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.

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.

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon-known as heterotachy-can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea Japan land separation. (c) 2005 Elsevier Inc. All rights reserved.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.

Antimalarial drugs based on artemisinin: DFT calculations on the principal reactions

Theoretical calculations have been carried out on the interactions of several endoperoxides which are potential antimalarials, including the clinically useful artemisinin, with two possible sources of iron in the parasite, namely the hexa-aquo ferrous ion [Fe(H2O)(6)](2+) and haeme. DFT calculations show that the reactions of all endoperoxides considered, with both sources of iron, initially generate a Fe-O bond followed by cleavage of the O-O bond to oxygen radical species. Subsequently, they can be transformed into carbon-centred radicals of greater stability. However, with [Fe(H2O)(6)](2+) as the iron source, the oxygen-centred radical species are more likely to react further akin to Fenton's reagent, whereby iron salts encourage hydrogen peroxide to act as an oxidizing agent, and that solvent plays a major role. In contrast, when reacting with haeme, the oxygen-centred radicals interconvert to more stable carbon-centred radicals, which can then alkylate haeme. Subsequent cleavage of the Fe-O bond leads to stable and inactive antimalarial products. These results indicate that the reactivity of the endoperoxides as antimalarials is greater with iron hexahydrates for radical-mediated damage as opposed to haeme, which leads to unreactive species. Since only nanomolar quantities of hydrated metal ions could catalyse the reactions leading to damage to the parasites, this could be an alternative or competitive reaction responsible for the antimalarial activity. (c) 2005 Elsevier B.V. All rights reserved.

Architectural, construction and environmental matters of Bahrain's international formula 1 circuit

The Bahrain International Circuit (BIC) is considered its one of the best international racing car track in terms of technical aspects and architectural quality. Two Formula 1 races have been hosted in the Kingdom of Bahrain, in 2004 and 2005, at BIC. The BIC had recently won the award of the best international racing car circuit. This paper highlights on the elements that contributed to the success of such project starting from the architectural aspects, construction, challenges, tendering process, risk management, the workforce, speed of the construction method, and future prospects for harnessing solar and wind energy for sustainable electrification and production of water for the circuit, i.e. making BIC green and environment-friendly international circuit.

Bahrain's Formula-1 racing circuit: energy and environmental considerations

The Bahrain International Circuit (BIC) and complex, at latitude 26.00N and longitude 51.54E, was built in 483 days and cost 150 million US$. The circuit consists of six different individual tracks with a 3.66 km outer track (involving 10 turns) and a 2.55 km inner track (having six turns). The complex has been designed to host a variety of other sporting activities. Fifty thousand spectators, including 10,500 in the main grandstand, can be accommodated simultaneously. State-of-the art on-site media and broadcast facilities are available. The noise level emitted from vehicles on the circuit during the Formula-1 event, on April 4th 2004, was acceptable and caused no physical disturbance to the fans in the VIP lounges or to scholars studying at the University of Bahrain's Shakeir Campus, which is only 1.5 km away from the circuit. The sound-intensity level (SIL) recorded on the balcony of the VIP lounge was 128 dB(A) and was 80 dB(A) inside the lounge. The calculated SIL immediately outside the lecture halls of the University of Bahrain was 70 dB(A) and 65 dB(A) within them. Thus racing at BIC can proceed without significantly disturbing the academic-learning process. The purchased electricity demand by the BIC complex peaked (at 4.5 MW) during the first Formula-1 event on April 4th 2004. The reverse-osmosis (RO) plant at the BIC provides 1000 m(3) of desalinated water per day for landscape irrigation. Renewable-energy inputs, (i.e., via solar and wind power), at the BIC could be harnessed to generate electricity for water desalination, air conditioning, lighting as well as for irrigation. If the covering of the BIC complex was covered by adhesively fixed modern photovoltaic cells, then similar to 1.2 MW of solar electricity could be generated. If two horizontal-axis, at 150 m height above the ground, three 75m bladed, wind turbines were to be installed at the BIC, then the output could reach 4 MW. Furthermore, if 10,000 Jojoba trees (a species renowned for having a low demand for water, needing only five irrigations per year in Bahrain and which remain green throughout the year) are planted near the circuit, then the local micro-climate would be improved with respect to human comfort as well as the local environment becoming cleaner.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

Enhancing change detection in low-quality surveillance footage using markov random fields

Urban surveillance footage can be of poor quality, partly due to the low quality of the camera and partly due to harsh lighting and heavily reflective scenes. For some computer surveillance tasks very simple change detection is adequate, but sometimes a more detailed change detection mask is desirable, eg, for accurately tracking identity when faced with multiple interacting individuals and in pose-based behaviour recognition. We present a novel technique for enhancing a low-quality change detection into a better segmentation using an image combing estimator in an MRF based model.