Reliability of Confidence Interval Estimators under Various Nested Design Parental Sample Sizes

The coverage probabilities of several confidence limit estimators of genetic parameters, obtained from North Carolina I designs, were assessed by means of Monte Carlo simulations. The reliability of the estimators was compared under three different parental sample sizes. The coverage of confidence intervals set on the Normal distribution, and using standard errors either computed by the “delta” method or derived using an approximation for the variance of a variance component estimated by means of a linear combination of mean squares, was affected by the number of males and females included in the experiment. The “delta” method was found to provide reliable standard errors of the genetic parameters only when at least 48 males were each mated to six different females randomly selected from the reference population. Formulae are provided for obtaining “delta” method standard errors, and appropriate statistical software procedures are discussed. The error rates of confidence limits based on the Normal distribution and using standard errors obtained by an approximation for the variance of a variance component varied widely. The coverage of F-distribution confidence intervals for heritability estimates was not significantly affected by parental sample size and consistently provided a mean coverage near the stated coverage. For small parental sample sizes, confidence intervals for heritability estimates should be based on the F-distribution.     

Estimation of population profiles of two strains of the fly Megaselia scalaris (Diptera: Phoridae) by bootstrap simulation

Based on experimental population profiles of strains of the fly Megaselia scalaris (Phoridae), the minimal number of sample profiles was determined that should be repeated by bootstrap simulation process in order to obtain a confident estimation of the mean population profile and present estimations of the standard error as a precise measure of the simulations made. The original data are from experimental populations founded with SR and R4 strains, with three replicates, which were kept for 33 weeks by serial transfer technique in a constant temperature room (25 +/- 1.0 degrees C). The variable used was population size and the model adopted for each profile was a stationary stochastic process. By these simulations, the three experimental population profiles were enlarged so as to determine minimum sample size. After sample size was determined, bootstrap simulations were made in order to calculate confidence intervals and to compare the mean population profiles of these two strains. The results show that with a minimum sample size of 50, stabilization of means begins.     

Berkson's paradox and weighted distributions: An application to Alzheimer's disease

One reason for observing in practice a false positive or negative correlation between two random variables, which are either not correlated or correlated with a different direction, is the overrepresentation in the sample of individuals satisfying specific properties. In 1946, Berkson first illustrated the presence of a false correlation due to this last reason, which is known as Berkson's paradox and is one of the most famous paradox in probability and statistics. In this paper, the concept of weighted distributions is utilized to describe Berskon's paradox. Moreover, a proper procedure is suggested to make inference for the population given a biased sample which possesses all the characteristics of Berkson's paradox. A real data application for patients with dementia due to Alzheimer's disease demonstrates that the proposed method reveals characteristics of the population that are masked by the sampling procedure.     

Frequency distribution of coliforms in water distribution systems.

Nine small water distribution systems were sampled intensively to determine the patterns of dispersion of coliforms. The frequency distributions of confirmed coliform counts were compatible with either the negative-binomial or the lognormal distribution. They were not compatible with either the Poisson or Poisson-plus-added zeroes distribution. The implications of the use of the lognormal distributional model were further evaluated because of its previous use in water quality studies. The geometric means from 14 data sets ranged from 10(-6) to 0.2 coliforms per 100 ml, and the geometric standard deviations were between 10 and 100, with one exception. If the lognormal model is representative of the coliform distribution; the arithmetic mean sample count is a poor estimator of the true mean coliform density, and the probability of water in a distribution system containing small patches with large coliform densities without detection by routine monitoring is finite. These conclusions have direct bearing on the interpretation of microbiological quality standards for drinking water.     

Quantitative trait loci affecting life span in replicated populations of Drosophila melanogaster. I. Composite interval mapping

Composite interval mapping was used to identify life-span QTL in F2 progeny of three crosses between different pairs of inbred lines. Each inbred line was derived from a different outbred population that had undergone long-term selection for either long or short life span. Microsatellite loci were used as genetic markers, and confidence intervals for QTL location were estimated by bootstrapping. A minimum of 10 QTL were detected, nine of which were located on the two major autosomes. Five QTL were present in at least two crosses and five were present in both sexes. Observation of the same QTL in more than one cross was consistent with the hypothesis that genetic variation for life span is maintained by balancing selection. For all QTL except one, allelic effects were in the direction predicted on the basis of outbred source population. Alleles that conferred longer life were always at least partially dominant.     

Sample size determination for confidence intervals on the population mean and on the difference between two population means

Sample size determination is usually based on the premise that a hypothesis test is to be used. A confidence interval can sometimes serve better than a hypothesis test. In this paper a method is presented for sample size determination based on the premise that a confidence interval for a simple mean, or for the difference between two means, with normally distributed data is to be used. For this purpose, a concept of power relevant to confidence intervals is given. Some useful tables giving required sample size using this method are also presented.     

Sodium and potassium intake and blood pressure change in childhood.

OBJECTIVE--To assess the association between sodium and potassium intake and the rise in blood pressure in childhood. DESIGN--Longitudinal study of a cohort of children with annual measurements during an average follow up period of seven years. SETTING--Epidemiological survey of the population of a suburban town in western Netherlands. SUBJECTS--Cohort of 233 children aged 5-17 drawn at random from participants in the population survey. MAIN OUTCOME MEASURES--At least six annual timed overnight urine samples were obtained. The mean 24 hour sodium and potassium excretion during the follow up period was estimated for each participant and the sodium to potassium ratio calculated. Individual slopes of blood pressure over time were calculated by linear regression analysis. RESULTS--No significant association was observed between sodium excretion and the change in blood pressure over time. The mean systolic blood pressure slopes, however, were lower when potassium intake was higher (coefficient of linear regression -0.045 mm Hg/year/mmol; 95% confidence interval -0.069 to -0.020), and the change in systolic pressure was greater when the urinary sodium to potassium ratio was higher (0.356 mm Hg/year/unit; 95% confidence interval 0.069 to 0.642). In relation to potassium this was interpreted as a rise in blood pressure that was on average 1.0 mm Hg (95% confidence interval -1.65 to -0.35) lower in children in the upper part of the distribution of intake compared with those in the lower part. The mean yearly rise in systolic blood pressure for the group as a whole was 1.95 mm Hg. Urinary electrolyte excretion was not associated with diastolic blood pressure. CONCLUSION--Dietary potassium and the dietary sodium to potassium ratio are related to the rise in blood pressure in childhood and may be important in the early pathogenesis of primary hypertension.     

The importance of within-year repeated counts and the influence of scale on long-term monitoring of sage-grouse

Long-term population monitoring is the cornerstone of animal conservation and management. The accuracy and precision of models developed using monitoring data can be influenced by the protocols guiding data collection. The greater sage-grouse (Centrocercus urophasianus) is a species of concern that has been monitored over decades, primarily, by counting the number of males that attend lek (breeding) sites. These lek count data have been used to assess long-term population trends and for multiple mechanistic studies. However, some studies have questioned the efficacy of lek counts to accurately identify population trends. In response, monitoring protocols were changed to have a goal of counting lek sites multiple times within a season. We assessed the influence of this change in monitoring protocols on model accuracy and precision applying generalized additive models to describe trends over time. We found that at large spatial scales including >50 leks, the absence of repeated counts within a year did not significantly alter population trend estimates or interpretation. Increasing sample size decreased the model confidence intervals. We developed a population trend model for Wyoming greater sage-grouse from 1965 to 2008, identifying significant changes in the population indices and capturing the cyclic nature of this species. Most sage-grouse declines in Wyoming occurred between 1965 and the 1990s and lek count numbers generally increased from the mid-1990s to 2008. Our results validate the combination of monitoring data collected under different protocols in past and future studies—provided those studies are addressing large-scale questions. We suggest that a larger sample of individual leks is preferable to multiple counts of a smaller sample of leks. © 2011 The Wildlife Society.     

ARES: software to compare allelic richness between uneven samples

Allelic richness is one of the most basic measures of genetic diversity. Its calculation is, however, still problematic because estimates depend on sample size. This paper describes an r library that calculates mean allelic richness with confidence bounds for a range of sample sizes. It takes a file in genepop format as input, or alternatively a binary data matrix with columns representing different individuals and rows representing different alleles. The output is tabular as well as graphical. Unlike existing tools, ares does extrapolate beyond the sample size and provides confidence bounds for these predictions.     

Progressive loss of bone in the femoral neck in elderly people: longitudinal findings from the Dubbo osteoporosis epidemiology study.

OBJECTIVES--To determine prospectively the rates of change in bone mineral density in elderly people and to examine the relation between lifestyle and demographic factors and these rates of change. DESIGN--Longitudinal population based study. SETTING--Dubbo, New South Wales, Australia. SUBJECTS--Representative sample (n = 769) of residents aged > or = 60 on 1 January 1989. MAIN OUTCOME MEASURE--Rates of change in bone mineral density measured prospectively (mean scan interval 2.5 years) at the femoral neck and lumbar spine by dual energy x ray absorptiometry. RESULTS--Summary rates of loss in the femoral neck were 0.96% per year (95% confidence interval 0.64% to 1.28%) in women and 0.82% per year (0.52% to 1.12%) in men. Importantly, rates of loss at the femoral neck (both percentage and absolute) increased in both sexes with advancing age. No significant loss was evident in either sex at the lumbar spine, probably because of coexistent osteoarthritis. Lifestyle factors had only modest effects on rates of loss at either site. CONCLUSIONS--These data show that bone density of the femoral neck declines at an increasing rate in elderly people, and as this site is predictive of fracture suggest that treatment to minimise bone loss may be important even in very elderly people.     

Can transposable element copy number distribution parameters be estimated from natural populations of Drosophila melanogaster?

The copy frequency distribution of a transposable element family in a Drosophila melanogaster natural population is generally characterised by the values of the Charlesworths' model parameters α and β (Charlesworth & Charlesworth, 1983). The estimation of these parameters is made using the observed distribution of the occupied sites in a population sample. Several results have been interpreted as due either to the influence of stochastic factors or to deterministic factors (transposition, excision, selection…). The accuracy of this method was tested by estimations performed on samples from simulated populations. The results show that with the sample size usually used for natural population studies, the confidence intervals are too large to reasonably deduce either the element copy number distribution or the values of transposition and excision rate and selective coefficients.     

Placebo controlled trial of nicotine chewing gum in general practice.

Of 2110 adult cigarette smokers originally recruited to a study of the effect of antismoking advice in general practice, 429 who reported at follow up after one year that they had tried unsuccessfully to stop smoking were offered "a special antismoking chewing gum," either nicotine gum or a placebo gum, in a double blind study. Of 200 who were willing to try the gum, 101 were randomly allocated to the nicotine gum and 99 to the placebo gum. They were followed up at six months by an unannounced home visit, at which they were interviewed and asked to provide a breath sample for analysis of carbon monoxide. Twenty five claimed that they had stopped smoking, but, of them, seven exhaled levels of carbon monoxide indicative of continued smoking. Of the 18 in whom giving up smoking was validated, 10 had received active gum and eight placebo gum, a difference which was not significant (odds in favour of nicotine gum = 1.25, 95% confidence limits 0.47-3.31). The value of nicotine chewing gum, if any, can be quite small when it is used in general practice.     

The heights of French-Canadian convicts, 1780s–1820s

This paper uses a novel dataset of heights collected from the records of the Quebec City prison between 1813 and 1847 to survey the French-Canadian population of Quebec—which was then known either as Lower Canada or Canada East. Using a birth-cohort approach with 10 year birth cohorts from the 1780s to the 1820s, we find that French-Canadian prisoners grew shorter over the period. Through the whole sample period, they were short compared to Americans. However, French-Canadians were taller either than their cousins in France or the inhabitants of Latin America (except Argentinians). In addition to extending anthropometric data in Canada to the 1780s, we are able to extend comparisons between the Old and New Worlds as well as comparisons between North America and Latin America. We highlight the key structural economic changes and shocks and discuss their possible impact on the anthropometric data.     

Mitochondrial mismatch analysis is insensitive to the mutational process

Mismatch distributions are histograms showing the pattern of nucleotide (or restriction) site differences between pairs of individuals in a sample. They can be used to test hypotheses about the history of population size and subdivision (if selective neutrality is assumed) or about selection (if a constant population size is assumed). Previous work has assumed that mutations never strike the same site twice, an assumption that is called the model of infinite sites. Fortunately, the results are surprisingly robust even when this assumption is violated. We show here that (1) confidence regions inferred using the infinite- sites model differ little from those inferred using a model of finite sites with uniform site-specific mutation rates, and (2) even when site- specific mutation rates follow a gamma distribution, confidence regions are little changed until the gamma shape parameter falls well below its plausible range, to roughly 0.01. In addition, we evaluate and reject the proposition that mismatch waves are produced by pooling data from several subdivisions of a structured population.      

Microtubules grow and shorten at intrinsically variable rates.

Microtubules were assembled from pure tubulin with axonemal pieces serving as nuclei. They were observed by video-enhanced differential-interference-contrast light microscopy. Their lengths were measured from videotaped images at frequent intervals (0.13-5 s). Error analysis indicated that the uncertainty in measuring a single length was quite small; the 95% confidence limit approximated the microscope's limit of resolution. Rates of growth and shortening of the dynamically unstable microtubules, obtained from the length-versus-time data, were found to be highly variable. The variability was far too large to be attributed to known random error of measurement and must be a property of the microtubules. Further experiments were aimed at finding its structural cause. The variability of rates exhibited by a single microtubule was as great as that of the whole population. The locations at which a growing microtubule changed its rate of growth were not related to the locations at which rates changed during its subsequent shortening. The cause of the variability must therefore be both small relative to the size of a microtubule and transient relative to its lifetime. Fluctuations in configuration of the microtubule's cap appear to be the likeliest source.     

Efficacy estimates from parasite count data that include zero counts

Because of the positive skewness of parasite distributions and the greater constancy of percentage of response of therapy in animal populations, parasite count data are conventionally transformed logarithmically before combining results from different animals, either all controls or all treated. Observations of zero counts raise difficulties, since the logarithm of zero is not useful. In this study, several types of zero count adjustments are compared. Two systems for assigning values to zero counts were considered: a fixed system, which assigns the same value to all zero counts regardless of the proportion of such counts in a treatment group, and a variable system, which replaces zero counts with a value based on the proportion of zero counts in the group. The values assigned by either system are then adjusted to reflect aliquot size. An evaluation was performed by using 32 compound Poisson lognormal distributions, three sample sizes, and three representatives of each zero count adjustment system. The Poisson lognormal distribution provides a convenient method with which to provide variability greater than Poisson. Expected values of the sample estimate of the (known) population mean were calculated for each of the 576 combinations of these factors, and the bias associated with each combination was derived. The bias associated with the three representatives of the variable adjustment system was similar. The variable adjustment system had a lower overall bias than any representatives of the fixed adjustment system.     

Genetic diversity and population structure of Aeromonas hydrophila, Aer. bestiarum, Aer. salmonicida and Aer. popoffii by multilocus enzyme electrophoresis (MLEE)

Genetic diversity, genetic relationship, identification and population structure of 120 Aeromonas strains (including Aer. hydrophila, Aer. bestiarum, Aer. salmonicida and Aer. popoffii) isolated from various sources were studied by analysis of 15 genetic loci by multilocus enzyme electrophoresis (MLEE). All 15 loci were polymorphic, with an average of 9.4 alleles per locus and a mean genetic diversity (H) of 0.64. Cluster analysis defined at H < or = 0.7 differentiated most of the taxa analysed except the Aer. popoffii and Aer. bestiarum strains, which showed a close genetic relationship. Allelic frequencies of five loci (EST1, HEX, IDH, LDH1 and MDH) identified 94% of the strains. The index of association (IA) for the total sample was 2.38 and IA values calculated for the different populations were always significantly different from zero. These results suggest that the population structure of this Aeromonas sample is strongly clonal, confirm the taxonomic status of the analysed species in population genetics terms, and show the usefulness of MLEE for identifying Aeromonas species.     

Combined analyses of data from quantitative trait loci mapping studies. Chromosome 4 effects on porcine growth and fatness

For many species several similar QTL mapping populations have been produced and analyzed independently. Joint analysis of such data could be used to increase power to detect QTL and evaluate population differences. In this study, data were collated on almost 3000 pigs from seven different F(2) crosses between Western commercial breeds and either the European wild boar or the Chinese Meishan breed. Genotypes were available for 31 markers on chromosome 4 (on average 8.3 markers per population). Data from three traits common to all populations (birth weight, mean backfat depth at slaughter or end of test, and growth rate from birth to slaughter or end of test) were analyzed for individual populations and jointly. A QTL influencing birth weight was detected in one individual population and in the combined data, with no significant interaction of the QTL effect with population. A QTL affecting backfat that had a significantly greater effect in wild boar than in Meishan crosses was detected. Some evidence for a QTL affecting growth rate was detected in all populations, with no significant differences between populations. This study is the largest F(2) QTL analysis achieved in a livestock species and demonstrates the potential of joint analysis.