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Heritable variation and mechanisms of inheritance of spore shape within a population of Scutellospora pellucida, an arbuscular mycorrhizal fungus.

Substantial variation was found among single-spore cultures established from a single population of the arbuscular mycorrhizal fungus Scutellospora pellucida. A common environment experiment demonstrated that five single-spore cultures differed in their average spore shape (as measured by length:width ratios) and size (volume) with interisolate heritabilities of offspring mean values of 0.96 and 0.87, respectively (0.66 and 0.43 for the shape and size of individual spores). The distribution of offspring spore shapes also differed in levels of variance, skewness, and kurtosis. In fact, these aspects of the distributions shifted with mean spore shape as predicted by the binomial distribution-the distribution expected due to the segregation of genetically diverse nuclei through dividing hyphae. Thus, the original parental spores generating these cultures appear to have contained genetically variable nuclei, which then segregate into the offspring spores to generate consistent differences in the mean, variance, skewness, and kurtosis of the distribution of offspring spore shapes. This nuclear segregation may be followed by the assemblage of novel combinations of nuclei through hyphal fusion. Together these processes are rarely considered mechanisms for the creation of novel genetic combinations and may contribute to the maintenance of the high level of heritable variation observed in this study.

Journal Article↗

Is modelling dental caries a 'normal' thing to do?

OBJECTIVE: To introduce and encourage the use of generalised linear models (GLMs) in analysing caries data that do not require the response to be treated necessarily as a sample from a normal distribution. BASIC RESEARCH DESIGN: At the present time, it is most likely that the sampling distribution of dmf/DMF in industrialised countries will not approximate normality. Generalised linear modelling can be conducted assuming many underlying distributions which, in fact, includes the normal distribution. In this paper three GLMs are employed (normal, Poisson, negative binomial) for modelling an example caries data set. In addition, a binomial model is used to model the dichotomous outcome of caries-free/caries-present. CLINICAL SETTING: The data comprised 871 Old Trafford, Manchester primary school children aged between 4 years 0 months and 5 years 11 months. RESULTS: The effect of one study covariate was prominent in a normal model applied to all available dmf data but not in two non-normal models which used dmf > 0 data only. Furthermore, the same covariate was significant at the 5% level in a binomial model indicating that it influenced whether or not caries was present and not the level of dmf. CONCLUSION: A suitable modelling approach for caries data is to employ a Poisson or a negative binomial model for the dmf/DMF response and a binomial model for the caries-free/caries-present outcome. This allows separate estimation of those factors which influence the magnitude of caries and those factors which influence whether caries is actually present or not.

Binomial Distribution↗

Distribution of chewing lice upon the polygynous peacock Pavo cristatus.

An opportunistic survey of louse distribution upon the peacock Pavo cristatus was undertaken following a cull of 23 birds from an English zoo. After complete skin and feather dissolution, 2 species of lice were retrieved, Goniodes pavonis and Amyrsidea minuta. The distribution of both louse species could be described by a negative binomial model. The significance of this is discussed in relation to transmission dynamics of lice in the atypical avian mating system found in the peacock, which involves no male parental care.

Animals↗

Use of the generalised linear model with Poisson distribution to compare caries indices.

In dental epidemiological studies, an analysis of variance assuming a normal distribution is commonly used to compare caries indices, which are often not normally distributed. As these indices represent discontinuous data, it would be preferable to use the negative binomial or the Poisson distribution. In this study, in order to compare the DMFS indices of adults working in the confectionery manufacturing industry in France, the results of the generalised linear model obtained using the normal and the Poisson distribution with identity or log built-in link function were compared. The negative binomial distribution was not used because it is very often unavailable in the most used statistical software. Analysis of the caries indices showed that the use of the normal distribution could lead to an incorrect interpretation of the data. Therefore it is concluded that the generalised linear model with Poisson distribution and over dispersion is to be preferred when comparing caries levels.

Adult↗

Survival equations for red blood cells with statistical distributions in life spans.

The survival equations for labelled RBCs taking into account a hypothetical Gaussian (or binomial) statistical distribution for the life spans, with and without random destruction, have been derived in this paper. The numerical integration of these equations emphasises some particularities which will result from the existence of broad life span distributions. The differences between the results obtained with hypothetical populations of RBCs having statistical distributions for the life spans and hypothetical populations of RBCs with life spans equal to the distributions mean value for every cell are also discussed.

Erythrocyte Aging↗

Frequency distribution of Echinococcus granulosus in dog populations in the Xinjiang Uygur Autonomous Region, China.

Age-prevalence and age-intensity data of Echinococcus granulosus in dog populations were collected in four counties in the Xinjiang Uygur Autonomous Region, People's Republic of China. The frequency distribution of the parasite per dog was adequately described by the negative binomial model, with parameter k being 0.0571. The mathematical model of the life cycle of E. granulosus constructed by Roberts et al. (1986--Parasitology, Vol. 92, pages 621-641) was used to estimate the epidemiologic parameters of E. granulosus in Xinjiang. This model showed that the prevailing infection pressure on dogs was 0.4560 infectious insults year-1 and the mean length of an infection was 1.4975 years. The effect of acquired immunity on the prevalence of E. granulosus in dogs was considered to be insignificant.

Age Factors↗

Epidemiology of bancroftian filariasis in three suburban areas of Matara, Sri Lanka.

The epidemiological parameters of bancroftian filariasis were investigated in three suburbs of Matara, within the south-western coastal belt of Sri Lanka where the disease is endemic. The overall prevalence of microfilaraemia and the geometric mean density of the microfilaraemias observed were 4.4% and 20.6 microfilariae/60 microl fingerprick blood, respectively. Prevalence was significantly lower in the female subjects than in the male, and in males aged < 20 years than in older males. Overall, 9.5% of the subjects had the clinical manifestations of bancroftian filariasis (6.4% had filarial fever, 3.0% had elephantiasis and/or oedema, and 6.2% had hydrocele). The prevalence of elephantiasis/oedema was generally higher among the female subjects (4.2%) than among the male (1.4%), and an age-prevalence plot for this manifestation showed a linear increase in prevalence after the age of 40 years. Hydrocele also became commoner with increasing age, but this increase in prevalence began at the lower age of 20 years. More than 60% of the cases of elephantiasis/oedema but only 26.3% of the subjects found to have hydroceles experienced filarial fever attacks. The cases of fever and elephantiasis/oedema (but not those of microfilaraemia or hydrocele) were aggregated within households. However, the children whose mothers were microfilaraemic were much more likely to be microfilaraemic themselves (8.7%) than the children who had amicrofilaraemic mothers (2.8%), microfilaraemic fathers (0.0%) or amicrofilaraemic fathers (2.7%). The results of entomological surveys indicated that transmission of Wuchereria bancrofti occurred throughout the year in the study community.

Adolescent↗

Analysis of body-length distribution of Dirofilaria immitis in the cardio-pulmonary blood vessel of naturally infected dogs in Shiga Prefecture, Japan.

Body-length frequencies of Dirofilaria immitis collected from the cardio-pulmonary blood vessel of the dogs were studied in Shiga Prefecture. Japan, in October 1983 and in January and May 1984. The frequencies were not distributed normally because they included the populations of shorter-bodied worms, probably the growing younger worms, whereas the distributions of the body length of worms collected in July 1983 were proved to fit the single normal distribution. From the results of body-length distribution analysis, the worms collected in different seasons were each composed of 1 to 3 groups with different mean body-lengths, standard deviations and composition rates and successive changes were observed in the distribution patterns. According to the analysis of population structures, the infective season was estimated to range from April or May to October or November in 1983 from the respective ages of shorter-bodied worm groups. The annual rates of first infection and re-infection in 1983 determined by the population of shorter-bodied females collected in January were 48% and 93% respectively and the number of newly infecting females per dog ranged from 1 to 27 with a geometric mean of 8.5. The numbers of newly infecting female worms were distributed following the negative binomial and Poisson distributions in newly infected and already infected dogs respectively.

Animals↗

Frequency distribution of Echinococcus granulosus hydatid cysts in sheep populations in the Xinjiang Uygur Autonomous Region, China.

Age-prevalence and age-intensity data of Echinococcus granulosus hydatid cysts in sheep populations were collected in an abattoir in the Xinjiang Uygur Autonomous Region, People's Republic of China. The frequency distribution of the larval cysts per sheep was empirically described by the negative binomial model, with parameter k being 0.5273. A mathematical model for the life cycle of E. granulosus was applied to the collected data and the results show that the infection pressure on sheep was 0.4362 (female) or 0.4119 (male) infections per year, the mean number of cysts increased linearly by 0.8824 (female) or 0.9971 (male) cysts every year and acquired immunity was too low to depress this rate of increase. According to certain definitions of steady states for taeniid populations, it was concluded that at least in some parts of Xinjiang, the life cycle of E. granulosus was and may still be in an endemic steady state. Consequently, the regular dog-dosing program would readily drive the infection from an endemic state towards extinction.

Age Factors↗

Seasonal activity and spatial distribution of host-seeking adults of the tick Dermacentor variabilis.

The seasonal temporal and spatial distribution and emergence of overwintering and summer cohorts of host-seeking American dog tick, Dermacentor variabilis (Say) (Acari: Ixodidae), adults were examined for 5 years in the Bluegrass region of Kentucky. Weekly drag cloth sampling was conducted from early March until late September 1992-1995 and early March until the end of May 1996. Overwintering adult cohorts became active in early to mid-April followed by bimodal host-seeking activity each year, with the duration and intensity of the first activity period being related to the previous year's summer cohort activity. The first activity peak extended from mid-April through late May and the second activity peak occurred in July. All host-seeking activity ceased by early August, except in 1995, when activity ended on 22 August. Laboratory survival of adults, collected weekly during 1993-1996, was used to estimate the emergence of summer adult cohorts. Summer adult cohorts became active in late May or early June and overlapped with overwintering adult host-seeking activity. The termination of host-seeking activity in overwintering adults could not be determined using the methods employed in this study and is most likely to have continued for the entire season. Host-seeking adults displayed contagious distribution patterns along trails bordering ecotone habitats, as determined by fitting a negative binomial frequency distribution to weekly sampling data. These patterns did not vary from year to year. In addition, the location of D. variabilis activity did not change from year to year, which suggests that microhabitats within apparently homogeneous environments enhance adult survival and lead to 'hot spots' of tick activity despite the ability of vertebrate hosts to disperse D. variabilis populations more widely. These data better define our understanding of D. variabilis adult seasonal and spatial host-seeking activity, estimate for the first time the intensity of summer cohort host-seeking activity, and relate summer cohort activity with spring activity the following year.

Animals↗

[A comparison of statistical methods for quantal analysis in computer and physiological experiments].

Amplitude distributions of postsynaptic potentials were simulated in computer experiments on the basis of binomial statistics. Influences of the sample size (N) and noise standard deviation (Sn) on the determination of the quantal content (m) and quantal size (v) were studied. Four methods of the quantal parameter estimation were modified and used: histogram, variance, failure and combined method. Three last methods gave satisfactory estimations (within +/- 10%) at N = 500-1000 and Sn less than 2v. The histogram method was adequate at Sn less than or equal to v. Similar results were obtained at N = 50-200, when the experiment was repeated about ten times. Applicability of similar methods was confirmed by the analysis of an intracellular record of inhibitory postsynaptic potentials (N = 1333) from the sensorimotor cortex of rabbit.

Action Potentials↗

Non-parametric Bayesian approach to hazard regression: a case study with a large number of missing covariate values.

A 'packaged' non-parametric multiplicative hazard regression model is proposed, and applied to a study of the effects of some genetic and viral factors in the development of spontaneous leukaemia in mice. Hierarchical modelling and data augmentation are used to deal with the large number of missing covariate values. A Bayesian procedure is adopted, and the Metropolis-Hastings algorithm is used in the numerical computation of the posterior distribution.

Algorithms↗

Distribution of voltage fluctuations in a current-biased conductor.

We calculate the fluctuating voltage V(t) over a conductor driven out of equilibrium by a current source. This is the dual of the shot noise problem of current fluctuations I(t) in a voltage-biased circuit. In the single-channel case the distribution of the accumulated phase Phi=(e/ variant Planck's over 2pi ) integral Vdt is the Pascal (or binomial waiting-time) distribution-distinct from the binomial distribution of transferred charge Q= integral Idt. The weak-coupling limit of a Poissonian P(Phi) is reached in the limit of a ballistic conductor, while in the tunneling limit P(Phi) has the chi-square form.

Journal Article↗

Stochastic models for aggregation processes.

Three models are presented, which describe the aggregation of objects into groups and the distributions of groups sizes and group numbers within habitats. The processes regarded are pure accumulation processes which involve only formation and invasion of groups. Invasion represents the special case of fusion when only single objects - and not groups - join a group of certain size. The basic model is derived by a single parameter, the formation probability q, which represents the probability of an object to form a new group. A novel, discrete and finite distribution that results for the group sizes is deduced from this aggregation process and it is shown that it converges to a geometric distribution if the number of objects tends to infinity. Two extensions of this model, which both converge to the Waring distribution, are added: the model can be extended either with a beta distributed formation probability or with the assumption that the invasion probability depends on the group size. Relationships between the limiting distributions involved are discussed.

Animals↗

Interdependence of udder quarters for new intramammary infection during the dry period in cows submitted to selective antibiotic therapy.

The aim was to investigate the interdependence of udder quarters within cow towards the incidence of intramammary infections during the dry period in herds under selective dry-cow antibiotic therapy. A total of 368 cows among 28 herds were included in a survey. Quarter milk samples collected at the last milking before drying-off and on day 3 after calving were submitted to microbiological procedures. An expected distribution of cows according to their number of newly infected quarters was calculated based on a binomial probability distribution from the overall quarter incidence (or from the quarter incidence in each herd) and compared with the observed distribution. Incidence of newly infected quarters ranged from 0.0 to 39.3%, depending on the herd (median: 17.7%). Interdependence of quarters towards new infection during the dry period was observed whatever the pathogen type, for both treated and untreated cows. Calculation of an expected distribution of cows according to their number of newly infected quarters using the quarter incidence in each herd (instead of the overall quarter incidence) reduced the distance to the observed distribution, but interdependence was still observed. Our results support the application of selective antibiotic therapy at the cow level rather than at the quarter level.

Animals↗

On the chi-square approximation to the exact distribution of goodness-of-fit statistics in multinomial models with composite hypotheses.

Multinomial models are increasingly being used in psychology, and this use always requires estimating model parameters and testing goodness of fit with a composite null hypothesis. Goodness of fit is customarily tested with recourse to the asymptotic approximation to the distribution of the statistics. An assessment of the quality of this approximation requires a comparison with the exact distribution, but how to compute this exact distribution when parameters are estimated from the data appears never to have been defined precisely. The main goal of this paper is to compare two different approaches to defining this exact distribution. One of the approaches uses the marginal distribution and is, therefore, independent of the data; the other approach uses the conditional distribution of the statistics given the estimated parameters and, therefore, is data-dependent. We carried out a thorough study involving various parameter estimation methods and goodness-of-fit statistics, all of them members of the general class of power-divergence measures. Included in the study were multinomial models with three to five cells and up to three parameters. Our results indicate that the asymptotic distribution is rarely a good approximation to the exact marginal distribution of the statistics, whereas it is a good approximation to the exact conditional distribution only when the vector of expected frequencies is interior to the sample space of the multinomial distribution.

Binomial Distribution↗

Estimation of the average correlation coefficient for stratified bivariate data.

If the relationship between two ordered categorical variables X and Y is influenced by a third categorical variable with K levels, the Cochran-Mantel-Haenszel (CMH) correlation statistic QC is a useful stratum-adjusted summary statistic for testing the null hypothesis of no association between X and Y. Although motivated by and developed for the case of K I x J contingency tables, the correlation statistic QC is also applicable when X and Y are continuous variables. In this paper we derive a corresponding estimator of the average correlation coefficient for K I x J tables. We also study two estimates of the variance of the average correlation coefficient. The first is a restricted variance based on the variances of the observed cell frequencies under the null hypothesis of no association. The second is an unrestricted variance based on an asymptotic variance derived by Brown and Benedetti. The estimator of the average correlation coefficient works well in tables with balanced and unbalanced margins, for equal and unequal stratum-specific sample sizes, when correlation coefficients are constant over strata, and when correlation coefficients vary across strata. When the correlation coefficients are zero, close to zero, or the cell frequencies are small, the confidence intervals based on the restricted variance are preferred. For larger correlations and larger cell frequencies, the unrestricted confidence intervals give superior performance. We also apply the CMH statistic and proposed estimators to continuous non-normal data sampled from bivariate gamma distributions. We compare our methods to statistics for data sampled from normal distributions. The size and power of the CMH and normal theory statistics are comparable. When the stratum-specific sample sizes are small and the distributions are skewed, the proposed estimator is superior to the normal theory estimator. When the correlation coefficient is zero or close to zero, the restricted confidence intervals provide the best performance. None of the confidence intervals studied provides acceptable performances across all correlation coefficients, sample sizes and non-normal distributions.

Aged↗

Effect of non-random missing data mechanisms in clinical trials.

A simple form of non-ignorable missing data mechanisms based on two parameters is used to characterize the amount of missing data and the severity of non-randomness in clinical trials. Based on the formulation, the effect of non-randomly missing data on simple analyses which ignore the missing data is studied for binary and normally distributed response variables. In general, the effect of the non-randomly missing data on the bias and the power increases with the severity of non-randomness. The bias can be positive or negative and the power can be less than or greater than when the data are missing at random. The results of the analysis, ignoring the missing data, can be seriously flawed if the non-randomness is severe, even when only a small proportion of the sample is missing. The problem is more pronounced in the case of normally distributed response variables with unequal variances.

Bias↗