Quantification of ruminal Clostridium proteoclasticum by real-time PCR using a molecular beacon approach

Aims: All members of the ruminal Butyrivibrio group convert linoleic acid (cis-9,cis-12-18 : 2) via conjugated 18 : 2 metabolites (mainly cis-9,trans-11-18 : 2, conjugated linoleic acid) to vaccenic acid (trans-11-18 : 1), but only members of a small branch, which includes Clostridium proteoclasticum, of this heterogeneous group further reduce vaccenic acid to stearic acid (18 : 0, SA). The aims of this study were to develop a real-time polymerase chain reaction (PCR) assay that would detect and quantify these key SA producers and to use this method to detect diet-associated changes in their populations in ruminal digesta of lactating cows. Materials and Results: The use of primers targeting the 16S rRNA gene of Cl. proteoclasticum was not sufficiently specific when only binding dyes were used for detection in real-time PCR. Their sequences were too similar to some nonproducing strains. A molecular beacon probe was designed specifically to detect and quantify the 16S rRNA genes of the Cl. proteoclasticum subgroup. The probe was characterized by its melting curve and validated using five SA-producing and ten nonproducing Butyrivibrio-like strains and 13 other common ruminal bacteria. Analysis of ruminal digesta collected from dairy cows fed different proportions of starch and fibre indicated a Cl. proteoclasticum population of 2-9% of the eubacterial community. The influence of diet on numbers of these bacteria was less than variations between individual cows. Conclusion: A molecular beacon approach in qPCR enables the detection of Cl. proteoclasticum in ruminal digesta. Their numbers are highly variable between individual animals. Signifance and Impact of the Study: SA producers are fundamental to the flow of polyunsaturated fatty acid and vaccenic acid from the rumen. The method described here enabled preliminary information to be obtained about the size of this population. Further application of the method to digesta samples from cows fed diets of more variable composition should enable us to understand how to control these bacteria in order to enhance the nutritional characteristics of ruminant-derived foods, including milk and beef.

Application of real-time and multiplex PCR assays to study leaf blotch epidemics in barley

Leaf blotch, caused by Rhynchosporium secalis, was studied in a range of winter barley cultivars using a combination of traditional plant pathological techniques and newly developed multiplex and real-time polymerase chain reaction (PCR) assays. Using PCR, symptomless leaf blotch colonization was shown to occur throughout the growing season in the resistant winter barley cv. Leonie. The dynamics of colonization throughout the growing season were similar in both Leonie and Vertige, a susceptible cultivar. However, pathogen DNA levels were approximately 10-fold higher in the susceptible cultivar, which expressed symptoms throughout the growing season. Visual assessments and PCR also were used to determine levels of R. secalis colonization and infection in samples from a field experiment used to test a range of winter barley cultivars with different levels of leaf blotch resistance. The correlation between the PCR and visual assessment data was better at higher infection levels (R(2) = 0.81 for leaf samples with >0.3% disease). Although resistance ratings did not correlate well with levels of disease for all cultivars tested, low levels of infection were observed in the cultivar with the highest resistance rating and high levels of infection in the cultivar with the lowest resistance rating.

Estimation of population growth or decline in genetically monitored populations

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.

Evaluating interval forecasts of high-frequency financial data

A number of methods of evaluating the validity of interval forecasts of financial data are analysed, and illustrated using intraday FTSE100 index futures returns. Some existing interval forecast evaluation techniques, such as the Markov chain approach of Christoffersen (1998), are shown to be inappropriate in the presence of periodic heteroscedasticity. Instead, we consider a regression-based test, and a modified version of Christoffersen's Markov chain test for independence, and analyse their properties when the financial time series exhibit periodic volatility. These approaches lead to different conclusions when interval forecasts of FTSE100 index futures returns generated by various GARCH(1,1) and periodic GARCH(1,1) models are evaluated.

Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

Methane in the atmosphere of the transiting hot Neptune GJ436b?

We present an analysis of seven primary transit observations of the hot Neptune GJ436b at 3.6, 4.5, and 8 μm obtained with the Infrared Array Camera on the Spitzer Space Telescope. After correcting for systematic effects, we fitted the light curves using the Markov Chain Monte Carlo technique. Combining these new data with the EPOXI, Hubble Space Telescope, and ground-based V, I, H, and Ks published observations, the range 0.5-10 μm can be covered. Due to the low level of activity of GJ436, the effect of starspots on the combination of transits at different epochs is negligible at the accuracy of the data set. Representative climate models were calculated by using a three-dimensional, pseudospectral general circulation model with idealized thermal forcing. Simulated transit spectra of GJ436b were generated using line-by-line radiative transfer models including the opacities of the molecular species expected to be present in such a planetary atmosphere. A new, ab-initio-calculated, line list for hot ammonia has been used for the first time. The photometric data observed at multiple wavelengths can be interpreted with methane being the dominant absorption after molecular hydrogen, possibly with minor contributions from ammonia, water, and other molecules. No clear evidence of carbon monoxide and carbon dioxide is found from transit photometry. We discuss this result in the light of a recent paper where photochemical disequilibrium is hypothesized to interpret secondary transit photometric data. We show that the emission photometric data are not incompatible with the presence of abundant methane, but further spectroscopic data are desirable to confirm this scenario.

Estimating detailed soil water profile records from point measurements

Temporal and spatial patterns of soil water content affect many soil processes including evaporation, infiltration, ground water recharge, erosion and vegetation distribution. This paper describes the analysis of a soil moisture dataset comprising a combination of continuous time series of measurements at a few depths and locations, and occasional roving measurements at a large number of depths and locations. The objectives of the paper are: (i) to develop a technique for combining continuous measurements of soil water contents at a limited number of depths within a soil profile with occasional measurements at a large number of depths, to enable accurate estimation of the soil moisture vertical pattern and the integrated profile water content; and (ii) to estimate time series of soil moisture content at locations where there are just occasional soil water measurements available and some continuous records from nearby locations. The vertical interpolation technique presented here can strongly reduce errors in the estimation of profile soil water and its changes with time. On the other hand, the temporal interpolation technique is tested for different sampling strategies in space and time, and the errors generated in each case are compared.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Bayesian ranking and selection of fishing boat efficiencies

The steadily accumulating literature on technical efficiency in fisheries attests to the importance of efficiency as an indicator of fleet condition and as an object of management concern. In this paper, we extend previous work by presenting a Bayesian hierarchical approach that yields both efficiency estimates and, as a byproduct of the estimation algorithm, probabilistic rankings of the relative technical efficiencies of fishing boats. The estimation algorithm is based on recent advances in Markov Chain Monte Carlo (MCMC) methods—Gibbs sampling, in particular—which have not been widely used in fisheries economics. We apply the method to a sample of 10,865 boat trips in the US Pacific hake (or whiting) fishery during 1987–2003. We uncover systematic differences between efficiency rankings based on sample mean efficiency estimates and those that exploit the full posterior distributions of boat efficiencies to estimate the probability that a given boat has the highest true mean efficiency.

Analysis of the calving pattern of herds in small-scale dairy systems in central Mexico

This study sets out to find the best calving pattern for small-scale dairy systems in Michoacan State, central Mexico. Two models were built. First, a linear programming model was constructed to optimize calving pattern and herd structure according to metabolizable energy availability. Second, a Markov chain model was built to investigate three reproductive scenarios (good, average and poor) in order to suggest factors that maintain the calving pattern given by the linear programming model. Though it was not possible to maintain the optimal linear programming pattern, the Markov chain model suggested adopting different reproduction strategies according to period of the year that the cow is expected to calve. Comparing different scenarios, the Markov model indicated the effect of calving interval on calving pattern and herd structure.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Evolutionary history of vegetative reproduction in Porpidia s. l. (lichen-forming ascomycota)

The evolutionary history of gains and losses of vegetative reproductive propagules (soredia) in Porpidia s.l., a group of lichen-forming ascomycetes, was clarified using Bayesian Markov chain Monte Carlo (MCMC) approaches to monophyly tests and a combined MCMC and maximum likelihood approach to ancestral character state reconstructions. The MCMC framework provided confidence estimates for the reconstructions of relationships and ancestral character states, which formed the basis for tests of evolutionary hypotheses. Monophyly tests rejected all hypotheses that predicted any clustering of reproductive modes in extant taxa. In addition, a nearest-neighbor statistic could not reject the hypothesis that the vegetative reproductive mode is randomly distributed throughout the group. These results show that transitions between presence and absence of the vegetative reproductive mode within Porpidia s.l. occurred several times and independently of each other. Likelihood reconstructions of ancestral character states at selected nodes suggest that - contrary to previous thought - the ancestor to Porpidia s.l. already possessed the vegetative reproductive mode. Furthermore, transition rates are reconstructed asymmetrically with the vegetative reproductive mode being gained at a much lower rate than it is lost. A cautious note has to be added, because a simulation study showed that the ancestral character state reconstructions were highly dependent on taxon sampling. However, our central conclusions, particularly the higher rate of change from vegetative reproductive mode present to absent than vice versa within Porpidia s.l., were found to be broadly independent of taxon sampling. [Ancestral character state reconstructions; Ascomycota, Bayesian inference; hypothesis testing; likelihood; MCMC; Porpidia; reproductive systems]