A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate- variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.

Modulation of the fecal microflora profile and immune function by a novel trans-galactooligosaccharide mixture (B-GOS) in healthy elderly volunteers

Background: Aging is associated with reduced numbers of beneficial colonic bifidobacteria and impaired immunity. Galactooligosaccharides (GOSs) stimulate the growth of bifidobacteria in younger adults, but little is known about their effects in the elderly and their immunomodulatory capacity. Objective: We assessed the effect of a prebiotic GOS mixture (B-GOS) on immune function and fecal microflora composition in healthy elderly subjects. Design: In a double-blind, placebo-controlled, crossover study, 44 elderly subjects were randomly assigned to receive either a placebo or the B-GOS treatment (5.5 g/d). Subjects consumed the treatments for 10 wk, and then went through a 4-wk washout period, before switching to the other treatment for the final 10 wk. Blood and fecal samples were collected at the beginning, middle (5 wk), and end of the test period. Predominant bacterial groups were quantified, and phagocytosis, natural killer (NK) cell activity, cytokine production, plasma cholesterol, and HDL cholesterol were measured. Results: B-GOS significantly increased the numbers of beneficial bacteria, especially bifidobacteria, at the expense of less beneficial groups compared with the baseline and placebo. Significant increases in phagocytosis, NK cell activity, and the production of antiinflammatory cytokine interleukin-10 (IL-10) and significant reduction in the production of proinflammatory cytokines (IL-6, IL-1 beta , and tumor necrosis factor-alpha) were also observed. B-GOS exerted no effects on total cholesterol or HDL-cholesterol production, however. Conclusions: B-GOS administration to healthy elderly persons resulted in positive effects on both the microflora composition and the immune response. Therefore, B-GOS may be a useful dietary candidate for the enhancement of gastrointestinal health and immune function in elderly persons. Am J Clin Nutr 2008; 88: 1438-46.

A novel galactooligosaccharide mixture increases the bifidobacterial population numbers in a continuous in vitro fermentation system and in the proximal colonic contents of pigs in vivo

Prebiotics are nondigestible food ingredients that encourage proliferation of selected groups of the colonic microflora, thereby altering the composition toward a more beneficial community. In the present study, the prebiotic potential of a novel galactooligosaccharide (GOS) mixture, produced by the activity of galactosyltransferases from Bifidobacterium bifidum 41171 on lactose, was assessed in vitro and in a parallel continuous randomized pig trial. In situ fluorescent hybridization with 16S rRNA-targeted probes was used to investigate changes in total bacteria, bifidobacteria, lactobacilli, bacteroides, and Clostridium histolyticum group in response to supplementing the novel GOS mixture. In a 3-stage continuous culture system, the bifidobacterial numbers for the first 2 vessels, which represented the proximal and traverse colon, increased (P < 0.05) after the addition of the oligosaccharide mixture. In addition, the oligosaccharide mixture strongly inhibited the attachment of enterohepatic Escherichia coli (P < 0.01) and Salmonella enterica serotype Typhimurium (P < 0.01) to HT29 cells. Addition of the novel mixture at 4% (wt:wt) to a commercial diet increased the density of bificlobacteria (P < 0.001) and the acetate concentration (P < 0.001), and decreased the pH (P < 0.001) compared with the control diet and the control diet supplemented with inulin, suggesting a great prebiotic potential for the novel oligosaccharide mixture. J. Nutr. 135: 1726-1731, 2005.

The effects of conjugated linoleic acid on human health-related outcomes

Conjugated linoleic acid (CLA) is a collective term for a mixture of positional and geometric isomers of conjugated dienoic derivatives of linoleic acid. CLA has received considerable attention as a result of animal experiments that report anti-carcinogenic, anti-atherogenic and anti-diabetic properties, and modulation of body composition and immune function. Several studies of CLA supplementation in human subjects have now been published, but in contrast to animal studies there has been marked variation between reports on the health-related outcomes. The consensus from seventeen published studies in human subjects is that CLA does not affect body weight or body composition. Some detrimental effects of the trans-10,cis-12 CLA isomer have also been reported in terms of altered blood lipid composition and impaired insulin sensitivity. Finally, CLA has only limited effects on immune functions in man. However, there have been reports of some interesting isomer-specific effects of CLA on the blood lipid profile, but not on immune function. These isomer-specific effects need further investigation. Until more is known, CLA supplementation in man should be considered with caution.

Evaluation of the inclusion of a mixture of organic acids or lactulose into the feed of pigs experimentally challenged with Salmonella Typhimurium

A mixture of organic acids and lactulose for preventing or reducing colonization of the gut by Salmonella Typhimurium was evaluated in pigs. A total of 63 4-week-old commercial piglets were randomly distributed into three different experimental dietary groups: a plain diet without additives (PD) and the same diet supplemented with either 0.4% (w/v) formic acid and 0.4% lactic acid (w/v) (AC) or 1% (w/v) lactulose (LC). After 7 days of adaptation, two-thirds of the pigs (14 from each diet) were challenged with a 2-mL oral dose of 10(8) CFU/mL of Salmonella Typhimurium, leaving the remaining animals unchallenged (UC). After 4 and 10 days post-challenge, pigs were euthanized and the ileum and caecum content were aseptically sampled to (a) quantify lactic, formic, and short-chain fatty acids (SCFA), (b) quantify bacterial populations and Salmonella by fluorescence in situ hybridization and (c) qualitatively analyse bacterial populations through denaturing gradient gel electrophoresis (DGGE). Modification of fermentation products and counts of some of the bacterial groups analysed in the challenged pigs receiving the treatments AC and LC were minimal. Treatments only influenced the bacterial diversity after 10 days post-challenge, with AC generating a lower number of DGGE bands than UC(P < 0.05). Neither the inclusion of a mixture of 0.4% (w/v) formic and 0.4% (w/v) lactic acids nor of 1% (w/v) lactulose in the feed influenced numbers of Salmonella in the ileum and caecum of experimentally challenged pigs. (C) 2009 Elsevier B.V. All rights reserved.

Dietary supplementation with a natural carotenoid mixture decreases oxidative stress

Objective: To determine whether dietary supplementation with a natural carotenoid mixture counteracts the enhancement of oxidative stress induced by consumption of fish oil. Design: A randomised double-blind crossover dietary intervention. Setting: Hugh Sinclair Unit of Human Nutrition, School of Food Biosciences, The University of Reading, Whiteknights PO Box 226, Reading RG6 6AP, UK. Subjects and intervention: A total of 32 free-living healthy nonsmoking volunteers were recruited by posters and e-mails in The University of Reading. One volunteer withdrew during the study. The volunteers consumed a daily supplement comprising capsules containing fish oil (4 x 1 g) or fish oil (4 x 1 g) containing a natural carotenoid mixture (4 x 7.6 mg) for 3 weeks in a randomised crossover design separated by a 12 week washout phase. The carotenoid mixture provided a daily intake of beta-carotene (6.0 mg), alpha-carotene (1.4 mg), lycopene (4.5 mg), bixin (11.7 mg), lutein (4.4 mg) and paprika carotenoids (2.2 mg). Blood and urine samples were collected on days 0 and 21 of each dietary period. Results: The carotenoid mixture reduced the fall in ex vivo oxidative stability of low-density lipoprotein (LDL) induced by the fish oil (P = 0.045) and it reduced the extent of DNA damage assessed by the concentration of 8-hydroxy-2'-deoxyguanosine in urine (P = 0.005). There was no effect on the oxidative stability of plasma ex vivo assessed by the oxygen radical absorbance capacity test. beta- Carotene, alpha-carotene, lycopene and lutein were increased in the plasma of subjects consuming the carotenoid mixture. Plasma triglyceride levels were reduced significantly more than the reduction for the fish oil control (P = 0.035), but total cholesterol, HDL and LDL levels were not significantly changed by the consumption of the carotenoid mixture. Conclusions: Consumption of the natural carotenoid mixture lowered the increase in oxidative stress induced by the fish oil as assessed by ex vivo oxidative stability of LDL and DNA degradation product in urine. The carotenoid mixture also enhanced the plasma triglyceride-lowering effect of the fish oil.

Prebiotic evaluation of a novel galactooligosaccharide mixture produced by the enzymatic activity of Bifidobacterium bifidum NCIMB 41171, in healthy humans: a randomized, double-blind, crossover, placebo-controlled intervention study

Background: Galactooligosaccharides are selectively fermented by the beneficial member of the colonic microflora contributing to the health of the host. Objective: We assessed the prebiotic potential of a novel galactooligosaccharide produced through the action of beta-galactosidases, originating from a probiotic Bifidobacterium bifidum strain, against a galactooligosaccharide produced through the action of an industrial P-galactosidase and a placebo. Design: Fifty-nine healthy human volunteers participated in this study. Initially, the effect of the matrix on the prebiotic properties of a commercially available galactooligosaccharide (7 g/d) was assessed during 7-d treatment periods with a 7-d washout period in between. During the second phase, 30 volunteers were assigned to a sequence of treatments (7 d) differing in the amount of the novel galactooligosaccharide (0, 3.6, or 7 g/d). Stools were recovered before and after each intervention, and bacteria numbers were determined by fluorescent in situ hybridization. Results: Addition of the novel galactooligosaccharide mixture significantly increased the bifidobacterial population ratio compared with the placebo (P < 0.05), whereas 7 g/d of the novel galactooligosaccharide significantly increased the bifidobacterial ratio compared with the commercial galactooligosaccharide (P < 0.05). Moreover, a significant relation (P < 0.001) between the bifidobacteria proportion and the novel galactooligosaccharide dose (0, 3.6, and 7 g/d) was observed. This relation was similar to the effect of the novel galactooligosaccharide on the prebiotic index of each dose. Conclusions: This study showed that galactooligosaccharide mixtures produced with different beta-galactosidases show different prebiotic properties and that, by using enzymes originating from bifidobacterial species, an increase in the bifidogenic properties of the prebiotic product is achievable.

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

A geometric approach to generalized Stokes conjectures

We consider the Stokes conjecture concerning the shape of extreme two-dimensional water waves. By new geometric methods including a nonlinear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.

A double-blind, placebo-controlled, randomized human study assessing the capacity of a novel galacto-oligosaccharide mixture in reducing travellers' diarrhoea.

Background/Objectives: Prebiotics have attracted interest for their ability to positively affect the colonic microbiota composition, thus increasing resistance to infection and diarrhoeal disease. This study assessed the effectiveness of a prebiotic galacto-oligosaccharide mixture (B-GOS) on the severity and/or incidence of travellers' diarrhoea (TD) in healthy subjects. Subjects/Methods: The study was a placebo-controlled, randomized, double blind of parallel design in 159 healthy volunteers, who travelled for minimum of 2 weeks to a country of low or high risk for TD. The investigational product was the B-GOS and the placebo was maltodextrin. Volunteers were randomized into groups with an equal probability of receiving either the prebiotic or placebo. The protocol comprised of a 1 week pre-holiday period recording bowel habit, while receiving intervention and the holiday period. Bowel habit included the number of bowel movements and average consistency of the stools as well as occurrence of abdominal discomfort, flatulence, bloating or vomiting. A clinical report was completed in the case of diarrhoeal incidence. A post-study questionnaire was also completed by all subjects on their return. Results: Results showed significant differences between the B-GOS and the placebo group in the incidence (P<0.05) and duration (P<0.05) of TD. Similar findings occurred on abdominal pain (P<0.05) and the overall quality of life assessment (P<0.05). Conclusions: Consumption of the tested galacto-oligosaccharide mixture showed significant potential in preventing the incidence and symptoms of TD.

A mixture of experts network structure construction algorithm for modelling and control

This paper introduces a new fast, effective and practical model structure construction algorithm for a mixture of experts network system utilising only process data. The algorithm is based on a novel forward constrained regression procedure. Given a full set of the experts as potential model bases, the structure construction algorithm, formed on the forward constrained regression procedure, selects the most significant model base one by one so as to minimise the overall system approximation error at each iteration, while the gate parameters in the mixture of experts network system are accordingly adjusted so as to satisfy the convex constraints required in the derivation of the forward constrained regression procedure. The procedure continues until a proper system model is constructed that utilises some or all of the experts. A pruning algorithm of the consequent mixture of experts network system is also derived to generate an overall parsimonious construction algorithm. Numerical examples are provided to demonstrate the effectiveness of the new algorithms. The mixture of experts network framework can be applied to a wide variety of applications ranging from multiple model controller synthesis to multi-sensor data fusion.

Neurofuzzy mixture of experts network parallel learning and model construction algorithms

A connection between a fuzzy neural network model with the mixture of experts network (MEN) modelling approach is established. Based on this linkage, two new neuro-fuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm. These two construction methods are equivalent in their effectiveness in overcoming the curse of dimensionality by reducing the dimensionality of the regression vector, but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.