Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.
We present a new parameterization of physiological epistasis that allows the measurement of epistasis separate from its effects on the interaction (epistatic) genetic variance component. Epistasis is the deviation of two-locus genotypic values from the sum of the contributing single-locus genotypic values. This parameterization leads to statistical tests for epistasis given estimates of two-locus genotypic values such as can be obtained from quantitative trait locus studies. The contributions of epistasis to the additive, dominance and interaction genetic variances are specified. Epistasis can make substantial contributions to each of these variance components. This parameterization of epistasis allows general consideration of the role of epistasis in evolution by defining its contribution to the additive genetic variance. ...
Microsatellite loci mutate at an extremely high rate and are generally thought to evolve through a stepwise mutation model. Several differentiation statistics taking into account the particular mutation scheme of the microsatellite have been proposed. The most commonly used is R(ST) which is independent of the mutation rate under a generalized stepwise mutation model. F(ST) and R(ST) are commonly reported in the literature, but often differ widely. Here we compare their statistical performances using individual-based simulations of a finite island model. The simulations were run under different levels of gene flow, mutation rates, population number and sizes. In addition to the per locus statistical properties, we compare two ways of combining R(ST) over loci. Our simulations show that even under a strict stepwise mutation model, no statistic is best overall. All estimators suffer to different extents from large bias and variance. While R(ST) better reflects population differentiation
Author Summary In genome-wide association studies, the multiple testing problem and confounding due to population stratification have been intractable issues. Family-based designs have considered only the transmission of genotypes from founder to nonfounder to prevent sensitivity to the population stratification, which leads to the loss of information. Here we propose a novel analysis approach that combines mutually independent FBAT and screening statistics in a robust way. The proposed method is more powerful than any other, while it preserves the complete robustness of family-based association tests, which only achieves much smaller power level. Furthermore, the proposed method is virtually as powerful as population-based approaches/designs, even in the absence of population stratification. By nature of the proposed method, it is always robust as long as FBAT is valid, and the proposed method achieves the optimal efficiency if our linear model for screening test reasonably explains the observed data
The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When mutation rate is positive, the Markov chain modeling an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution, yet, rather little is known about the stationary distribution. On the other hand, knowing the stationary distribution may provide some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population genetics to assess whats called a ``genetic load (see the introduction for more details). In this talk I will show how the quotient construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the ...
The objective of this study was to estimate genetic parameters for weekly body weight of feed intake of individually fed beef bulls at centralized testing stations in South Africa using random regression models (RRM). The model for cumulative feed intake included the fixed linear regression on third order orthogonal Legendre polynomials of the actual days on test (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 and 84 day) for starting age group and contemporary group effects. Random regressions on third order orthogonal Legendre polynomials were included for the additive genetic effect of the animal and the additional random effect of weaning-herd-year (WHY) and on fourth order for the additional random permanent environmental effect of the animal. The model for body weights included the fixed linear regression on fourth order orthogonal Legendre polynomials of the actual days on test for starting age group and contemporary group effects. Random regressions on fourth order orthogonal Legendre ...
View Notes - Slides7_v1 from ECON 404 at University of Michigan. Sampling Distributions Utku Suleymanoglu UMich Utku Suleymanoglu (UMich) Sampling Distributions 1 / 21 Introduction Population
In 1994, Muse & Gaut (MG) and Goldman & Yang (GY) proposed evolutionary models that recognize the coding structure of the nucleotide sequences under study, by defining a Markovian substitution process with a state space consisting of the 61 sense codons (assuming the universal genetic code). Several variations and extensions to their models have since been proposed, but no general and flexible framework for contrasting the relative performance of alternative approaches has yet been applied. Here, we compute Bayes factors to evaluate the relative merit of several MG- and GY-style of codon substitution models, including recent extensions acknowledging heterogeneous nonsynonymous rates across sites, as well as selective effects inducing uneven amino acid or codon preferences. Our results on three real data sets support a logical model construction following the MG formulation, allowing for a flexible account of global amino acid or codon preferences, while maintaining distinct parameters governing overall
A key question in molecular evolutionary biology concerns the relative roles of mutation and selection in shaping genomic data. Moreover, features of mutation and selection are heterogeneous along the genome and over time. Mechanistic codon substitution models based on the mutation-selection framework are promising approaches to separating these effects. In practice, however, several complications arise, since accounting for such heterogeneities often implies handling models of high dimensionality (e.g., amino acid preferences), or leads to across-site dependence (e.g., CpG hypermutability), making the likelihood function intractable. Approximate Bayesian Computation (ABC) could address this latter issue. Here, we propose a new approach, named Conditional ABC (CABC), which combines the sampling efficiency of MCMC and the flexibility of ABC. To illustrate the potential of the CABC approach, we apply it to the study of mammalian CpG hypermutability based on a new mutation-level parameter implying
We have demonstrated that a simple one-locus two-allele model of genomic imprinting produces large differences in predictions for additive (Table 2) and dominance terms from a number of standard approaches for partitioning the genotypic value of an individual. These approaches are equivalent in the absence of imprinting under standard Mendelian expression (where heterozygotes have equivalent genotypic values and hence k1 = k2). Although all approaches give identical total genetic variance, there are differences in the partitioning of the genetic variance into additive, dominance and covariance terms (Table 3).. The major differences in the approaches arise due to differences in how breeding values and additive effects are defined. Approaches 1 and 2b incorporate both sex- and generation-dependent terms, and breeding values are equivalent for these approaches (Table 2). However, Approaches 2a and the regression methods (Approaches 3a and 3b) are unable to partition separate male and female terms. ...
A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exist no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present likelihood methods to estimate selection intensity under k-allele models with overdominance.;The stationary distribution of allele frequencies under a variety of Wright-Fisher k-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of parameters under these models are not well understood. We show that under each of these models, there is a point in data space which carries the strongest possible signal for selection, yet, at this point, the likelihood is unbounded. This result remains valid even if all of the mutation parameters are assumed to be known. Therefore, ...
For this problem, we know $p=0.43$ and $n=50$. First, we should check our conditions for the sampling distribution of the sample proportion.. \(np=50(0.43)=21.5\) and \(n(1-p)=50(1-0.43)=28.5\) - both are greater than 5.. Since the conditions are satisfied, $\hat{p}$ will have a sampling distribution that is approximately normal with mean \(\mu=0.43\) and standard deviation [standard error] \(\sqrt{\dfrac{0.43(1-0.43)}{50}}\approx 0.07\).. \begin{align} P(0.45,\hat{p},0.5) &=P\left(\frac{0.45-0.43}{0.07}, \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}},\frac{0.5-0.43}{0.07}\right)\\ &\approx P\left(0.286,Z,1\right)\\ &=P(Z,1)-P(Z,0.286)\\ &=0.8413-0.6126\\ &=0.2287\end{align}. Therefore, if the true proportion of American who own an iPhone is 43%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 50.. ...
Although complex diseases and traits are thought to have multifactorial genetic basis, the common methods in genome-wide association analyses test each variant for association independent of the others. This computational simplification may lead to reduced power to identify variants with small effect sizes and requires correcting for multiple hypothesis tests with complex relationships. However, advances in computational methods and increase in computational resources are enabling the computation of models that adhere more closely to the theory of multifactorial inheritance. Here, a Bayesian variable selection and model averaging approach is formulated for searching for additive and dominant genetic effects. The approach considers simultaneously all available variants for inclusion as predictors in a linear genotype-phenotype mapping and averages over the uncertainty in the variable selection. This leads to naturally interpretable summary quantities on the significances of the variants and their ...
Biological systems are resistant to perturbations caused by the environment and by the intrinsic noise of the system. Robustness to mutations is a particular aspect of robustness in which the phenotype is resistant to genotypic variation. Mutational robustness has been linked to the ability of the system to generate heritable genetic variation (a property known as evolvability). It is known that greater robustness leads to increased evolvability. Therefore, mechanisms that increase mutational robustness fuel evolvability. Two such mechanisms, molecular chaperones and gene duplication, have been credited with enormous importance in generating functional diversity through the increase of systems robustness to mutational insults. However, the way in which such mechanisms regulate robustness remains largely uncharacterized. In this review, I provide evidence in support of the role of molecular chaperones and gene duplication in innovation. Specifically, I present evidence that these mechanisms ...
We prove a result concerning the joint distribution of alleles at linked loci on a chromosome drawn from the population at stationarity. For a neutral locus, the allele is a draw from the stationary distribution of the mutation process. Furthermore, this allele is independent of the alleles at different loci on any chromosomes in the population.. ...
View Notes - Normal rvs_bb from BUS 45730 at Carnegie Mellon. THE NORMAL DISTRIBUTION, OTHER CONTINUOUS DISTRIBUTIONS, AND SAMPLING DISTRIBUTION 1. In its standardized form, the normal distribution
It is demonstrated that the structured coalescent model can readily be extended to include phenomena such as partial selfing and background selection through the use of an approximation based on separation of time scales. A model that includes these phenomena, as well as geographic subdivision and linkage to a polymorphism maintained either by local adaptation or by balancing selection, is derived, and the expected coalescence time for a pair of genes is calculated. It is found that background selection reduces coalescence times within subpopulations and allelic classes, leading to a high degree of apparent differentiation. Extremely high levels of subpopulation differentiation are also expected for regions of the genome surrounding loci important in local adaptation. These regions will be wider the stronger the local selection, and the higher the selfing rate. ...
Use our video lessons and quizzes to learn about sampling distributions. Each lesson breaks down a concept into bite-sized pieces to help you...
Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the ...
The dominant character of leaf size varies with different genetic models and leaf positions. In Model 1, the dominant characters of top and lower leaves are small size, but for the middle leaves it is large size. In Model 2, large size is dominant for three types of leaves. In Model 3, small size is dominant for the top and middle leaves, but recessive for lower leaves. In Model 4, small size is dominant in the top and lower leaves, but recessive in the middle leaves (Table 6). Therefore, we can not conclude and illustrate the inheritance of leaf size for tobacco leaves. Leaf size was determined by genetics and environment (Gurevitch, 1992); hence it may be suitable to illustrate the genetic mechanism for leaf size in a fixed position of single leaf, or increase the number of planted locations to increase the generational mean. This would allow us to estimate the effect of genetic-environmental interaction and understand the inheritance of leaf size.. Genetic Models and Inheritance of Leaf ...
In this work, we built a pipeline, extTADA, for the integrated Bayesian analysis of DN mutations and rare CC variants to infer rare-variant genetic architecture parameters and identify risk genes. We applied extTADA to data available for SCZ and four other NDDs (Additional file 1: Figure S1).. The extTADA pipeline extTADA is based on previous work in autism sequencing studies, TADA [16, 31]. It conducts a full Bayesian analysis of a simple rare-variant genetic architecture model and it borrows information across all annotation categories and DN and CC samples in genetic parameter inference, which is critical for sparse rare-variant sequence data. Using MCMC, extTADA samples from the joint posterior density of risk-gene proportion and mean relative risk parameters, and provides gene-level disease-association BFs, PPs, and FDRs. We hope that extTADA (https://github.com/hoangtn/extTADA) will be generally useful for rare-variant analyses across complex traits. extTADA can be used for rare CC variant ...
Background: Localization of complex traits by genetic linkage analysis may involve exploration of a vast multidimensional parameter space. The posterior probability of linkage (PPL), a class of statistics for complex trait genetic mapping in humans, is designed to model the trait model complexity represented by the multidimensional parameter space in a mathematically rigorous fashion. However, the method requires the evaluation of integrals with no functional form, making it difficult to compute, and thus further test, develop and apply. This paper describes MLIP, a multiprocessor two-point genetic linkage analysis system that supports statistical calculations, such as the PPL, based on the full parameter space implicit in the linkage likelihood. Results: The fundamental question we address here is whether the use of additional processors effectively reduces total computation time for a PPL calculation. We use a variety of data - both simulated and real - to explore the question how close can ...
Legendre, Thomas (2017) Blaise. The Moth, 31 (Winter). pp. 8-11. Legendre, Thomas (2017) Great falls. The Curlew, Populus . pp. 38-45. Legendre, Thomas (2017) John McEnroes omelet. Copper Nickel, 24 . Legendre, Thomas (2016) Ultraviolet. Superstition Review, 18 . ISSN 1938-324X Legendre, Thomas (2016) Tenure tracks. Columbia Journal . Legendre, Thomas (2016) Ghostly desires in Edith Whartons Miss Mary Pask. Journal of the Short Story in English . ISSN 1969-6108 (In Press) Legendre, Thomas (2011) Landscape-mindscape: writing in Scotlands prehistoric future. Scottish Literary Review, 3 (2). pp. 121-132. ISSN 1756-5634 ...
For any statistical analysis, Model selection is necessary and required. In many cases of selection, Bayes factor is one of the important basic elements. For the unilateral hypothesis testing problem, we extend the harmony of frequency and Bayesian evidence to the generalized p-value of unilateral hypothesis testing problem, and study the harmony of generalized P-value and posterior probability of original hypothesis. For the problem of single point hypothesis testing, the posterior probability of the Bayes evidence under the traditional Bayes testing method, that is, the Bayes factor or the single point original hypothesis is established, is analyzed, a phenomenon known as the Lindley paradox, which is at odds with the classical frequency evidence of p-value. At this point, many statisticians have been worked for this from both frequentist and Bayesian perspective. In this paper, I am going to focus on Bayesian approach to model selection, starting from Bayes factors and going within Lindley Paradox,
In JMP Genomics, the Relationship Matrix analysis is used for computing and displaying relatedness among lines. The Relationship Matrix tool estimates the relationships among the lines using marker data, rather than pedigree information (Kinship Matrix tool), and computes the relationship measures directly while also accounting for selection and genetic drift. The Relationship Matrix computes one of three options: Identity-by-Descent, Identity-by-State, or Allele-Sharing-Similarity. Output from this procedure can serve as the K matrix, representing familial relatedness, in a Q-K mixed model. This post will focus on the Relationship Matrix using a data set containing 343 rice lines with 8,336 markers.
Neutron spin rotation is expected from quark-quark weak interactions in the Standard Model, which induce weak interactions among nucleons that violate parity.
Overview press publications with toplists of bulls. The file with breeding values of sire opens when clicking on download. The lists are sorted according to NVI with the exception of the beef merit index. Sire that are not included in the toplists can be found with the function Sire Search.. Information on the publication. For information about the publication, see News. The national toplists contains breeding values based on Dutch/Flemish daughter information. The Interbull toplists contains converted breeding values based on information from abroad. The genomic toplists contains breeding values based on pedigree information combined with genomic information. The combined toplists contains the top 500 bulls on NVI-base from the described list ...
3. The last point we discussed, which is maybe the most interesting, is the issue of the infinitesimal model. The infinitesimal model, originated by Fisher, assumes that contributions to the genetic variance are additive, relatively small and coming from many loci. The multiplication of QTL studies and other genomic approaches this last years has led to numerous discussions questioning this model, assuming that the reason for the lack of evidence for phenotypic traits controlled by few loci was more or less technological. We have ourselves discussed this issue in this very blog including when studies about human height and some QTLs found to explain just a few percents of variation. Well in light of this article it seems that it is again the case in drosophila, as control for height is seems to be largely polygenic, and the estimates presented here are even a low estimate as the methodology used is quite conservative (polymorphisms with population frequencies under 10% were not even analyzed ...
The complex correlation structure of a collection of orthologous DNA sequences is uniquely captured by the ancestral recombination graph (ARG), a complete record of coalescence and recombination events in the history of the sample. However, existing methods for ARG inference are computationally in …
Lahrouz, A. and Omari, L. (2013) Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence. Statistics & Probability Letters, 83, 960-968.
I started this guide with a problem that gives conventional statistics extreme difficulty but is strikingly simple for Bayesian analysis: Conventional statistics do not allow researchers to make claims about one of the models being tested (sometimes the only model). This inferential asymmetry is toxic to interpreting research results. Bayes factors solve the problem of inferential asymmetry by treating all models equally, and have many other benefits: 1) No penalty for optional stopping or multiple comparisons. Collect data until you feel like stopping or run out of money and make as many model comparisons as you like; 2) Bayes factors give directly interpretable outputs. A Bayes factor means the same thing whether n is 10 or 10,000, and whether we compared 2 or 20 models. A credible interval ranging from .38 to .94 means that we should believe with 95% certainty that the true value lies in that range. 3) Prior probability distributions allow researchers to intimately connect their theories to ...
We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.. ...
The deviance is profiled with respect to the fixed-effects parameters but not with respect to sigma; that is, the function takes parameters for the variance-covariance parameters and for the residual standard deviation. The random-effects variance-covariance parameters are on the standard deviation/correlation scale, not the theta (Cholesky factor) scale.
Populations diverge from each other as a result of evolutionary forces such as genetic drift, natural selection, mutation, and migration. For certain types of genetic markers, and for single-nucleotide polymorphisms (SNPs), in particular, it is reasonable to presume that genotypes at most loci are selectively neutral. Because demographic parameters (e.g. population size and migration rates) are common across all loci, locus-specific variation, which can be measured by Wrights FST, will depart from a common mean only for loci with unusually high/low rate of mutation or for loci closely associated with genomic regions having a substantial effect on fitness. We propose two alternative Bayesian hierarchical-beta models to estimate locus-specific effects on FST. To detect loci for which locus-specific effects are not well explained by the common FST, we use the Kullback-Leibler divergence measure (KLD) to measure the divergence between the posterior distributions of locus-specific effects and the common FST
CiteSeerX - Scientific documents that cite the following paper: On the Asymptotic Distribution of the Moran I Test Statistic with Applications
Genetic algorithms (GA) are a computational paradigm inspired by the mechanics of natural evolution, including survival of the fittest, reproduction, and mutation. Surprisingly, these mechanics can be used to solve (i.e. compute) a wide range of practical problems, including numeric problems. Concrete examples illustrate how to encode a problem for solution as a genetic algorithm, and help explain why genetic algorithms work. Genetic algorithms are a popular line of current research, and there are many references describing both the theory of genetic algorithms and their use in practical problem solving ...
Math has an impact on just about every aspect of our lives including some that we dont often think about. Math helped change the outcome of WWII, it also shows up in the way we drive our cars and the way we manage our finances. In celebration of Math Awareness Month, here are four TI-Nspire activities to use in your classes - whether you teach algebra, calculus or statistics. 1: German Tanks: Exploring Sampling Distributions. In this activity, your students will be challenged with the same problem the WWII Allies generals had: How do you determine how many German tanks there are? In WWII, the statisticians working for the Allies used sample statistics and sampling distributions to help determine the number of German tanks. Students explore different sample statistics and use simulation to develop a statistic that is effective in approximating the maximum number in a population. ...
Mode: for a discrete random variable, the value with highest probability (the location at which the probability mass function has its peak); for a continuous random variable, the location at which the probability density function has its peak ...
We present SumHer, software for estimating confounding bias, SNP heritability, enrichments of heritability and genetic correlations using summary statistics from genome-wide association studies. The key difference between SumHer and the existing software LD Score Regression (LDSC) is th...read more ...
An organisms genome is continually being alteredby mutations, the vast majority of which are harmful to the organism or its descendants, because they reduce the bearers viability or fertility
Nucleotide substitution in both coding and noncoding regions is context-dependent, in the sense that substitution rates depend on the identity of neighboring bases. Context-dependent substitution has been modeled in the case of two sequences and an unrooted phylogenetic tree, but it has only been ac …
This paper derives (by a new method) an equation due to Macdonald for determining the zeros of the associated Legendre functions of order m and non-integral degree n when the argument is close to -1. A closed form solution is obtained for the values of Q subscript n superscript m (mu) and Q subscript n superscript -m (mu) for mu close to 1. Certain observations are made concerning errors in a recently published article.(*RADAR CROSS SECTIONS
My main disagreement with the authors is over their use of confirmatory/exploratory as the distinction between analyses that have been planned, and preferably preregistered, and those that are exploratory. Its a vital distinction, of course, but confirmatory, while a traditional and widely-used term, does not capture well the intended meaning. Confirmatory vs exploratory probably originates with the two approaches to using factor analysis. It could make sense to follow an exploratory FA that identified a promising factor structure with a test of that now-prespecified structure with a new set of data. That second test might reasonably be labelled confirmatory of that structure, although the data could of course cast doubt on rather than confirm the FA model under test.. By contrast, a typical preregistered investigation, in which the research questions and the corresponding data analysis are fully planned, asks questions about the sizes of effects. It estimates effect sizes rather than seeks ...
TY - JOUR. T1 - A quantitative genetic model for mixed diploid and triploid hybrid progenies in tree breeding and evolution. AU - Wu, Rongling. PY - 1995/4/1. Y1 - 1995/4/1. N2 - Interspecific hybridization has played a critical role in tree evolution and breeding. The findings of triploidy in forest trees stimulate the development of a quantitative genetic model to estimate the nature of gene action. The model is based on clonally replicated triploid progenies derived from a two-level population and individual-within-population mating design in which offspring have a double dose of alleles from the parent and a single dose of alleles from the other parent. With the same genetic assumptions of a diploid model, except non-Mendelian behavior at meiosis, and the experimental variances estimated from a linear statistical model, total genetic variances in the triploid progenies are separated into additive, dominance, and epistatic components. In addition, by combining the new model with the already ...
Looking for online definition of polygenic inheritance in the Medical Dictionary? polygenic inheritance explanation free. What is polygenic inheritance? Meaning of polygenic inheritance medical term. What does polygenic inheritance mean?
Genome-wide expression profiling using microarrays or sequence-based technologies allows us to identify genes and genetic pathways whose expression patterns influence complex traits. Different methods to prioritize gene sets, such as the genes in a given molecular pathway, have been described. In many cases, these methods test one gene set at a time, and therefore do not consider overlaps among the pathways. Here, we present a Bayesian variable selection method to prioritize gene sets that overcomes this limitation by considering all gene sets simultaneously. We applied Bayesian variable selection to differential expression to prioritize the molecular and genetic pathways involved in the responses to Escherichia coli infection in Danish Holstein cows. We used a Bayesian variable selection method to prioritize Kyoto Encyclopedia of Genes and Genomes pathways. We used our data to study how the variable selection method was affected by overlaps among the pathways. In addition, we compared our approach to
In population genetics, linkage disequilibrium is the non-random association of alleles at different loci in a given population. Loci are said to be in linkage disequilibrium when the frequency of association of their different alleles is higher or lower than what would be expected if the loci were independent and associated randomly.[1]. Linkage disequilibrium is influenced by many factors, including selection, the rate of recombination, the rate of mutation, genetic drift, the system of mating, population structure, and genetic linkage. As a result, the pattern of linkage disequilibrium in a genome is a powerful signal of the population genetic processes that are structuring it.. In spite of its name, linkage disequilibrium may exist between alleles at different loci without any genetic linkage between them and independently of whether or not allele frequencies are in equilibrium (not changing with time).[1] Furthermore, linkage disequilibrium is sometimes referred to as gametic phase ...
The stepwise mutation model (SMM) is a mathematical theory, developed by Motoo Kimura and Tomoko Ohta, that allows for investigation of the equilibrium distribution of allelic frequencies in a finite population where neutral alleles are produced in step-wise fashion. The original model assumes that if an allele has a mutation that causes it to change in state, mutations that occur in repetitive regions of the genome will increase or decrease by a single repeat unit at a fixed rate (i.e. by the addition or subtraction of one repeat unit per generation) and these changes in allele states are expressed by an integer (. . . A-1, A, A1, .. .). The model also assumes random mating and that all alleles are selectively equivalent for each locus. The SMM is distinguished from the Kimura-Crow model, also known as the infinite alleles model (IAM), in that as the population size increases to infinity, while the product of the Ne (effective population size) and the mutation rate is fixed, the mean number of ...
The coalescent process is a widely used approach for inferring the demographic history of a population, from samples of its genetic diversity. Several parametric and non-parametric coalescent inference methods, involving Markov chain Monte Carlo, Gaussian processes, and other algorithms, already exist. However, these techniques are not always easy to adapt and apply, thus creating a need for alternative methodologies. We introduce the Bayesian Snyder filter as an easily implementable and flexible minimum mean square error estimator for parametric demographic functions on fixed genealogies. By reinterpreting the coalescent as a self-exciting Markov process, we show that the Snyder filter can be applied to both isochronously and heterochronously sampled datasets. We analytically solve the filter equations for the constant population size Kingman coalescent, derive expressions for its mean squared estimation error, and estimate its robustness to prior distribution specification. For populations with
The distribution of fitness effects (DFE) encompasses the fraction of deleterious, neutral, and beneficial mutations. It conditions the evolutionary trajectory of populations, as well as the rate of adaptive molecular evolution (alpha). Inferring DFE and a from patterns of polymorphism, as given through the site frequency spectrum (SFS) and divergence data, has been a longstanding goal of evolutionary genetics. A widespread assumption shared by previous inference methods is that beneficial mutations only contribute negligibly to the polymorphism data. Hence, a DFE comprising only deleterious mutations tends to be estimated from SFS data, and alpha is then predicted by contrasting the SFS with divergence data from an outgroup. We develop a hierarchical probabilistic framework that extends previous methods to infer DFE and alpha from polymorphism data alone. We use extensive simulations to examine the performance of our method. While an outgroup is still needed to obtain an unfolded SFS, we show ...
Model violations constitute the major limitation in inferring accurate phylogenies. Characterizing properties of the data that are not being correctly handled by current models is therefore of prime importance. One of the properties of protein evolution is the variation of the relative rate of substitutions across sites and over time, the latter is the phenomenon called heterotachy. Its effect on phylogenetic inference has recently obtained considerable attention, which led to the development of new models of sequence evolution. However, thus far focus has been on the quantitative heterogeneity of the evolutionary process, thereby overlooking more qualitative variations. We studied the importance of variation of the site-specific amino-acid substitution process over time and its possible impact on phylogenetic inference. We used the CAT model to define an infinite mixture of substitution processes characterized by equilibrium frequencies over the twenty amino acids, a useful proxy for qualitatively
Downloadable (with restrictions)! The higher-order asymptotic bias for the Akaike information criterion (AIC) in factor analysis or covariance structure analysis is obtained when the parameter estimators are given by the Wishart maximum likelihood. Since the formula of the exact higher-order bias is complicated, simple approximations which do not include unknown parameter values are obtained. Numerical examples with simulations show that the approximations are reasonably similar to their corresponding exact asymptotic values and simulated values. Simulations for model selection give consistently improved results by the approximate correction of the higher-order bias for the AIC over the usual AIC.
I am currently using fastsimcoal2 to model European and Asian demography.. A relatively recent development in population genetics is the use of maximum likelihood approaches to estimate demographic parameters from the site frequency spectrum (SFS). The SFS gives the number of SNPs observed at given frequencies in a sample. The distribution of these frequencies is affected by the demographic history of the population. For example, population expansion leads to long external branches on coalescent trees and consequently to an abundance of low-frequency variants. Population contraction leads to long internal coalescent branches and a skew toward intermediate frequency variants. Programs such as fastsimcoal2 (Excoffier et al. 2013) have developed methods to estimate the likelihood of an observed SFS under a particular set of demographic parameters.. fastsimcoal2 uses a maximum likelihood approach to estimate demographic parameters from the site frequency spectrum. The user provides a template file ...
And you know for sure that I will then announce the result of the lottery.. Heres the oddity. No matter what my announcement, you will end up all but certain-i.e., assigning a probability infinitesimally short of 1-that the coin was heads. Heres why. Suppose I announce ticket n. Now, P(n,heads)=2−n but P(n,tails) is infinitesimal. Plugging these facts into Bayes theorem, and assuming that your prior probability for heads was 1/2 (actually, all thats needed is that it be neither zero nor infinitesimal), your posterior probability P(heads,n) ends up equal to 1−a where a is infinitesimal.. So I can rationally force you to be all but certain that it was heads, simply by telling you the result of my lottery experiment. And by reversing the arrangement, I could force you to be all but certain that it was tails. Thus there is something pathological about the infinite lottery with infinitesimal probabilities.. This is, to me, yet another of the somewhat unhappy results that show that probability ...
function [logPrior,gradient] = logPDFBVS(params,mu,vin,vout,pGamma,a,b) %logPDFBVS Log joint prior for Bayesian variable selection % logPDFBVS is the log of the joint prior density of a % normal-inverse-gamma mixture conjugate model for a Bayesian linear % regression model with numCoeffs coefficients. logPDFBVS passes % params(1:end-1), the coefficients, to the PDF of a mixture of normal % distributions with hyperparameters mu, vin, vout, and pGamma, and also % passes params(end), the disturbance variance, to an inverse gamma % density with shape a and scale b. % % params: Parameter values at which the densities are evaluated, a % (numCoeffs + 1)-by-1 numeric vector. The first numCoeffs % elements correspond to the regression coefficients and the last % element corresponds to the disturbance variance. % % mu: Multivariate normal component means, a numCoeffs-by-1 numeric % vector of prior means for the regression coefficients. % % vin: Multivariate normal component scales, a numCoeffs-by-1 vector ...
Associations between selected alleles and the genetic backgrounds on which they are found can reduce the efficacy of selection. We consider the extent to which such interference, known as the Hill-Robertson effect, acting between weakly selected alleles, can restrict molecular adaptation and affect patterns of polymorphism and divergence. In particular, we focus on synonymous-site mutations, considering the fate of novel variants in a two-locus model and the equilibrium effects of interference with multiple loci and reversible mutation. We find that weak selection Hill-Robertson (wsHR) interference can considerably reduce adaptation, e.g., codon bias, and, to a lesser extent, levels of polymorphism, particularly in regions of low recombination. Interference causes the frequency distribution of segregating sites to resemble that expected from more weakly selected mutations and also generates specific patterns of linkage disequilibrium. While the selection coefficients involved are small, the fitness
In population genetics models, such as the Hardy-Weinberg model, it is assumed that species have no overlapping generations. In nature, however, many species do have overlapping generations. The overlapping generations are considered the norm rather than the exception. Overlapping generations are found in species that live for many years, and reproduce many times. Many birds, for instance, have new nests every (couple of) year(s). Therefore, the offspring will, after they have matured, also have their own nests of offspring while the parent generation could be breeding again as well. An advantage of overlapping generations can be found in the different experience levels of generations in a population. The younger age group will be able to acquire social information from the older and more experienced age groups.[3] Overlapping generations can, similarly, promote altruistic behaviour.[4]. Non-overlapping generations are found in species in which the adult generation dies after one breeding ...
The Wright-Fisher family of diffusion processes is a class of evolutionary models widely used in population genetics. Simulation and inference from these diffusions is therefore of widespread interest. However, simulating a Wright-Fisher diffusion is difficult because there is no known closed-form formula for its transition function. In this talk I show how it is possible to simulate exactly from the scalar Wright-Fisher diffusion with general drift, extending ideas based on retrospective simulation. The key idea is to exploit an eigenfunction expansion representation of the transition function. This approach also yields methods for exact simulation from several processes related to the Wright-Fisher diffusion: (i) the ancestral process of an infinite-leaf Kingman coalescent tree; (ii) its infinite-dimensional counterpart, the Fleming-Viot process; and (iii) its bridges. This is joint work with Dario Spano.. ...
Probabilistic methods for phylogenetic inference are based on mathematical models of sequence evolution [1]. In the last 20 years, several approaches have been proposed for developing more sophisticated models, accounting for various properties of substitution processes [2-8]. One of the most well-characterized example of such an improvement is provided by the Rate Across Sites (RAS) model [2], which relaxes the assumption that all sites of a protein or a nucleotide sequence evolve at the same rate. More specifically, the RAS model includes site-specific substitution rates, modeled as random variables following a gamma distribution. It generally has a better fit to the data, and it allows to circumvent certain artefacts in phylogenetic inference [9]. It has been implemented in most maximum-likelihood and Bayesian phylogenetic software, and is now widely used for routine phylogenetic inference. More sophisticated distributions of substitution rates, such as mixtures of gamma distributions [10], ...
the likelihood ratio is therefore a statistic. The likelihood ratio test rejects the null hypothesis if the value of this statistic is too small. How small is too small depends on the significance level of the test, i.e., on what probability of Type I error is considered tolerable (Type I errors consist of the rejection of a null hypothesis that is true).. The numerator corresponds to the likelihood of an observed outcome under the null hypothesis. The denominator corresponds to the maximum likelihood of an observed outcome varying parameters over the whole parameter space. The numerator of this ratio is less than the denominator. The likelihood ratio hence is between 0 and 1. Low values of the likelihood ratio mean that the observed result was less likely to occur under the null hypothesis as compared to the alternative. High values of the statistic mean that the observed outcome was nearly as likely to occur under the null hypothesis as the alternative, and the null hypothesis cannot be ...
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic variants within and between populations. For candidate models we numerically compute the expected spectrum using a diffusion approximation to the one-locus, two-allele Wright-Fisher process, involving up to three simultaneous populations. Our approach is a composite likelihood scheme, since linkage between neutral loci alters the variance but not the expectation of the frequency spectrum. We thus use bootstraps incorporating linkage to estimate uncertainties for parameters and significance values for hypothesis tests. Our method can also incorporate selection on single sites, predicting the joint distribution of selected alleles among populations experiencing a bevy of evolutionary forces, including expansions, contractions, migrations, and admixture. We ...
Under a Markov model of evolution, recoding, or lumping, of the four nucleotides into fewer groups may permit analysis under simpler conditions but may unfortunately yield misleading results unless the evolutionary process of the recoded groups remains Markovian. If a Markov process is lumpable, then the evolutionary process of the recoded groups is Markovian. We consider stationary, reversible, and homogeneous Markov processes on two taxa and compare three tests for lumpability: one using an ad hoc test statistic, which is based on an index that is evaluated using a bootstrap approximation of its distribution; one that is based on a test proposed specifically for Markov chains; and one using a likelihood-ratio test. We show that the likelihood-ratio test is more powerful than the index test, which is more powerful than that based on the Markov chain test statistic. We also show that for stationary processes on binary trees with more than two taxa, the tests can be applied to all pairs. Finally, we show
In population genetics overlapping generations refers to mating systems where more than one breeding generation is present at any one time. In systems where this is not the case there are non-overlapping generations (or discrete generations) in which every breeding generation lasts just one breeding season. If the adults reproduce over multiple breeding seasons the species is considered to have overlapping generations. Examples of species which have overlapping generations are many mammals, including humans, and many invertebrates in seasonal environments. Examples of species which consist of non-overlapping generations are annual plants and several insect species. Non-overlapping generations is one of the characteristics that needs to be met in the Hardy-Weinberg model for evolution to occur. This is a very restrictive and unrealistic assumption, but one that is difficult to dispose of. In population genetics models, such as the Hardy-Weinberg model, it is assumed that species have no ...
Knowledge of the effective size of populations, Ne, and the ratio of effective population size to the size of the mature population Ne/N, provide important information of the genetic diversity and fitness of populations. However, the theoretical parameter Ne was originally defined for populations with discrete generations, and most models that aim to estimate Ne for populations with overlapping generations relies on a set of simplifying, often unrealistic assumptions. Whenever these assumptions are violated, the predicted size of Ne may be highly biased and this may potentially lead to erroneous decisions in conservation and management. Hence, there is a need for more knowledge about how different processes occurring in natural populations affect the effective size of populations, and the Ne/N ratio. The main goal of this thesis was to relax one of the most unrealistic assumptions underlying many models: constant population size, or at the very best that fluctuations are only caused by density ...
ABSTRACT: The measurement of genetic variability and assessment of population genetic losses are important components of environmental management programs. Twenty-three natural populations of the Mediterranean brackish-water toothcarp Aphanius fasciatus were investigated using different statistical approaches based on genetic data at 13 polymorphic allozyme loci. In general, no differences between values of within-population genetic variability estimates occurred. The Wilcoxon sign-rank test for heterozygosity excess due to a recent bottleneck was conducted on the array of populations. In addition, a qualitative descriptor of allele frequency distribution was used to infer bottlenecks. Only populations from the Orbetello lagoon and La Salina at Elba Island revealed significant heterozygosity excess under both the infinite allele model (IAM) and stepwise mutation model (SMM). A recent dystrophic crisis may account for the genetic loss detected in the population of A. fasciatus from the Orbetello ...
The estimation of (co)variance components for multiple traits with maternal genetic effects was found to be influenced by population structure. Two traits in a closed breeding herd with random mating were simulated over nine generations. Population structures were simulated on the basis of different proportions of dams not having performance records (0, 0.1, 0.5, 0.8 and 0.9): three genetic correlations (−0.5, 0.0 and +0.5) between direct and maternal effects and three genetic correlations (0, 0.3 and 0.8) between two traits. Three ratios of direct to maternal genetic variances, (1:3, 1:1, 3:1), were also considered. Variance components were estimated by restricted maximum likelihood. The proportion of dams without records had an effect on the SE of direct-maternal covariance estimates when the proportion was 0.8 or 0.9 and the true correlation between direct and maternal effects was negative. The ratio of direct to maternal genetic variances influenced the SE of the (co)variance estimates ...
Analysis of Variance for Random Models (Volume I: Balanced Data Theory, Methods, Applications and Data Analysis) by Sahai Hardeo (ISBN: 978-1-4612-6470-5); Published by Birkhäuser Bostonin Mar 2013. Compare book prices on Bookwire.com to buy books from the lowest price among top online book retailers
Tatistic, is calculated, testing the association between transmitted/non-transmitted and high-risk/low-risk genotypes. The phenomic evaluation procedure aims to assess the impact of Computer on this association. For this, the strength of association involving transmitted/non-transmitted and high-risk/low-risk genotypes in the various Pc levels is compared using an evaluation of variance model, resulting in an F statistic. The final MDR-Phenomics statistic for every single multilocus model could be the item of the C and F statistics, and significance is assessed by a non-fixed permutation test. Aggregated MDR The original MDR method doesnt account for the accumulated effects from multiple interaction effects, because of choice of only a single optimal model during CV. The Aggregated Multifactor Daporinad web dimensionality Reduction (A-MDR), proposed by Dai et al. [52],A roadmap to multifactor dimensionality reduction techniques,makes use of all important interaction effects to develop a gene ...
BACKGROUND: Fitness epistasis, the interaction effect of genes at different loci on fitness, makes an important contribution to adaptive evolution. Although fitness interaction evidence has been observed in model organisms, it is more difficult to detect and remains poorly understood in human populations as a result of limited statistical power and experimental constraints. Fitness epistasis is inferred from non-independence between unlinked loci. We previously observed ancestral block correlation between chromosomes 4 and 6 in African Americans. The same approach fails when examining ancestral blocks on the same chromosome due to the strong confounding effect observed in a recently admixed population. RESULTS: We developed a novel approach to eliminate the bias caused by admixture linkage disequilibrium when searching for fitness epistasis on the same chromosome. We applied this approach in 16,252 unrelated African Americans and identified significant ancestral correlations in two pairs of ...
NeEstimator v2 is a completely revised and updated implementation of software that produces estimates of contemporary effective population size, using several different methods and a single input file. NeEstimator v2 includes three single-sample estimators (updated versions of the linkage disequilibrium and heterozygote-excess methods, and a new method based on molecular coancestry), as well as the two-sample (moment-based temporal) method. New features include the following: (i) an improved method for accounting for missing data; (ii) options for screening out rare alleles; (iii) confidence intervals for all methods; (iv) the ability to analyse data sets with large numbers of genetic markers (10000 or more); (v) options for batch processing large numbers of different data sets, which will facilitate cross-method comparisons using simulated data; and (vi) correction for temporal estimates when individuals sampled are not removed from the population (Plan I sampling). The user is given ...
Abstract: Consider a reflecting diffusion in a domain in $R^d$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting process and the value of the drift vector has a product form. Moreover, the first component is the symmetrizing measure on the domain for the reflecting diffusion without inert drift, and the second component has a Gaussian distribution. We also consider processes where the drift is given in terms of the gradient of a potential ...
Modelling the evolution of variational properties requires modelling multi-loci dynamics with gene interaction and multiple phenotypic characters under directional selection including the effect of LD. In most mathematical models most, if not all, of these complications are ignored in order to make the models tractable. The recent pioneering work by Jones et al. [30-32] focuses on stabilizing selection. In this project, we chose to make a number of alternative simplifications that preserve the presence of gene interaction and LD but use other abstractions. Specifically, we model the evolution of genes affecting two characters in the form of a phenotypic Lande equation and represent LD by an association between rQTL alleles and the genotypic values of the quantitative traits. To our knowledge, this model is the first to accommodate gene interaction, LD and directional selection and is still mathematically tractable. Certainly, the model is an abstraction that involves several simplifications. In ...
In all populations, we observed a reduction in the narrow-sense heritability of all evaluated traits when dominance effects were accounted for (e.g., using MAD instead of MA). The smallest decrease in narrow-sense heritability was observed for number of teats (4.2%) and the highest for lifetime daily gain (21.3%), both in the Landrace population (Table 3). The broad-sense heritability (sum of the heritabilities due to all genetic effects used in the model) of all evaluated traits increased in all three populations when dominance and imprinting effects were added to the model. The broad-sense heritability of lifetime daily gain was ,30% greater when using MADI compared to using MA (Table 3, Table 4, and Table 5). A reduction of additive genetic variance and an increase in the broad-sense heritability was previously reported (Su et al. 2012) when nonadditive genetic effects were included in the model to evaluate daily gain in pigs. For height in trees, the narrow-sense heritability was found to ...
When it comes to applying statistics for measuring goodness-of-fit, the Pearson χ2 test is the dominant player in a race and the Kolmogorov-Smirnoff test statistic trails far behind. Although it seems almost invisible in this race, there are more various non-parametric statistics for testing goodness-of-fit and for comparing the sampling distribution to a reference distribution as legitimate race participants trained by many statisticians. Listing their names probably useful to some astronomers when they find the underlying assumptions for the χ2 test do not match the data. Perhaps, some astronomers want to try other nonparametric test statistics other than the K-S test. Ive seen other test statistics in astronomical journals from time to time. Depending on data and statistical properties, one test statistic could work better than the other; therefore, its worthwhile to keep the variety in ones mind that there are other tests beyond the χ2 test goodness-of-fit test statistic. Continue ...
According to the neutral theory of evolution most mutations are expected to be neutral, nearly neutral, or deleterious. It is the class of nearly neutral and deleterious mutations that may, in fact, predominantly drive the evolution and structure of the genome. The removal of deleterious mutations by purifying selection can affect genetic variation at linked neutral sites by a process called background selection. There is renewed interested in understanding background selection across diverse organisms, and comparing diversity between the sex chromosomes and the autosomes to distinguish its effects from other evolutionary forces, such as demography and positive selection. Recent advances include new theoretical approaches to more comprehensively model the complexity of background selection in a coalescent framework. These models are especially powerful when combined with recent developments resulting in dramatically increased sample sizes, improved identification of rare variants, and the ...
TY - JOUR. T1 - Statistical models for genetic susceptibility in toxicological and epidemiological investigations. AU - Piegorsch, W. W.. PY - 1994/1/1. Y1 - 1994/1/1. N2 - Models are presented for use in assessing genetic susceptibility to cancer (or other diseases) with animal or human data. Observations are assumed to be in the form of proportions, hence a binomial sampling distribution is considered. Generalized linear models are employed to model the response as a function of the genetic component; these include logistic and complementary log forms. Susceptibility is measured via odds ratios of response. relative to a background genetic group. Significance tests and confidence intervals for these odds ratios are based on maximum likelihood estimates of the regression parameters. Additional consideration is given to the problem of gene-environment interactions and to testing whether certain genetic identifiers/categories may be collapsed into a smaller set of categories. The collapsibility ...
We describe the formal verification of two theorems of theoretical biology. These theorems concern genetic regulatory networks: they give, in a discrete modeling framework, relations between the topology and the dynamics of these biological networks. In the considered discrete modeling framework, the dynamics is described by a transition graph, where vertices are vectors indicating the expression level of each gene, and where edges represent the evolution of these expression levels. The topology is also described by a graph, called interaction graph, where vertices are genes and where edges correspond to influences between genes. The two results we formalize show that circuits of some kind must be present in the interaction graph if some behaviors are possible in the transition graph. This work was performed with the ssreflect extension of the Coq system.
Perception & Psychophysics 28, 7 (2), doi:.3758/pp Type I error rates and power analyses for single-point sensitivity measures Caren M. Rotello University of Massachusetts, Amherst, Massachusetts
The difficulty in elucidating the genetic basis of complex diseases roots in the many factors that can affect the development of a disease. Some of these genetic effects may interact in complex ways, proving undetectable by current single-locus methodology. We have developed an analysis tool called Hypothesis Free Clinical Cloning (HFCC) to search for genome-wide epistasis in a case-control design. HFCC combines a relatively fast computing algorithm for genome-wide epistasis detection, with the flexibility to test a variety of different epistatic models in multi-locus combinations. HFCC has good power to detect multi-locus interactions simulated under a variety of genetic models and noise conditions. Most importantly, HFCC can accomplish exhaustive genome-wide epistasis search with large datasets as demonstrated with a 400,000 SNP set typed on a cohort of Parkinsons disease patients and controls. With the current availability of genetic studies with large numbers of individuals and genetic markers,
When it comes to applying statistics for measuring goodness-of-fit, the Pearson χ2 test is the dominant player in a race and the Kolmogorov-Smirnoff test statistic trails far behind. Although it seems almost invisible in this race, there are more various non-parametric statistics for testing goodness-of-fit and for comparing the sampling distribution to a reference distribution as legitimate race participants trained by many statisticians. Listing their names probably useful to some astronomers when they find the underlying assumptions for the χ2 test do not match the data. Perhaps, some astronomers want to try other nonparametric test statistics other than the K-S test. Ive seen other test statistics in astronomical journals from time to time. Depending on data and statistical properties, one test statistic could work better than the other; therefore, its worthwhile to keep the variety in ones mind that there are other tests beyond the χ2 test goodness-of-fit test statistic. Continue ...
This paper examines the correlation between numbers of computer cores in parallel genetic algorithms. The objective to determine the linear polynomial complementary equation in order represent the relation between number of parallel processing and optimum solutions. Model this relation as optimization function (f(x)) which able to produce many simulation results. F(x) performance is outperform genetic algorithms. Compression results between genetic algorithm and optimization function is done. Also the optimization function give model to speed up genetic algorithm. Optimization function is a complementary transformation which maps a TSP given to linear without changing the roots of the polynomials.