Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

A genetic and spatial Bayesian analysis of mastitis resistance

A nationwide health card recording system for dairy cattle was introduced in Norway in 1975 (the Norwegian Cattle Health Services). The data base holds information on mastitis occurrences on an individual cow basis. A reduction in mastitis frequency across the population is desired, and for this purpose risk factors are investigated. In this paper a Bayesian proportional hazards model is used for modelling the time to first veterinary treatment of clinical mastitis, including both genetic and environmental covariates. Sire effects were modelled as shared random components, and veterinary district was included as an environmental effect with prior spatial smoothing. A non-informative smoothing prior was assumed for the baseline hazard, and Markov chain Monte Carlo methods (MCMC) were used for inference. We propose a new measure of quality for sires, in terms of their posterior probability of being among the, say 10% best sires. The probability is an easily interpretable measure that can be directly used to rank sires. Estimating these complex probabilities is straightforward in an MCMC setting. The results indicate considerable differences between sires with regards to their daughters disease resistance. A regional effect was also discovered with the lowest risk of disease in the south-eastern parts of Norway.     

Parameter estimation techniques for interaction and redistribution models: a predator-prey example

Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.     

Aspects of the mineral nutrition of some native British plants — inter-site variation

Fifteen common native British plants were each sampled at a range of sites in Great Britain and green tissues analysed for several inorganic nutrients. Sampling criteria are discussed. The inter-site variation of each element within a species is assessed as a frequency distribution of raw data. Sample values of parameters including arithmetic mean, variance (coefficient of variation), skewness and kurtosis are presented. Their stability is assessed from nitrogen in sub-samples of Pteridium. This suggested sample sizes were adequate but some distributions had sufficient kurtosis to affect the variance. These parameters showed distinctions between macro- and micro-elements and between species. Some mean values sharply distinguished between species and may help to assess current theories of strategy and adaptation but a wider range of species is needed to clarify trends. Coefficients of variation are discussed and were relatively low for a nation-wide survey after allowing for sampling constraints. Coefficients of skewness and kurtosis showed two-thirds of the sample distributions were non-normal. Ecological aspects of the distributions are discussed and are relevant to studies along environmental gradients. Published hypotheses linking positive skewness to stress in the field are considered and two other postulates discussed. Distribution bounds such as those confining 95% of the values are discussed in relation to possible critical levels of nutrients.Nomenclature follows Clapham et al. (1981), Excursion flora of the British Isles. 3rd ed. University Press, Cambridge, except Chamaenerion.     

Ultrastructure of Macadamia (Proteaceae) embryos: implications for their breakage properties

BACKGROUND AND AIMS: Macadamia integrifolia, M. tetraphylla and their hybrids are cultivated for their edible kernels. Whole kernels, i.e. intact mature embryos with cotyledons fused together, are highly valued and breakage of embryos into halves results in loss of value for the commercial macadamia industry. The morphology and ultrastructure of the mature macadamia embryo, with particular emphasis on the break zone between cotyledons, were investigated. Differences in breakage between different macadamia cultivars were also examined. METHODS: Manual cracking was used to compare breakage in five cultivars and the ultrastructure of the break zone between the cotyledons was examined using light and transmission electron microscopy. KEY RESULTS: Breakage of macadamia embryos was strongly dependent on genotype of the female parent, with cultivars 'HAES 344' and 'HAES 741' much more likely to break than 'HV A16' and 'HAES 835'. Cotyledons were surrounded by a layer of cuticle resulting in a double cuticle in the break zone between the cotyledons. Three major differences have been found in the ultrastructure of the double cuticle between cultivars: a thicker cuticle in the low-whole cultivar; convolutions in the cuticle of a low-whole cultivar, and the presence of more electron-dense objects in the high-whole cultivar. CONCLUSIONS: Breakage of macadamia embryos depends on the cultivar, with clear ultrastructural differences in the break zone between cultivars. To ensure commercial benefits, macadamia breeding programs should identify germplasm with structural characteristics that ensure high percentages of whole kernel.     

Distance-based analysis of variance for brain connectivity

The field of neuroimaging dedicated to mapping connections in the brain is increasingly being recognized as key for understanding neurodevelopment and pathology. Networks of these connections are quantitatively represented using complex structures, including matrices, functions, and graphs, which require specialized statistical techniques for estimation and inference about developmental and disorder-related changes. Unfortunately, classical statistical testing procedures are not well suited to high-dimensional testing problems. In the context of global or regional tests for differences in neuroimaging data, traditional analysis of variance (ANOVA) is not directly applicable without first summarizing the data into univariate or low-dimensional features, a process that might mask the salient features of high-dimensional distributions. In this work, we consider a general framework for two-sample testing of complex structures by studying generalized within-group and between-group variances based on distances between complex and potentially high-dimensional observations. We derive an asymptotic approximation to the null distribution of the ANOVA test statistic, and conduct simulation studies with scalar and graph outcomes to study finite sample properties of the test. Finally, we apply our test to our motivating study of structural connectivity in autism spectrum disorder.     

Estimation in independent observer line transect surveys for clustered populations

This paper introduces a framework for animal abundance estimation in independent observer line transect surveys of clustered populations. The framework generalizes an approach given in Chen (1999, Environmental and Ecological Statistics 6, in press) to accommodate heterogeneity in detection caused by cluster size and other covariates. Both parametric and nonparametric estimators for the local effective search widths, given the covariates, can be derived from the framework. A nonparametric estimator based on conditional kernel density estimation is proposed and studied owing to its flexibility in modeling the detection functions. A real data set on harbor porpoise in the North Sea is analyzed.     

Reducing variability of crossvalidation for smoothing-parameter choice

One of the attractions of crossvalidation, as a tool for smoothing-parameterchoice, is its applicability to a wide variety of estimatortypes and contexts. However, its detractors comment adverselyon the relatively high variance of crossvalidatory smoothingparameters, noting that this compromises the performance ofthe estimators in which those parameters are used. We show thatthe variability can be reduced simply, significantly and reliablyby employing bootstrap aggregation or bagging. We establishthat in theory, when bagging is implemented using an adaptivelychosen resample size, the variability of crossvalidation canbe reduced by an order of magnitude. However, it is arguablymore attractive to use a simpler approach, based for exampleon half-sample bagging, which can reduce variability by approximately50%.