Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data

Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08]; doubling time, 1.08 years (95% C.I. 0.64, 1.82); and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.     

Using mtDNA sequences to estimate SNP parameters in ESTs

Discovery of single nucleotide polymorphisms (SNPs) requires analysis of redundant sequences such as those available in large public databases. The ability to detect SNPs, especially those of low frequency, is dependent on the depth and scale of the discovery effort. Large numbers of SNPs have been identified by mining large-scale EST surveys and whole genome sequencing projects. These surveys however are subject to ascertainment bias and the inherent errors in large-scale single pass sequencing efforts. For example, the number of steps involved in the construction and sequencing of cDNA libraries make ESTs highly error prone, resulting in an increased frequency of nonvalid SNPs obtained in these surveys. Sequences of mtDNA genes are often incorporated into cDNA libraries as an artifact of the library construction process and are typically either subtracted from cDNA libraries or are considered superfluous when evaluating the information content of EST datasets. Sequences of mtDNA genes provide a unique resource for the analysis of SNP parameters in EST projects. This study uses sequences from four turkey muscle cDNA libraries to demonstrate how mtDNA sequences gleaned from collections of ESTs can be used to estimate SNP parameters and thus help predict the validity of SNPs.     

Using reproductive value to estimate key parameters in density-independent age-structured populations

The dynamics of reproductive value are used to provide a simple derivation of Tuljapurkar's approximation for the long-run growth rate and environmental variance of lnN, in a density-independent age-structured population in a random environment. With no environmental autocorrelation, the dynamics of total population size, N, generally shows time lags and autocorrelation caused by life history, which may strongly bias estimates of environmental variance obtained by ignoring age structure. In contrast, the total reproductive value, V, is Markovian and obeys a first-order autoregressive process. This suggests a simple method for estimating the environmental variance, and avoiding potentially large bias due to age-structure fluctuations, by converting a multivariate time series of age structure to a univariate time series of lnV. We illustrate the method by estimating the long-run growth rate and the environmental variance in an exponentially growing population of Bighorn Sheep.     

Using seed purity data to estimate an average pollen mediated gene flow from crops to wild relatives

Gene flow from crops to wild related species has been recently under focus in risk-assessment studies of the ecological consequences of growing transgenic crops. However, experimental studies addressing this question are usually temporally or spatially limited. Indirect population-structure approaches can provide more global estimates of gene flow, but their assumptions appear inappropriate in an agricultural context. In an attempt to help the committees providing advice on the release of transgenic crops, we present a new method to estimate the quantity of genes migrating from crops to populations of related wild plants by way of pollen dispersal. This method provides an average estimate at a landscape level. Its originality is based on the measure of the inverse gene flow, i.e. gene flow from the wild plants to the crop. Such gene flow results in an observed level of impurities from wild plants in crop seeds. This level of impurity is usually known by the seed producers and, in any case, its measure is easier than a direct screen of wild populations because crop seeds are abundant and their genetic profile is known. By assuming that wild and cultivated plants have a similar individual pollen dispersal function, we infer the level of pollen-mediated gene flow from a crop to the surrounding wild populations from this observed level of impurity. We present an example for sugar beet data. Results suggest that under conditions of seed production in France (isolation distance of 1,000 m) wild beets produce high numbers of seeds fathered by cultivated plants. Received: 5 February 2001 / Accepted: 26 March 2001     

Design of multivariate selection experiments to estimate genetic parameters

Summary The precision of estimates of genetic variances and covariances obtained from multivariate selection experiments of various designs are discussed. The efficiencies of experimental designs are compared using criteria based on a confidence region of the estimated genetic parameters, with estimation using both responses and selection differentials and offspring-parent regression. A good selection criterion is shown to be to select individuals as parents using an index of the sums of squares and crossproducts of the phenotypic measurements. Formulae are given for the optimum selection proportion when the relative numbers of individuals in the parent and progeny generations are fixed or variable. Although the optimum depends on a priori knowledge of the genetic parameters to be estimated, the designs are very robust to poor estimates. For bivariate uncorrelated data, the variance of the estimated genetic parameters can be reduced by approximately 0.4 relative to designs of a more conventional nature when half of the individuals are selected on one trait and half on the other trait. There are larger reductions in variances if the traits are correlated.     

Using evolutionary Expectation Maximization to estimate indel rates

MOTIVATION: The Expectation Maximization (EM) algorithm, in the form of the Baum-Welch algorithm (for hidden Markov models) or the Inside-Outside algorithm (for stochastic context-free grammars), is a powerful way to estimate the parameters of stochastic grammars for biological sequence analysis. To use this algorithm for multiple-sequence evolutionary modelling, it would be useful to apply the EM algorithm to estimate not only the probability parameters of the stochastic grammar, but also the instantaneous mutation rates of the underlying evolutionary model (to facilitate the development of stochastic grammars based on phylogenetic trees, also known as Statistical Alignment). Recently, we showed how to do this for the point substitution component of the evolutionary process; here, we extend these results to the indel process. RESULTS: We present an algorithm for maximum-likelihood estimation of insertion and deletion rates from multiple sequence alignments, using EM, under the single-residue indel model owing to Thorne, Kishino and Felsenstein (the 'TKF91' model). The algorithm converges extremely rapidly, gives accurate results on simulated data that are an improvement over parsimonious estimates (which are shown to underestimate the true indel rate), and gives plausible results on experimental data (coronavirus envelope domains). Owing to the algorithm's close similarity to the Baum-Welch algorithm for training hidden Markov models, it can be used in an 'unsupervised' fashion to estimate rates for unaligned sequences, or estimate several sets of rates for sequences with heterogenous rates. AVAILABILITY: Software implementing the algorithm and the benchmark is available under GPL from http://www.biowiki.org/     

Program to estimate parameters of linear systems without numerical differentiation

This paper describes a computer program for estimating the parameters of a linear differential equation system with constant coefficients by use of a nonlinear least-squares method. For minimization the sum of squares of an existing standard program, the Gauss-Newton gradient procedure, is employed. The differential equation system is solved by the Taylor expansion method. The advantage of this approach is that the derivatives with respect to the parameters are available without numerical differentiation. Therefore the inaccuracy inherent in numerical differentiation and the problem of choosing the modification of the parameters are eliminated. The given procedure is applicable for all the first order gradient methods. The presented method was tested with generated data from a four-compartmental model.     

Jaatha: a fast composite-likelihood approach to estimate demographic parameters

While information about a species’ demography is interesting in its own right, it is an absolute necessity for certain types of population genetic analyses. The most widely used methods to infer a species’ demographic history do not take intralocus recombination or recent divergence into account, and some methods take several weeks to converge. Here, we present Jaatha, a new composite‐likelihood method that does incorporate recent divergence and is also applicable when intralocus recombination rates are high. This new method estimates four demographic parameters. The accuracy of Jaatha is comparable to that of other currently available methods, although it is superior under certain conditions, especially when divergence is very recent. As a proof of concept, we apply this new method to estimate demographic parameters for two closely related wild tomato species, Solanum chilense and S. peruvianum. Our results indicate that these species likely diverged 1.44·N generations ago, where N is the effective population size of S. chilense, and that some introgression between these species continued after the divergence process initiated. Furthermore, S. peruvianum likely experienced a population expansion following speciation.     

Observations on programs to estimate the parameters of enzyme kinetics

This paper gives a critical account of the two major programs so far published specifically to estimate the parameters of enzyme kinetics. The dangers of submitting data to the programs without proper checks are discussed, and a screening test is described to identifty sets of data which may not be best fitted by a rectangular hyperbola.     

Using ion mobility data to improve peptide identification: intrinsic amino acid size parameters

A new method for enhancing peptide ion identification in proteomics analyses using ion mobility data is presented. Ideally, direct comparisons of experimental drift times (t(D)) with a standard mobility database could be used to rank candidate peptide sequence assignments. Such a database would represent only a fraction of sequences in protein databases and significant difficulties associated with the verification of data for constituent peptide ions would exist. A method that employs intrinsic amino acid size parameters to obtain ion mobility predictions that can be used to rank candidate peptide ion assignments is proposed. Intrinsic amino acid size parameters have been determined for doubly charged peptide ions from an annotated yeast proteome. Predictions of ion mobilities using the intrinsic size parameters are more accurate than those obtained from a polynomial fit to t(D) versus molecular weight data. More than a 2-fold improvement in prediction accuracy has been observed for a group of arginine-terminated peptide ions 12 residues in length. The use of this predictive enhancement as a means to aid peptide ion identification is discussed, and a simple peptide ion scoring scheme is presented.     

Using Dirichlet tessellation to help estimate microbial biomass concentrations

Dirichlet tessellation was applied to estimate microbial concentrations from microscope well slides. The use of microscopy/Dirichlet tessellation to quantify biomass was illustrated with two species of morphologically distinct cyanobacteria (Microcystis aeruginosa and Anabaena flos aquae), and validated empirically by comparison with chlorophyll a and Coulter count analyses. Biomass estimates obtained by microscopy/Dirichlet tessellation were significantly correlated with the results obtained from chlorophyll a and Coulter analyses.     

Using circular dichroism spectra to estimate protein secondary structure

Circular dichroism (CD) is an excellent tool for rapid determination of the secondary structure and folding properties of proteins that have been obtained using recombinant techniques or purified from tissues. The most widely used applications of protein CD are to determine whether an expressed, purified protein is folded, or if a mutation affects its conformation or stability. In addition, it can be used to study protein interactions. This protocol details the basic steps of obtaining and interpreting CD data, and methods for analyzing spectra to estimate the secondary structural composition of proteins. CD has the advantage that measurements may be made on multiple samples containing < or =20 microg of proteins in physiological buffers in a few hours. However, it does not give the residue-specific information that can be obtained by x-ray crystallography or NMR.     

The necessity of biokinetic information in the interpretation of in vitro toxicity data

Data derived from in vitro toxicity studies are not directly applicable in an assessment of the toxicity of compounds in intact organisms. The major limitation is the lack of knowledge of biokinetic behaviour in vivo. Since the toxicity of a compound will be determined by the critical concentration (or other dose metric) of the critical compound (or a metabolite thereof) at the critical site of toxic action, biokinetic behaviour must be taken into account. Possibilities of biokinetic modelling on the basis of in vitro and other non-animal data are discussed, and the application of the results in hazard and risk-assessment schedules is considered.     

Using sex ratios to estimate what limits reproduction in parasitoids

The reproductive success of a foraging parasitoid may be limited by the number of eggs that she produces and/or the number of hosts that she can locate. Despite the significance for population dynamics and numerous areas of behavioural ecology, the relative importance of these factors remains an issue of contention. Attempts to resolve this controversy have been hindered because estimating the importance of factors limiting reproduction in the field can be extremely laborious and time consuming. We show how sex ratio data can be used as a relatively easy method to indirectly estimate the relative importance of the factors limiting reproduction. Sex ratio data from 48 samples of eight species suggest that: (a) the extent of host or egg limitation in a species varies between site collected and time of year; and (b) on average, species are at an intermediate position on the egg/host limitation continuum, with a bias towards host limitation.     

Using interpolation to estimate system uncertainty in gene expression experiments

The widespread use of high-throughput experimental assays designed to measure the entire complement of a cell's genes or gene products has led to vast stores of data that are extremely plentiful in terms of the number of items they can measure in a single sample, yet often sparse in the number of samples per experiment due to their high cost. This often leads to datasets where the number of treatment levels or time points sampled is limited, or where there are very small numbers of technical and/or biological replicates. Here we introduce a novel algorithm to quantify the uncertainty in the unmeasured intervals between biological measurements taken across a set of quantitative treatments. The algorithm provides a probabilistic distribution of possible gene expression values within unmeasured intervals, based on a plausible biological constraint. We show how quantification of this uncertainty can be used to guide researchers in further data collection by identifying which samples would likely add the most information to the system under study. Although the context for developing the algorithm was gene expression measurements taken over a time series, the approach can be readily applied to any set of quantitative systems biology measurements taken following quantitative (i.e. non-categorical) treatments. In principle, the method could also be applied to combinations of treatments, in which case it could greatly simplify the task of exploring the large combinatorial space of future possible measurements.     

How to obtain a precise and representative estimate for parameters in LCA

Background, Aim and Scope  Quite often there is need for precise and representative parameters in LCA studies. Probably the most relevant have direct influence on the functional unit, whose definition is crucial in the conduct of any LCA. Changes in the functional unit show directly in LCI and LCIA results. In comparative assertions, a bias in the functional unit may lead to a bias in the overall conclusions. Since quantitative data for the functional unit, such as geometric dimensions and specific weight, often vary, the question arises how to determine the functional unit, especially if a comparative assertion shall be representative for a region or market. Aim and scope of the study is to develop and apply methods for obtaining precise and representative estimates for the functional unit as one important parameter in an LCA study. Materials and Methods  Statistical sampling is applied in order to get empirical estimates for the weight of yoghurt cups, as a typical parameter for the functional unit. We used a two-stage sampling design, with stratified sampling in the first stage and three different sampling designs in the second stage, namely stratified, clustered, and a posteriori sampling. Sampling designs are motivated and described. In a case study, they are each used to determined a representative weight for 150 g yoghurt cups in Berlin, at the point of sale and within a specific time. In the first sampling stage, food markets are randomly selected, while in the second stage, yoghurt cups in these food markets are sampled. The sampling methods are applicable due to newly available internet data. These data sources and their shortcomings are described. Results  The random sampling procedure yields representative estimates, which are compared to figures for market leaders, i.e. yoghurt cups with very high occurrence in the supermarkets. While single types of yoghurt cups showed moderate uncertainty, representative estimates were highly precise. Discussion results show, for one, the performance of the applied statistical estimation procedures, and they show further that adding more information in the estimation procedure (on the shape of the cup, on the type of plastic, on the specific brand) helps reducing uncertainty. Conclusions  As conclusions, estimates and their uncertainty depend on the measurement procedure in a sensitive manner; any uncertainty information should be coupled with information on the measurement procedure, and it is recommended to use statistical sampling in order to reduce uncertainty for important parameters of an LCA study. Recommendations and Perspectives  Results for market leaders differed considerably from representative estimates. This implies to not use market leader data, or data with a high market share, as substitute for representative data in LCA studies. Statistical sampling has been barely used for Life Cycle Assessment. It turned out to be a feasible means for obtaining highly precise and representative estimates for the weight of yoghurt cups in the case study, based on empirical analysis. Further research is recommended in order to detect which parameters should best be investigated in LCA case studies; which data sources are available and recommended, and which sampling designs are appropriate for different application cases. ESS-Submission Editor: Seungdo Kim. PhD (kimseun@msu.edu)     

Determination of biokinetic parameters for ingestion of radionuclides of zirconium in animals using stable tracers

Exposure to the radioactive isotope ⁹⁵Zr, as in nuclear accidents, and to stable zirconium, due to its use in industry, has increased the interest in the biokinetics of this element. Information has been derived mainly from tests performed on animals by means of radioactive tracers. Due to the fact that extrapolation from animals to humans is always open to question, there is an increasing need of a methodology which allows data to be obtained directly from humans. The use of stable tracers, being ethically justifiable, is a powerful tool for providing this information. As two tracers of the same element must be utilized in order to evaluate gut absorption, an analytical technique which is capable of distinguishing and measuring simultaneously different isotopes of zirconium in biological samples is required. Preliminary tests on laboratory animals were performed in order to assess the feasibility of the double tracer technique combined with proton activation analysis. Received: 7 April 1999 / Accepted in revised form: 4 November 1999     

Using genetic markers to directly estimate gene flow and reproductive success parameters in plants on the basis of naturally regenerated seedlings

Estimating seed and pollen gene flow in plants on the basis of samples of naturally regenerated seedlings can provide much needed information about "realized gene flow," but seems to be one of the greatest challenges in plant population biology. Traditional parentage methods, because of their inability to discriminate between male and female parentage of seedlings, unless supported by uniparentally inherited markers, are not capable of precisely describing seed and pollen aspects of gene flow realized in seedlings. Here, we describe a maximum-likelihood method for modeling female and male parentage in a local plant population on the basis of genotypic data from naturally established seedlings and when the location and genotypes of all potential parents within the population are known. The method models female and male reproductive success of individuals as a function of factors likely to influence reproductive success (e.g., distance of seed dispersal, distance between mates, and relative fecundity--i.e., female and male selection gradients). The method is designed to account for levels of seed and pollen gene flow into the local population from unsampled adults; therefore, it is well suited to isolated, but also wide-spread natural populations, where extensive seed and pollen dispersal complicates traditional parentage analyses. Computer simulations were performed to evaluate the utility and robustness of the model and estimation procedure and to assess how the exclusion power of genetic markers (isozymes or microsatellites) affects the accuracy of the parameter estimation. In addition, the method was applied to genotypic data collected in Scots pine (isozymes) and oak (microsatellites) populations to obtain preliminary estimates of long-distance seed and pollen gene flow and the patterns of local seed and pollen dispersal in these species.