Enhancing Causal Assessment of Estuarine Fishkills Using Graphical Models

It is not possible to determine the causal relationship between fishkills and the toxic dinoflagellate Pfiesteria piscicida in the Neuse River Estuary, North Carolina, using observational data on these two variables alone. However, consideration of a third variable, indicating the presence of a broader class of more easily measured Pfiesteria-like organisms (PLOs), leads to causal model structures from which the nature of this relationship can be distinguished. We use reported field data to evaluate alternative models and find that the suggestion that toxic Pfiesteria cause fishkills is inconsistent with observation. The data are more indicative of a model in which PLOs (including potentially toxic Pfiesteria) are stimulated to become actively toxic by the presence of already dead or dying fish. Laboratory experiments performed to date do not provide evidence contradictory to this finding. However, neither can the existence of a common cause of both Pfiesteria toxicity and fishkills be ruled out. The differing implications for ecosystem management suggest that these causal associations should be further investigated through additional modeling and data collection efforts. Graphical methods of model construction and evaluation can assist in this process. Received 22 May 2002; accepted 3 October 2002.     

A New Statistical Goodness-of-Fit Test Based on Graphical Representation

A statistical goodness-of-fit test, based on representing the sample observations by linked vectors, is developed. The direction and the length of the linked vectors are defined as functions of the expected values of the order statistics and sample order statistics, respectively. The underlying method can be used to test distributional assumptions for any location-scale family. A test statistic Q_n is introduced and some of its properties are studied. It is shown that the proposed test can be generalized to test if two or more independent samples come from the same distribution. The test procedure provides a graphical method of identifying the true distribution when the null hypothesis is rejected.     

The Coalescent Process in Models with Selection

Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the ancestral frequency process can be approximated by a diffusion, then the mean and the variance of the number of segregating sites due to selectively neutral mutations in random samples can be numerically calculated. The calculations are greatly simplified if the frequencies of the alleles are tightly regulated. If the mutation rates between alleles maintained by balancing selection are low, then the number of selectively neutral segregating sites in a random sample of genes is expected to substantially exceed the number predicted under a neutral model.     

The Genealogy of Samples in Models with Selection

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman''s well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman''s coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models, DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.     

MSMBuilder: Statistical Models for Biomolecular Dynamics

MSMBuilder is a software package for building statistical models of high-dimensional time-series data. It is designed with a particular focus on the analysis of atomistic simulations of biomolecular dynamics such as protein folding and conformational change. MSMBuilder is named for its ability to construct Markov state models (MSMs), a class of models that has gained favor among computational biophysicists. In addition to both well-established and newer MSM methods, the package includes complementary algorithms for understanding time-series data such as hidden Markov models and time-structure based independent component analysis. MSMBuilder boasts an easy to use command-line interface, as well as clear and consistent abstractions through its Python application programming interface. MSMBuilder was developed with careful consideration for compatibility with the broader machine learning community by following the design of scikit-learn. The package is used primarily by practitioners of molecular dynamics, but is just as applicable to other computational or experimental time-series measurements.     

Dynamics of Genetic Variability in Two-Locus Models of Stabilizing Selection

We study a two locus model, with additive contributions to the phenotype, to explore the dynamics of different phenotypic characteristics under stabilizing selection and recombination. We demonstrate that the interaction of selection and recombination results in constraints on the mode of phenotypic evolution. Let V(g) be the genic variance of the trait and C(L) be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that, independent of the initial conditions, the dynamics of the system on the plane (V(g), C(L)) are typically characterized by a quick approach to a straight line with slow evolution along this line afterward. We analyze how the mode and the rate of phenotypic evolution depend on the strength of selection relative to recombination, on the form of fitness function, and the difference in allelic effect. We argue that if selection is not extremely weak relative to recombination, linkage disequilibrium generated by stabilizing selection influences the dynamics significantly. We demonstrate that under these conditions, which are plausible in nature and certainly the case in artificial stabilizing selection experiments, the model can have a polymorphic equilibrium with positive linkage disequilibrium that is stable simultaneously with monomorphic equilibria.     

肝糖代谢研究中的模型选择

在肝糖代谢的研究中,经常用到的模型有整体动物、离体灌流肝、精细肝切片、分离肝细胞、原代培养肝细胞、肝细胞株等,它们各有利弊又相互补充。通过介绍几种模型的制作要点并分析其特点与利弊,为糖代谢研究中实验手段的选择提供思路。     

Fluctuating Selection Models and Mcdonald-Kreitman Type Analyses

It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate the consequences of fluctuating selection pressures on the quantification of adaptive evolution using McDonald-Kreitman (MK) style approaches. In agreement with previous work, we show that fluctuating selection can generate evidence of adaptive evolution even when the expected strength of selection on a mutation is zero. However, we also find that the mutations, which contribute to both polymorphism and divergence tend, on average, to be positively selected during their lifetime, under fluctuating selection models. This is because mutations that fluctuate, by chance, to positive selected values, tend to reach higher frequencies in the population than those that fluctuate towards negative values. Hence the evidence of positive adaptive evolution detected under a fluctuating selection model by MK type approaches is genuine since fixed mutations tend to be advantageous on average during their lifetime. Never-the-less we show that methods tend to underestimate the rate of adaptive evolution when selection fluctuates.     

The Coalescent Process in Models with Selection and Recombination

The statistical properties of the process describing the genealogical history of a random sample of genes at a selectively neutral locus which is linked to a locus at which natural selection operates are investigated. It is found that the equations describing this process are simple modifications of the equations describing the process assuming that the two loci are completely linked. Thus, the statistical properties of the genealogical process for a random sample at a neutral locus linked to a locus with selection follow from the results obtained for the selected locus. Sequence data from the alcohol dehydrogenase (Adh) region of Drosophila melanogaster are examined and compared to predictions based on the theory. It is found that the spatial distribution of nucleotide differences between Fast and Slow alleles of Adh is very similar to the spatial distribution predicted if balancing selection operates to maintain the allozyme variation at the Adh locus. The spatial distribution of nucleotide differences between different Slow alleles of Adh do not match the predictions of this simple model very well.     

Thresholds in genotoxicity responses

It has been commonly accepted that risk assessments of genotoxic chemicals are based on linear extrapolation methods. However, there is substantial evidence that some chemicals may be genotoxic only at high doses by mechanisms that do not occur at low doses, or only under specific conditions in genotoxicity assays, but are inactive at concentrations within the range of human exposure levels. There are a variety of possible mechanisms of thresholded genotoxicity, including disruption of cell division and chromosome segregation, inhibition of DNA synthesis, overloading of oxidative defence mechanisms, metabolism or plasma binding capacity, disturbances of metal homeostasis, cytotoxicity and physiological perturbations in in vivo assays. The degrees of evidence supporting the proposed mechanisms are variable and not all are sufficiently robust to be universally accepted as yet by the scientific community. However, a survey of industrial companies indicated that data have been accepted by some regulatory authorities indicating thresholds contributing to genotoxicity responses.     

Investigating Polycyclic Aromatic Hydrocarbons Profiles in Higher Plants Using Statistical Models

Thirty-six higher plants sampled from Olomoro, Irri, Uzere, and Oginni exploration sites in the Niger Delta region of Nigeria were subjected to GC/MS analysis to assess the occurrence, distribution and profiles of polycyclic aromatic hydrocarbons (PAHs) contained in them. The Σ₂₈PAHs ranged from 335 to 3094 ng/g. The results of the nonparametric regression models showed that PAHs concentration in a plant cannot be used in isolation to deduce the total PAHs concentration in soils hosting the plant since PAHs concentration in a plant is influenced by the presence (or absence) of other plants in that location. A combination of Factor analysis (FA) and principal component analysis (PCA) were used to recognize PAHs concentration patterns among the plants in the studied locations and individual PAHs compounds. Woody annuals and perennial plants formed similar patterns in Oginni and Irri locations. Three main clusters were formed by all the compounds with naphthalene and 2-methylnaphthalene standing as outliers in all the four locations.

Supplemental materials are available for this article. Go to the publisher's online edition of International Journal of Phytoremediation to view the supplemental file.     

Comparison of Statistical Models for Analyzing Wheat Yield Time Series

The world''s population is predicted to exceed nine billion by 2050 and there is increasing concern about the capability of agriculture to feed such a large population. Foresight studies on food security are frequently based on crop yield trends estimated from yield time series provided by national and regional statistical agencies. Various types of statistical models have been proposed for the analysis of yield time series, but the predictive performances of these models have not yet been evaluated in detail. In this study, we present eight statistical models for analyzing yield time series and compare their ability to predict wheat yield at the national and regional scales, using data provided by the Food and Agriculture Organization of the United Nations and by the French Ministry of Agriculture. The Holt-Winters and dynamic linear models performed equally well, giving the most accurate predictions of wheat yield. However, dynamic linear models have two advantages over Holt-Winters models: they can be used to reconstruct past yield trends retrospectively and to analyze uncertainty. The results obtained with dynamic linear models indicated a stagnation of wheat yields in many countries, but the estimated rate of increase of wheat yield remained above 0.06 t ha⁻¹ year⁻¹ in several countries in Europe, Asia, Africa and America, and the estimated values were highly uncertain for several major wheat producing countries. The rate of yield increase differed considerably between French regions, suggesting that efforts to identify the main causes of yield stagnation should focus on a subnational scale.     

The Maintenance of Genetic Variability in Two-Locus Models of Stabilizing Selection

The maintenance of genetic variability at two diallelic loci under stabilizing selection is investigated. Generations are discrete and nonoverlapping; mating is random; mutation and random genetic drift are absent; selection operates only through viability differences. The determination of the genotypic values is purely additive. The fitness function has its optimum at the value of the double heterozygote and decreases monotonically and symmetrically from its optimum, but is otherwise arbitrary. The resulting fitness scheme is identical to the symmetric viability model. Linkage disequilibrium is neglected, but the results are otherwise exact. Explicit formulas are found for all the equilibria, and explicit conditions are derived fro their existence and stability. A complete classification of the six possible global convergence patterns is presented. In addition to the symmetric equilibrium (with gene frequency 1/2 at both loci), a pair of unsymmetric equilibria may exist; the latter are usually, but not always, unstable. If the ratio of the effect of the major locus to that of the minor one exceeds a critical value, both loci will be stably polymorphic. If selection is weak at the minor locus, the more rapidly the fitness function decreases near the optimum, the lower is this critical value; for rapidly decreasing fitness functions, the critical value is close to one. If the fitness function is smooth at the optimum, then a stable polymorphism exists at both loci only if selection is strong at the major locus.     

Adaptive Topography in Fertility-Viability Selection Models: The Haplodiploid Case

A linear combination of partial changes of mean fitnesses from one generation to the next one is shown to be approximately equal to the additive genetic variance in fitness after enough generations and away from equilibrium in random mating haplodiploid populations under arbitrary weak frequency-dependent selection on sex-differentiated viability of individuals and sex-differentiated fertility of matings controlled at a single multiallelic locus. The result can be applied to X-linked locus models in diploid populations. The result is used to deduce approximate adaptive topographies far frequency-independent selection models in the cases of nonsex-differentiated fertilities and multiplicative sex-differentiated fertilities and for kin selection models in family-structured populations under the assumptions of single insemination and multiple insemination of females. Multiple insemination creates frequency-dependent selection regimes.     

Models of Frequency-Dependent Selection with Mutation from Parental Alleles

Frequency-dependent selection (FDS) remains a common heuristic explanation for the maintenance of genetic variation in natural populations. The pairwise-interaction model (PIM) is a well-studied general model of frequency-dependent selection, which assumes that a genotype’s fitness is a function of within-population intergenotypic interactions. Previous theoretical work indicated that this type of model is able to sustain large numbers of alleles at a single locus when it incorporates recurrent mutation. These studies, however, have ignored the impact of the distribution of fitness effects of new mutations on the dynamics and end results of polymorphism construction. We suggest that a natural way to model mutation would be to assume mutant fitness is related to the fitness of the parental allele, i.e., the existing allele from which the mutant arose. Here we examine the numbers and distributions of fitnesses and alleles produced by construction under the PIM with mutation from parental alleles and the impacts on such measures due to different methods of generating mutant fitnesses. We find that, in comparison with previous results, generating mutants from existing alleles lowers the average number of alleles likely to be observed in a system subject to FDS, but produces polymorphisms that are highly stable and have realistic allele-frequency distributions.     

Statistical Power of Model Selection Strategies for Genome-Wide Association Studies

Genome-wide association studies (GWAS) aim to identify genetic variants related to diseases by examining the associations between phenotypes and hundreds of thousands of genotyped markers. Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level. Although a number of model selection methods have been proposed in the literature, including marginal search, exhaustive search, and forward search, their relative performance has only been evaluated through limited simulations due to the lack of an analytical approach to calculating the power of these methods. This article develops a novel statistical approach for power calculation, derives accurate formulas for the power of different model selection strategies, and then uses the formulas to evaluate and compare these strategies in genetic model spaces. In contrast to previous studies, our theoretical framework allows for random genotypes, correlations among test statistics, and a false-positive control based on GWAS practice. After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models. For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy. An example is provided for the application of our approach to empirical research. The statistical approach used in our derivations is general and can be employed to address the model selection problems in other random predictor settings. We have developed an R package markerSearchPower to implement our formulas, which can be downloaded from the Comprehensive R Archive Network (CRAN) or http://bioinformatics.med.yale.edu/group/.     

Estimating Material and Energy Flows in Life Cycle Inventory with Statistical Models

Data (un)availability and uncertainty are recurring problems in life cycle assessment, and particularly inventory analysis. Advances in life cycle inventory have focused on the propagation and management of uncertainty, but this article addresses the question of how to account for unavailable data and corresponding uncertainty. Large and complicated systems often lack complete data due to confidential practices or the efforts required in the data collection process. Electricity production with multiple processes generating a single product is a classic example. Instead of the conventional process‐based models to estimate missing data, the approach developed in this article divides systems based on functionally equivalent objects. Each one of these objects is then described in terms of characteristic variables, such as power capacity. Kriging, a flexible statistical estimator, allows for the estimation of unknown material and energy flows based on the objects’ characteristic variables. Both univariate and multivariate kriging are tested and compared to regression analysis. It is found that kriging performs better than linear regression, according to the mean absolute error criterion. Multivariate kriging provides an even more accurate joint estimation method to bridge data gaps scattered across inventories and when observable values of material and energy flows differ from one object to the next. Parameters of the underlying models are interpreted in terms of data uncertainty.     

Statistical Methods for Using Nonlinear Models to Compare Silage Treatments

Statistical methods are described which can be used to compare treatments where the response is described by a nonlinear model. The nonlinear analysis of covariance is described for a one-way treatment structure and a two-way treatment structure. Methods for constructing confidence bands about a model and about the difference of two models are described. Examples involving the dynamics of silage fermentation are used to demonstrate the methods.