Estimating the product‐moment correlation in samples with censoring on both variables

Bivariate samples may be subject to censoring of both random variables. For example, for two toxins measured in batches of wheat grain, there may be specific detection limits. Alternatively, censoring may be incomplete over a certain domain, with the probability of detection depending on the toxin level. In either case, data are not missing at random, and the missing data pattern bears some information on the parameters of the underlying model (informative missingness), which can be exploited for a fully efficient analysis. Estimation (after suitable data transformation) of the correlation in such samples is the subject of the present paper. We consider several estimators. The first is based on the tetrachoric correlation. It is simple to compute, but does not exploit the full information. The other two estimators exploit all information and use full maximum likelihood, but involve heavier computations. The one assumes fixed detection limits, while the other involves a logistic model for the probability of detection. For a real data set, a logistic model for the probability of detection fitted markedly better than a model with fixed detection limits, suggesting that censoring is not complete.     

Dominant vs. codominant genetic markers in the estimation of male mating success

Although a major component of fitness, male reproductive success is generally extremely difficult to estimate. As a result, genetic methods and maximum likelihood models have been developed to estimate male parentage, but all are limited in practice by the degree of genetic variation observable. Scoring individuals phenotypically at a large number of random loci exhibiting dominance (e.g. RAPD markers) may provide a means of detecting sufficient genetic variation. Dominance, however, represents a loss of information and therefore greater variation in the estimate of paternity. A mixture model describing mating in a population is presented to quantify the trade-off between marker types when estimates of male fertility are sought. A sample size 1.5-2.0 times greater is required for dominant markers under some conditions to obtain the same confidence in fertility estimates as for codominant markers, although with large sample sizes the fertility estimates are similar for either marker type. Since the number of dominant DN A markers is not limited in the same manner as is the number of codominant protein markers, one's confidence in the estimates can be increased above that possible from proteins by surveying additional loci. However, for a fixed sample size a trade-off exists between the number of progeny assayed per female and the number of loci surveyed. In many cases more progeny per female provide better estimates of fertility than more loci.     

Convergence to Normality of the Asymptotic Quasi‐Score Function on a Linear Model

The asymptotic quasi‐likelihood method is considered for the model y_t = f_t(θ) + M_t, t = 0,1, …,T where f_tθ) is a linear predictable process of the parameter of interest θ, M_t is a martingale difference, and the nature of E(M_t² | ℱ_t–1) is unknown. This paper is concerned with the limiting distribution of the asymptotic quasi‐score function of such a model. Confidence intervals and hypothesis testing of θ is derived from the limiting distribution. Comparison is made between the estimates obtained through this method and those obtained through the least squares method.     

Direct electrochemical oxidation of Clostridium pasteurianum ferredoxin: Identification of facile electron-transfer processes relevant to cluster degradation

Rapid oxidation processes relevant to the degradation of [4Fe4S] clusters in Clostridium pasteurianum ferredoxin were studied via direct (unmediated) heterogeneous electron transfer at a pyrolytic graphite electrode. Differential-pulse voltammograms of native [4Fe4S] ferredoxin showed two well-defined oxidation peaks corresponding to apparent E-values of +793 and +1120 mV at 5°C. Direct involvement of the cluster was established through parallel experiments with the 2[4Fe4Se] derivative for which peak positions were shifted. Square-wave voltammetry showed that the product of the first electron transfer, which may correspond to the ‘super-oxidised’ [4Fe4S]³⁺ oxidation level, undergoes rapid degradation (t_{$\text{1}\text{2}$} < 1.6 ms at 5°C). The second oxidation process, as characterised by a significant (?100 mV) negative shift upon selenium substitution, very likely represents oxidation of S(Se) still associated with the protein and possibly contained within the remaining FES(Se) substructure.     

Hidden Markov model analysis of intermediate gating steps associated with the pore gate of shaker potassium channels.

Cooperativity among the four subunits helps give rise to the remarkable voltage sensitivity of Shaker potassium channels, whose open probability changes tenfold for a 5-mV change in membrane potential. The cooperativity in these channels is thought to arise from a concerted structural transition as the final step in opening the channel. Recordings of single-channel ionic currents from certain other channel types, as well as our previous recordings from T442S mutant Shaker channels, however, display intermediate conductance levels in addition to the fully open and closed states. These sublevels might represent stepwise, rather than concerted, transitions in the final steps of channel activation. Here, we report a similar fine structure in the closing transitions of Shaker channels lacking the mutation. Describing the deactivation time course with hidden Markov models, we find that two subconductance levels are rapidly traversed during most closing transitions of chimeric, high conductance Shaker channels. The lifetimes of these levels are voltage-dependent, with maximal values of 52 and 22 micros at -100 mV, and the voltage dependences of transitions among these states suggest that they arise from equivalent conformational changes occurring in individual subunits. At least one subconductance level is found to be traversed in normal conductance Shaker channels. We speculate that voltage-dependent conformational changes in the subunits give rise to changes in a "pore gate" associated with the selectivity filter region of the channel, producing the subconductance states. As a control for the hidden Markov analysis, we applied the same procedures to recordings of the recovery from N-type inactivation in Shaker channels. These transitions are found to be instantaneous in comparison.     

A mathematical framework for inferring connectivity in probabilistic neuronal networks

We describe an approach for determining causal connections among nodes of a probabilistic network even when many nodes remain unobservable. The unobservable nodes introduce ambiguity into the estimate of the causal structure. However, in some experimental contexts, such as those commonly used in neuroscience, this ambiguity is present even without unobservable nodes. The analysis is presented in terms of a point process model of a neuronal network, though the approach can be generalized to other contexts. The analysis depends on the existence of a model that captures the relationship between nodal activity and a set of measurable external variables. The mathematical framework is sufficiently general to allow a large class of such models. The results are modestly robust to deviations from model assumptions, though additional validation methods are needed to assess the success of the results.     

使用估计的反应自由能预测组成性和可变剪接位点

基因结构预测中的一个重要步骤是精确地识别剪接位点。基于剪接反应的基本物理原则,最大信息原理被应用到剪接反应的理论分析中,进而导出了反应自由能估计表达式。作为一个简化模型,这个表达式能被用来估计一个5′剪接区或者3′剪接区所参与的剪接反应中的自由能变化。它不但较全面地概括了各个碱基之间的关联,而且还考虑了基因组背景概率的影响。这个反应自由能表达式被用来预测了人类基因中的组成性和可变剪接位点,预测结果是令人满意的,其预测能力比得上当前的一些流行方法。这说明最大信息原理可以作为研究某些核酸-蛋白质相互作用系统（如剪接反应）的理论出发点,导出的反应自由能表达式较好地符合了剪接反应过程。     

TECHNICAL ADVANCES: A maximum-likelihood relatedness estimator allowing for negative relatedness values

Previously reported maximum-likelihood pairwise relatedness (r) estimator of Thompson and Milligan (M) was extended to allow for negative r estimates under the regression interpretation of r. This was achieved by establishing the equivalency of the likelihoods used in the kinship program and the likelihoods of Thompson. The new maximum-likelihood (ML) estimator was evaluated by Monte Carlo simulations. It was found that the new ML estimator became unbiased significantly faster compared to the original M estimator when the amount of genotype information was increased. The effects of allele frequency estimation errors on the new and existing relatedness estimators were also considered.     

River islands,refugia and genetic structuring in the endemic brown frog Rana kukunoris (Anura,Ranidae) of the Qinghai‐Tibetan Plateau

Frequently, Pleistocene climatic cycling has been found to be the diver of genetic structuring in populations, even in areas that did not have continental ice sheets, such as on the Qinghai‐Tibetan Plateau (QTP). Typically, species distributed on the plateau have been hypothesized to re‐treat to south‐eastern refugia, especially during the Last Glacial Maximum (LGM). We evaluated sequence variation in the mitochondrial DNA gene Cytb and the nuclear DNA gene RAG‐1 in Rana kukunoris, a species endemic to the QTP. Two major lineages, N and S, were identified, and lineage N was further subdivided into N1 and N2. The geographical distribution and genealogical divergences supported the hypothesis of multiple refugia. However, major lineages and sublineages diverged prior to the LGM. Demographical expansion was detected only in lineage S and sublineage N2. Sublineage N1 might have survived several glacial cycles in situ and did not expand after the LGM because of the absence of suitable habitat; it survived in river islands. Genetic analysis and environment modelling suggested that the north‐eastern edge of QTP contained a major refugium for R. kukunoris. From here, lineage S dispersed southwards after the LGM. Two microrefugia in northern Qilian Mountains greatly contributed to current level of intraspecific genetic diversity. These results were found to have important implications for the habitat conservation in Northwest China.