Closing the gap between rocks and clocks.
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Animals↗
Biomedical subjects
B Rannala
Publications and source records attributed to B Rannala.
Joint Bayesian estimation of mutation location and age using linkage disequilibrium.
Associations between disease and marker alleles on chromosomes in populations can arise as a consequence of historical forces such as mutation, selection and genetic drift, and is referred to as "linkage disequilibrium" (LD). LD can be used to estimate the map position of a disease mutation relative to a set of linked markers, as well as to estimate other parameters of interest, such as mutation age. Parametric methods for estimating the location of a disease mutation using marker linkage disequilibrium in a sample of normal and affected individuals require a detailed knowledge of population demography, and in particular require users to specify the postulated age of a mutation and past population growth rates. A new Bayesian method is presented for jointly estimating the position of a disease mutation and its age. The method is illustrated using haplotype data for the cystic fibrosis deltaF508 mutation in Europe and the DTD mutation in Finland. It is shown that, for these datasets, the posterior probability distribution of disease mutation location is insensitive to the population growth rate when the model is averaged over possible mutation ages using a prior probability distribution for the mutation age based on the population frequency of the disease mutation. Fewer assumptions are therefore needed for parametric LD mapping.
Bayes Theorem↗
Methylation patterns and mathematical models reveal dynamics of stem cell turnover in the human colon.
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Aging↗
High-resolution multipoint linkage-disequilibrium mapping in the context of a human genome sequence.
A new method is presented for fine-scale linkage disequilibrium (LD) mapping of a disease mutation; it uses multiple linked single-nucleotide polymorphisms, restriction-fragment-length polymorphisms, or microsatellite markers and incorporates information from an annotated human genome sequence (HGS) and from a human mutation database. The method takes account of population demographic effects, using Markov chain Monte Carlo methods to integrate over the unknown gene genealogy and gene coalescence times. Information about the relative frequency of disease mutations in exons, introns, and other regions, from mutational databases, as well as assumptions about the completeness of the gene annotation, are used with an annotated HGS, to generate a prior probability that a mutation lies at any particular position in a specified region of the genome. This information is updated with information about mutation location, from LD at a set of linked markers in the region, to generate the posterior probability density of the mutation location. The performance of the method is evaluated by simulation and by analysis of a data set for diastrophic dysplasia (DTD) in Finland. The DTD disease gene has been positionally cloned, so the actual location of the mutation is known and can be compared with the position predicted by our method. For the DTD data, the addition of information from an HGS results in disease-gene localization at a resolution that is much higher than that which would be possible by LD mapping alone. In this case, the gene would be found by sequencing a region < or =7 kb in size.
Algorithms↗
Using linked markers to infer the age of a mutation.
Advances in sequencing and genotyping technologies over the last decade have enabled geneticists to easily characterize genetic variation at the nucleotide level. Hundreds of genes harboring mutations associated with genetic disease have now been identified by positional cloning. Using variation at closely linked genetic markers, it is possible to predict the times in the past at which particular mutations arose. Such studies suggest that many of the rare mutations underlying human genetic disorders are relatively young. Studies of variation at genetic markers linked to particular mutations can provide insights into human geographic history, and historical patterns of natural selection and disease, that are not available from other sources. We review two approaches for estimating allele age using variation at linked genetic markers. A phylogenetic approach aims to reconstruct the gene tree underlying a sample of chromosomes carrying a particular mutation, obtaining a "direct" estimate of allele age from the age of the root of this tree. A population genetic approach relies on models of demography, mutation, and/or recombination to estimate allele age without explicitly reconstructing the gene tree. Phylogenetic methods are best suited for studies of ancient mutations, while population genetic methods are better suited for studies of recent mutations. Methods that rely on recombination to infer the ages of alleles can be fine-tuned by choosing linked markers at optimal map distances to maximize the information available about allele age. A limitation of methods that rely on recombination is the frequent lack of a fine-scale linkage map. Maximum likelihood and Bayesian methods for estimating allele age that rely on intensive numerical computation are described, as well as "composite" likelihood and moment-based methods that lead to simple estimators. The former provide more accurate estimates (particularly for large samples of chromosomes) and should be employed if computationally practical.
Alleles↗
Finding genes influencing susceptibility to complex diseases in the post-genome era.
During the last decade, hundreds of genes that harbor mutations causing simple Mendelian disorders have been identified using a combination of linkage analysis and positional cloning techniques. Traditional approaches to gene mapping have been largely unsuccessful in mapping genes influencing so-called 'complex' genetic diseases, however, because of low power and other factors. Complex genetic diseases do not display simple Mendelian patterns of inheritance, although genes do have an influence and close relatives of probands consequently have an increased risk. These disorders are thought to be due to the combined effects of variation at multiple interacting genes and the environment. Complex diseases have a significant impact on human health because of their high population incidence (unlike simple Mendelian disorders, which tend to be rare). New techniques are being developed aimed specifically at mapping genes conferring susceptibility to complex diseases. A project aimed at mapping genes influencing susceptibility to a complex disease may be undertaken in several stages: establishing a genetic basis for the disease in one or more populations; measuring the distribution of gene effects; studying statistical power using models; carrying out marker-based mapping studies using linkage or association. Quantitative genetic models can be used to estimate the heritability of a complex (polygenic) disease, as well as to predict the distribution of gene effects and to test whether one or more quantitative trait loci (QTLs) exist. Such models can be used to predict the power of different mapping approaches, but are often unrealistic and therefore provide only approximate predictions. Linkage analyses, association studies and family-based association tests are all hindered by low power and other specific problems. Association studies tend to be more powerful but can generate spurious associations due to population admixture. Alternative strategies for association mapping include the use of recent founder populations or unique isolated populations that are genetically homogeneous, and the use of unlinked markers (so-called genomic controls) to assign different regions of the genome of an admixed individual to particular source populations. Linkage disequilibrium observed in a sample of unrelated affected and normal individuals can also be used to fine-map a disease susceptibility locus in a candidate region. New Bayesian strategies make use of an annotated human genome sequence to further refine the position of a candidate disease susceptibility locus.
Genetic Diseases, Inborn↗
Accommodating phylogenetic uncertainty in evolutionary studies.
Many evolutionary studies use comparisons across species to detect evidence of natural selection and to examine the rate of character evolution. Statistical analyses in these studies are usually performed by means of a species phylogeny to accommodate the effects of shared evolutionary history. The phylogeny is usually treated as known without error; this assumption is problematic because inferred phylogenies are subject to both stochastic and systematic errors. We describe methods for accommodating phylogenetic uncertainty in evolutionary studies by means of Bayesian inference. The methods are computationally intensive but general enough to be applied in most comparative evolutionary studies.
Animals↗
Methods for multipoint disease mapping using linkage disequilibrium.
A disease-associated mutation arises on a single chromosome such that alleles at linked markers are initially in complete linkage disequilibrium (LD) with the mutation. LD can be used as a tool for high-resolution mapping of the position of a disease mutation relative to a set of linked marker loci. When more than two linked marker loci are considered, developing a maximum likelihood approach is a challenging mathematical problem. To reduce the complexity, approximate and composite likelihood (CL) methods have been developed for multipoint LD mapping that use simplified models of population history, or of recombination, that ignore some of the statistical dependence among disease chromosomes and among marker loci. We describe the relationship among several composite likelihood methods for multipoint LD mapping, and suggest an alternative CL method that takes better account of the statistical dependence among marker loci.
Alleles↗
Methods for estimating gene frequencies and detecting selection in bacterial populations.
Recent breakthroughs in molecular technology, most significantly the polymerase chain reaction (PCR) and in situ hybridization, have allowed the detection of genetic variation in bacterial communities without prior cultivation. These methods often produce data in the form of the presence or absence of alleles or genotypes, however, rather than counts of alleles. Using relative allele frequencies from presence-absence data as estimates of population allele frequencies tends to underestimate the frequencies of common alleles and overestimate those of rare ones, potentially biasing the results of a test of neutrality in favor of balancing selection. In this study, a maximum-likelihood estimator (MLE) of bacterial allele frequencies designed for use with presence-absence data is derived using an explicit stochastic model of the host infection (or bacterial sampling) process. The performance of the MLE is evaluated using computer simulation and a method is presented for evaluating the fit of estimated allele frequencies to the neutral infinite alleles model (IAM). The methods are applied to estimate allele frequencies at two outer surface protein loci (ospA and ospC) of the Lyme disease spirochete, Borrelia burgdorferi, infecting local populations of deer ticks (Ixodes scapularis) and to test the fit to a neutral IAM.
Alleles↗
A Bayesian framework for the analysis of cospeciation.
Information on the history of cospeciation and host switching for a group of host and parasite species is contained in the DNA sequences sampled from each. Here, we develop a Bayesian framework for the analysis of cospeciation. We suggest a simple model of host switching by a parasite on a host phylogeny in which host switching events are assumed to occur at a constant rate over the entire evolutionary history of associated hosts and parasites. The posterior probability density of the parameters of the model of host switching are evaluated numerically using Markov chain Monte Carlo. In particular, the method generates the probability density of the number of host switches and of the host switching rate. Moreover, the method provides information on the probability that an event of host switching is associated with a particular pair of branches. A Bayesian approach has several advantages over other methods for the analysis of cospeciation. In particular, it does not assume that the host or parasite phylogenies are known without error; many alternative phylogenies are sampled in proportion to their probability of being correct.
Animals↗
Estimating allele age.
The age of an allele can be estimated both from genetic variation among different copies (intra-allelic variation) and from its frequency. Estimates based on intra-allelic variation follow from the exponential decay of linkage disequilibrium because of recombination and mutation. The confidence interval depends both on the uncertainty in recombination and mutation rates and on randomness of the genealogy of chromosomes that carry the allele (the intra-allelic genealogy). Several approximate methods to account for variation in the intra-allelic genealogy have been derived. Allele frequency alone also provides an estimate of age. Estimates based on frequency and on intra-allelic variability can be combined to provide a more accurate estimate or can be contrasted to show that an allele has been subject to natural selection. These methods have been applied to numerous cases, including alleles associated with cystic fibrosis, idiopathic torsion dystonia, and resistance to infection by HIV. We emphasize that estimates of allele age depend on assumptions about demographic history and natural selection.
Acquired Immunodeficiency Syndrome↗
Taxon sampling and the accuracy of large phylogenies.
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Models, Biological↗
Likelihood analysis of disequilibrium mapping, and related problems.
In this paper a theory is developed that provides the sampling distribution of alleles at a diallelic marker locus closely linked to a low-frequency allele that arose as a single mutant. The sampling distribution provides a basis for maximum-likelihood estimation of either the recombination rate, the mutation rate, or the age of the allele, provided that the two other parameters are known. This theory is applied to (1) the data of Hästbacka et al., to estimate the recombination rate between a locus associated with diastrophic dysplasia and a linked RFLP marker; (2) the data of Risch et al., to estimate the age of a presumptive allele causing idiopathic distortion dystonia in Ashkenazi jews; and (3) the data of Tishkoff et al., to estimate the date at which, at the CD4 locus, non-African lineages diverged from African lineages. We conclude that the extent of linkage disequilibrium can lead to relatively accurate estimates of recombination and mutation rates and that those estimates are not very sensitive to parameters, such as the population age, whose values are not known with certainty. In contrast, we also conclude that, in many cases, linkage disequilibrium may not lead to useful estimates of allele age, because of the relatively large degree of uncertainly in those estimates.
Africa↗
Detecting immigration by using multilocus genotypes.
Immigration is an important force shaping the social structure, evolution, and genetics of populations. A statistical method is presented that uses multilocus genotypes to identify individuals who are immigrants, or have recent immigrant ancestry. The method is appropriate for use with allozymes, microsatellites, or restriction fragment length polymorphisms (RFLPs) and assumes linkage equilibrium among loci. Potential applications include studies of dispersal among natural populations of animals and plants, human evolutionary studies, and typing zoo animals of unknown origin (for use in captive breeding programs). The method is illustrated by analyzing RFLP genotypes in samples of humans from Australian, Japanese, New Guinean, and Senegalese populations. The test has power to detect immigrant ancestors, for these data, up to two generations in the past even though the overall differentiation of allele frequencies among populations is low.
Emigration and Immigration↗
Phylogenetic methods come of age: testing hypotheses in an evolutionary context.
The use of molecular phylogenies to examine evolutionary questions has become commonplace with the automation of DNA sequencing and the availability of efficient computer programs to perform phylogenetic analyses. The application of computer simulation and likelihood ratio tests to evolutionary hypotheses represents a recent methodological development in this field. Likelihood ratio tests have enabled biologists to address many questions in evolutionary biology that have been difficult to resolve in the past, such as whether host-parasite systems are cospeciating and whether models of DNA substitution adequately explain observed sequences.
Animals↗
On the genealogy of a rare allele.
The gene genealogy is derived for a rare allele that is descended from a mutant ancestor that arose at a fixed time in the past. Following Thompson (1976, Amer. J. Human Genet. 28, 442-452), the fractional linear branching process is used as a model of the demography of a rare allele. The model does not require the total population size to be constant or the mutant class to be neutral; so long as individuals in the class are selectively equivalent, the class as a whole may have a selective advantage, or disadvantage, relative to other alleles in the population. An exact result is given for the joint probability distribution of the coalescence times among a sample of alleles descended from the mutant. A method is described for rapidly simulating these coalescence times. The relationship between the genealogical structure of a discrete generation branching process and a continuous generation birth-death process is elucidated. The theory may be applied to the problem of estimating the ages of rare nonrecurrent mutations.
Alleles↗
Gene genealogy in a population of variable size.
The genealogical properties of a small population with continuous overlapping generations that fluctuates randomly in size are studied using a model based on a stochastic birth-death process. The distribution of the coalescence times is presented, as well as a method for computing the expected overall length of the genealogy as a function of the individual birth rate gamma, the individual death rate mu, and the present population size. The relationship between the birth and death rates and the shape of the resulting genealogy is studied. The total length of the genealogy is shown to be maximized when gamma = mu. The joint distribution of the coalescence times is shown to be invariant in gamma and mu, conditional on the current population size, so that exponential growth of a population cannot be distinguished from exponential decline based on the shape of the resulting genealogy. The model is used to predict the probability that all genetic variation is lost from a recent founder population.
Founder Effect↗
The sampling distribution of disease-associated alleles.
A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.
Alleles↗