贝叶斯统计在QTL作图中的应用研究进展

在许多复杂情况下, 贝叶斯统计方法比经典数理统计方法能更直接解决问题, 且可有效整合部分先验信息, 但其需要高强度计算的特性曾限制了其广泛应用。近几十年来, 随着高速计算机的发展以及MCMC算法的不断提出, 贝叶斯方法已被用于群体遗传学、分子进化、连锁作图和数量遗传学等研究领域, 文章综述了数量遗传学中QTL作图的贝叶斯方法从简单到复杂的发展历程。     

A Comparison of Three Weight-of-Evidence Approaches for Integrating Sediment Contamination Data within and Across Lines of Evidence

Multiple lines of evidence (LOE) are often considered when examining the potential impact of contaminated sediment. Three strategies are explored for combining information within and/or among different LOE. One technique uses a multivariate strategy for clustering sites into groups of similar impact. A second method employs meta-analysis to pool empirically derived P-values. The third method uses a quantitative estimation of probability derived from odds ratios. These three strategies are compared with respect to a set of data describing reference conditions and a contaminated area in the Great Lakes. Common themes in these three strategies include the critical issue of defining an appropriate set of reference/control conditions, the definition of impact as a significant departure from the normal variation observed in the reference conditions, and the use of distance from the reference distribution to define any of the effect measures. Reasons for differences in results between the three approaches are explored and strategies for improving the approaches are suggested.     

Evidential statistics as a statistical modern synthesis to support 21st century science

During the 20th century, population ecology and science in general relied on two very different statistical paradigms to solve its inferential problems: error statistics (also referred to as classical statistics and frequentist statistics) and Bayesian statistics. A great deal of good science was done using these tools, but both schools suffer from technical and philosophical difficulties. At the turning of the 21st century (Royall in Statistical evidence: a likelihood paradigm. Chapman & Hall, London, 1997 ; Lele in The nature of scientific evidence: statistical, philosophical and empirical considerations. The University of Chicago Press, Chicago, pp 191–216, 2004a ), evidential statistics emerged as a seriously contending paradigm. Drawing on and refining elements from error statistics, likelihoodism, Bayesian statistics, information criteria, and robust methods, evidential statistics is a statistical modern synthesis that smoothly incorporates model identification, model uncertainty, model comparison, parameter estimation, parameter uncertainty, pre-data control of error, and post-data strength of evidence into a single coherent framework. We argue that evidential statistics is currently the most effective statistical paradigm to support 21st century science. Despite the power of the evidential paradigm, we think that there is no substitute for learning how to clarify scientific arguments with statistical arguments. In this paper we sketch and relate the conceptual bases of error statistics, Bayesian statistics and evidential statistics. We also discuss a number of misconceptions about the paradigms that have hindered practitioners, as well as some real problems with the error and Bayesian statistical paradigms solved by evidential statistics.     

Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses

Throughout the last two decades, Bayesian statistical methods have proliferated throughout ecology and evolution. Numerous previous references established both philosophical and computational guidelines for implementing Bayesian methods. However, protocols for incorporating prior information, the defining characteristic of Bayesian philosophy, are nearly nonexistent in the ecological literature. Here, I hope to encourage the use of weakly informative priors in ecology and evolution by providing a ‘consumer's guide’ to weakly informative priors. The first section outlines three reasons why ecologists should abandon noninformative priors: 1) common flat priors are not always noninformative, 2) noninformative priors provide the same result as simpler frequentist methods, and 3) noninformative priors suffer from the same high type I and type M error rates as frequentist methods. The second section provides a guide for implementing informative priors, wherein I detail convenient ‘reference’ prior distributions for common statistical models (i.e. regression, ANOVA, hierarchical models). I then use simulations to visually demonstrate how informative priors influence posterior parameter estimates. With the guidelines provided here, I hope to encourage the use of weakly informative priors for Bayesian analyses in ecology. Ecologists can and should debate the appropriate form of prior information, but should consider weakly informative priors as the new ‘default’ prior for any Bayesian model.     

Bayesian statistical treatment of the fluorescence of AFLP bands leads to accurate genetic structure inference

Ever since the introduction of allozymes in the 1960s, evolutionary biologists and ecologists have continued to search for more powerful molecular markers to estimate important parameters such as effective population size and migration rates and to make inferences about the demographic history of populations, the relationships between individuals and the genetic architecture of phenotypic variation (Bensch & Akesson 2005; Bonin et al. 2007). Choosing a marker requires a thorough consideration of the trade-offs associated with the different techniques and the type of data obtained from them. Some markers can be very informative but require substantial amounts of start-up time (e.g. microsatellites), while others require very little time but are much less polymorphic. Amplified fragment length polymorphism (AFLP) is a firmly established molecular marker technique that falls in this latter category. AFLPs are widely distributed throughout the genome and can be used on organisms for which there is no a priori sequence information (Meudt & Clarke 2007). These properties together with their moderate cost and short start-up time have made them the method of choice for many molecular ecology studies of wild species (Bensch & Akesson 2005). However, they have a major disadvantage, they are dominant. This represents a very important limitation because many statistical genetics methods appropriate for molecular ecology studies require the use of codominant markers. In this issue, Foll et al. (2010) present an innovative hierarchical Bayesian method that overcomes this limitation. The proposed approach represents a comprehensive statistical treatment of the fluorescence of AFLP bands and leads to accurate inferences about the genetic structure of natural populations. Besides allowing a quasi-codominant treatment of AFLPs, this new method also solves the difficult problems posed by subjectivity in the scoring of AFLP bands.     

Erroneous behaviour of MixSIR, a recently published Bayesian isotope mixing model: a discussion of Moore & Semmens (2008)

The application of Bayesian methods to stable isotopic mixing problems, including inference of diet has the potential to revolutionise ecological research. Using simulated data we show that a recently published model MixSIR fails to correctly identify the true underlying dietary proportions more than 50% of the time and fails with increasing frequency as additional unquantified error is added. While the source of the fundamental failure remains elusive, mitigating solutions are suggested for dealing with additional unquantified variation. Moreover, MixSIR uses a formulation for a prior distribution that results in an opaque and unintuitive covariance structure.     

Bayesian approaches for the analysis of population genetic structure: an example from Platanthera leucophaea (Orchidaceae)

We describe four extensions to existing Bayesian methods for the analysis of genetic structure in populations: (i) use of beta distributions to approximate the posterior distribution of f and theta(B); (ii) use of an entropy statistic to describe the amount of information about a parameter derived from the data; (iii) use of the Deviance Information Criterion (DIC) as a model choice criterion for determining whether there is evidence for inbreeding within populations or genetic differentiation among populations; and (iv) use of samples from the posterior distributions for f and theta(B) derived from different data sets to determine whether the estimates are consistent with one another. We illustrate each of these extensions by applying them to data derived from previous allozyme and random amplified polymorphic DNA surveys of an endangered orchid, Platanthera leucophaea, and we conclude that differences in theta(B) from the two data sets may represent differences in the underlying mutational processes.     

The Bayesian "star paradox" persists for long finite sequences

The "star paradox" in phylogenetics is the tendency for a particular resolved tree to be sometimes strongly supported even when the data is generated by an unresolved ("star") tree. There have been contrary claims as to whether this phenomenon persists when very long sequences are considered. This note settles one aspect of this debate by proving mathematically that the chance that a resolved tree could be strongly supported stays above some strictly positive number, even as the length of the sequences becomes very large.     

Priors for the Bayesian star paradox

We show that the Bayesian star paradox, first proved mathematically by Steel and Matsen for a specific class of prior distributions, occurs in a wider context including less regular, possibly discontinuous, prior distributions.     

Bayesian Prediction Regions for the Extreme Order Statistics

In this paper, prediction bounds for the order statistics are dealt with. For this purpose, predictive distributions derived by Bayesian approach, are utilized. In particular, bounds for the smallest and the largest order statistics are set when a series of samples are drawn from exponential, Pareto and power function populations. These bounds assist in knowing the nature of these predicted statistics even without actually having the sample observations.     

长白山阔叶红松林表层土壤木本植物细根生物量及其空间分布

2008年在长白山北坡原始阔叶红松林内选择3块50 m×50 m样地,采用地统计学方法对表层土壤中木本植物细根生物量及其分布特征进行了定量研究.结果表明：3块样地0～20 cm土层中木本植物活细根生物量分别为3.195、1.930和2.058 t·hm^-2,死细根生物量分别为0.971、0.581和0.790 t·hm^-2,0～10 cm土层中,死、活细根生物量之间无显著相关关系,而10～20 cm土层中,二者呈显著正相关关系(r=0.352,P<0.05）,死、活细根生物量的实际变异函数大多符合球状理论模型.空间自相关引起的空间异质性占总空间异质性的百分比平均大于70%,各样地活、死细根生物量变程分别为5.2、14.6、9.8 m和4.3、20.4、20.1 m.采用贝叶斯统计方法对3块样地活细根生物量空间自相关范围进行估计的结果与地统计学方法的统计结果一致.     

Brief communication: A probabilistic approach to age estimation from infracranial sequences of maturation

Infracranial sequences of maturation are commonly used to estimate the age at death of nonadult specimens found in archaeological, paleoanthropological, or forensic contexts. Typically, an age assessment is made by comparing the degree of long‐bone epiphyseal fusion in the target specimen to the age ranges for different stages of fusion in a reference skeletal collection. While useful as a first approximation, this approach has a number of shortcomings, including the potential for “age mimicry,” being highly dependent on the sample size of the reference sample and outliers, not using the entire fusion distribution, and lacking a straightforward quantitative way of combining age estimates from multiple sites of fusion. Here we present an alternative probabilistic approach based on data collected on 137 individuals, ranging in age from 7‐ to 29‐years old, from a documented skeletal collection from Coimbra, Portugal. We then use cross validation to evaluate the accuracy of age estimation from epiphyseal fusion. While point estimates of age can, at least in some circumstances, be both accurate and precise based on the entire skeleton, or many sites of fusion, there will often be substantial error in these estimates when they derive from one or only a few sites. Because a probabilistic approach to age estimation from epiphyseal fusion is computationally intensive, we make available a series of spreadsheets or computer programs that implement the approach presented here. Am J Phys Anthropol 142:655–664, 2010. © 2010 Wiley‐Liss, Inc.     

High variation in developmental instability under non-normal developmental error: a Bayesian perspective

The developmental mechanisms behind developmental instability (DI) are only poorly understood. Nevertheless, fluctuating asymmetry (FA) is often used a surrogate for DI. Based on statistical arguments it is often assumed that individual levels of FA are only weakly associated with the underlying DI. Patterns in FA therefore need to be interpreted with caution, and should ideally be transformed into patterns in DI. In order to be able to achieve that, assumptions about the distribution of developmental errors must be made. Current models assume that errors during development are additive and independent such that they yield a normal distribution. The observation that the distribution of FA is often leptokurtic has been interpreted as evidence for between-individual variation in DI. This approach has led to unrealistically high estimates of between-individual variation in DI, and potentially incorrect interpretations of patterns in FA, especially at the individual level. Recently, it has been suggested that the high estimates of variation in DI may be biased upward because either developmental errors are log-normal or gamma distributed and/or low measurement resolution of FA. A proper estimation of the amount (and shape) of heterogeneity in DI is crucial for the interpretation of patterns in FA and their transformation into patterns in DI. Yet, incorrect model assumptions may render misleading inferences. We therefore develop a statistical model to evaluate the sensitivity of results under the normal error model against the two alternative distributions as well as to investigate the importance of low measurement resolution. An analysis of simulated and empirical data sets indicated that bias due to misspecification of the developmental error distribution can be substantial, yet, did not appear to reduce estimates of variation in DI in empirical data sets to a large extent. Effects of low measurement resolution were neglectable. The importance of these results are discussed in the context of the interpretation of patterns in FA.     

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf.     

A Bayesian mixture model for metaanalysis of microarray studies

The increased availability of microarray data has been calling for statistical methods to integrate findings across studies. A common goal of microarray analysis is to determine differentially expressed genes between two conditions, such as treatment vs control. A recent Bayesian metaanalysis model used a prior distribution for the mean log-expression ratios that was a mixture of two normal distributions. This model centered the prior distribution of differential expression at zero, and separated genes into two groups only: expressed and nonexpressed. Here, we introduce a Bayesian three-component truncated normal mixture prior model that more flexibly assigns prior distributions to the differentially expressed genes and produces three groups of genes: up and downregulated, and nonexpressed. We found in simulations of two and five studies that the three-component model outperformed the two-component model using three comparison measures. When analyzing biological data of Bacillus subtilis, we found that the three-component model discovered more genes and omitted fewer genes for the same levels of posterior probability of differential expression than the two-component model, and discovered more genes for fixed thresholds of Bayesian false discovery. We assumed that the data sets were produced from the same microarray platform and were prescaled.     

Quantifying population structure using the F-model

We review a model-based approach to estimate local population F(ST) 's that is based on the multinomial-Dirichlet distribution, the so-called F-model. As opposed to the standard method of estimating a single F(ST) value, this approach takes into account the fact that in most if not all realistic situations, local populations differ in their effective sizes and migration rates. Therefore, the use of this approach can help better describe the genetic structure of populations. Despite this obvious advantage, this method has remained largely underutilized by molecular ecologists. Thus, the objective of this review is to foster its use for studying the genetic structure of metapopulations. We present the derivation of the Bayesian formulation for the estimation of population-specific F(ST) 's based on the multinomial-Dirichlet distribution. We describe several recent applications of the F-model and present the results of a small simulation study that explains how the F-model can help better describe the genetic structure of populations.     

Local Adaptation and Genetics of Acid-Stress Tolerance in the Moor Frog, Rana arvalis

As potential to adapt to environmental stress can be essential for population persistence, knowledge on the genetic architecture of local adaptation is important for conservation genetics. We investigated the relative importance of additive genetic, dominance and maternal effects contributions to acid stress tolerance in two moor frog (Rana arvalis) populations originating from low and neutral pH habitats. Experiments with crosses obtained from artificial matings revealed that embryos from the acid origin population were more tolerant to low pH than embryos from the neutral origin population in embryonic survival rates, but not in terms of developmental stability, developmental and growth rates. Strong maternal effect and small additive genetic contributions to variation were detected in all traits in both populations. In general, dominance contributions to variance in different traits were of similar magnitude to the additive genetic effects, but dominance effects outweighed the additive genetic and maternal effects contributions to early growth in both populations. Furthermore, the expression of additive genetic variance was independent of pH treatment, suggesting little additive genetic variation in acid stress tolerance. The results suggest that although local genetic adaptation to acid stress has taken place, the current variation in acid stress tolerance in acidified populations may owe largely to non-genetic effects. However, low but significant heritabilities (h ² 0.07–0.22) in all traits – including viability itself – under a wide range of pH conditions suggests that environmental stress created by low pH is unlikely to lower moor frog populations' ability to respond to selection in the traits studied. Nevertheless, acid conditions could lower populations' ability to respond to selection in the long run through reduction in effective population size.