the flexible method that is based on the Type I error rate spending function. The SAS syntax for performing the calculations is provided. Using these procedures, the inspection times or the sample sizes in the consecutive stages need to be chosen independently of the data observed so far.     

Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

Random-Effects,Fixed-Effects and the within-between Specification for Clustered Data in Observational Health Studies: A Simulation Study

Background

When unaccounted-for group-level characteristics affect an outcome variable, traditional linear regression is inefficient and can be biased. The random- and fixed-effects estimators (RE and FE, respectively) are two competing methods that address these problems. While each estimator controls for otherwise unaccounted-for effects, the two estimators require different assumptions. Health researchers tend to favor RE estimation, while researchers from some other disciplines tend to favor FE estimation. In addition to RE and FE, an alternative method called within-between (WB) was suggested by Mundlak in 1978, although is utilized infrequently.

Methods

We conduct a simulation study to compare RE, FE, and WB estimation across 16,200 scenarios. The scenarios vary in the number of groups, the size of the groups, within-group variation, goodness-of-fit of the model, and the degree to which the model is correctly specified. Estimator preference is determined by lowest mean squared error of the estimated marginal effect and root mean squared error of fitted values.

Results

Although there are scenarios when each estimator is most appropriate, the cases in which traditional RE estimation is preferred are less common. In finite samples, the WB approach outperforms both traditional estimators. The Hausman test guides the practitioner to the estimator with the smallest absolute error only 61% of the time, and in many sample sizes simply applying the WB approach produces smaller absolute errors than following the suggestion of the test.

Conclusions

Specification and estimation should be carefully considered and ultimately guided by the objective of the analysis and characteristics of the data. The WB approach has been underutilized, particularly for inference on marginal effects in small samples. Blindly applying any estimator can lead to bias, inefficiency, and flawed inference.     

Effects of mean intensity and temporal variability of disturbance on the invasion of <Emphasis Type="Italic">Caulerpa racemosa</Emphasis> var. <Emphasis Type="Italic">cylindracea</Emphasis> (Caulerpales) in rock pools

Disturbance is a key factor influencing the invasibility of habitats and assemblages. This relationship was extensively studied in terrestrial systems, but it was scarcely tested in the marine environment. We investigated experimentally the interactive effects of changes in the intensity and temporal variability of mechanical disturbance by boulders on invasion dynamics of the green alga Caulerpa racemosa var. cylindracea in littoral rock pools. We tested the hypothesis that the success of invasion of C. racemosa would be (1) greater under large than under low intensity of disturbance, (2) greater under large than under low temporal variability of disturbance and that (3) interactive effects could also occur, with variability of disturbance magnifying the effects of intensity. C. racemosa was virtually absent in pools maintained under high intensity of disturbance, independently of temporal variability. High intensity of disturbance was also associated with lower density and length of fronds and thinner diameter of the stolons of the alga. The total number of native taxa and the abundance of encrusting coralline algae increased under high intensity of disturbance. Differently, turf-forming algae were positively affected by temporal variability of disturbance, while canopy-forming algae did not respond to experimental treatments. Our results suggest a direct negative effect of the most severe experimental conditions on the spread of C. racemosa in rock pools. This likely overwhelmed likely concomitant positive and negative effects mediated by resident organisms. The results of this study help anticipating invasion dynamics of C. racemosa in rock pools under climate change scenarios, in which both intensity and temporal variability of extreme meteorological events are predicted to increase.