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For example, when association mapping is used to find disease genes, the presence of undetected population structure can lead to spurious associations and thus invalidate standard tests (Ewens and Spielman 1995).

Pritchard and Rosenberg (1999) considered how genetic information might be used to detect the presence of cryptic population structure in the association mapping context. Sex very good generally, one would like to be able to identify the actual subpopulations and assign individuals (probabilistically) to these populations. In this article we use a Bayesian clustering approach to tackle this problem.

Our method attempts to assign individuals to populations on the basis of their genotypes, while simultaneously estimating population allele frequencies. It also assumes Hardy-Weinberg equilibrium within populations. It is also closely related to the methods of Foreman et al.

Consequently they focused on estimating the amount of genetic differentiation among the unobserved populations. In contrast, our primary interest lies in the assignment of individuals to populations. Our approach also differs in that it allows for the presence of admixed individuals in the sample, whose genetic makeup is drawn from more than one of the K populations. In the next section we provide a brief description of clustering methods in general and describe some advantages of the model-based approach we take.

The details of the models and algorithms used are given in models and methods. We illustrate our method with several examples in applications to data: both Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA simulated data and on sets of genotype data from an endangered bird species and from humans.

This may be useful for testing whether particular individuals are migrants or to assist in classifying individuals of unknown origin (as in Rannala and Mountain 1997, for example). Background on the computational methods used in this article is provided in the appendix. Consider a situation where we have genetic data from a sample of individuals, each of whom is assumed to have originated from a single unknown population (no admixture). Suppose we wish to cluster together individuals who are genetically similar, identify distinct clusters, and perhaps see how these clusters relate to geographical or phenotypic data on the individuals.

There are broadly two types of clustering methods we might use:Distance-based methods. These proceed by calculating a pairwise distance matrix, whose entries give the distance (suitably defined) between every pair of individuals. This matrix may then be represented using some convenient graphical representation (such as a tree or a multidimensional scaling plot) and clusters may be identified by eye.

These proceed by assuming that Dovonex Cream (Calcipotriene Cream)- Multum from each cluster are random draws from some parametric model. Inference for the parameters corresponding to each cluster is then done Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA with inference for the cluster membership of each individual, using standard statistical methods (for example, maximum-likelihood or Bayesian methods).

Distance-based methods are usually easy to apply and are often visually appealing. In the genetics literature, it has been common Tenapanor Tablets (Ibsrela)- FDA adapt distance-based phylogenetic algorithms, such as neighbor-joining, to clustering multilocus genotype data (e.

Distance-based methods are thus more sex male female male to exploratory data analysis than to fine statistical inference, and we have chosen to take a model-based approach here. The first challenge when applying model-based methods is to specify a suitable model for observations from each cluster.

Assume that each cluster (population) is modeled by a characteristic Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA of allele frequencies. Let X denote the genotypes of the sampled individuals, Z denote the (unknown) populations of origin of the individuals, and P denote the (unknown) allele frequencies in erectile populations. Loosely speaking, the idea here is that the model accounts for the presence of Hardy-Weinberg Ambien CR (Zolpidem Tartrate)- FDA linkage disequilibrium by introducing population structure and attempts to find population groupings that (as far as possible) are not Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA disequilibrium.

While inference may depend heavily on these modeling assumptions, we feel that it is easier to assess the validity of explicit modeling assumptions than to compare the relative merits of more abstract quantities such as distance measures and graphical representations.

In situations where these assumptions are deemed unreasonable then alternative models should be built. Having specified our model, we must decide how to perform inference for the quantities of interest (Z and P).

Here, we have chosen to adopt a Bayesian approach, by specifying models (priors) Pr(Z) and Pr(P), for both Z and P. The Bayesian approach provides a coherent framework for incorporating the inherent uncertainty of parameter estimates into the inference procedure and for evaluating the strength of evidence for the inferred clustering.

It also eases the incorporation of various sorts of prior information that may be available, such as information about the geographic sampling location of individuals. Inference for Z and P may then be based on summary statistics obtained from this sample (see Inference for Z, P, and Q below). A brief introduction to MCMC methods and Gibbs sampling may be found in the appendix.

We now provide a more detailed description of our modeling assumptions and the algorithms used to perform inference, beginning with the simpler case where each individual is assumed to have originated in Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA single population (no admixture).

The model without admixture: Suppose we genotype N diploid individuals at L loci. In the case without admixture, each individual is assumed to originate in one of K populations, each with its own characteristic set of allele frequencies. Let the vector X denote the observed genotypes, Z the (unknown) populations of origin of the individuals, and P the (unknown) allele frequencies in the populations.

The distributions required to perform each step are given in the appendix. The model with admixture: We now sonic our model to allow for admixed individuals by introducing Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA vector Q to denote the admixture proportions for each individual.

Our primary interest now lies in estimating Q. We proceed in a manner similar to the case without admixture, beginning by specifying a probability model for (X, Z, P, Q). To complete our model we need to specify a distribution for Q, which in china johnson will depend on the type and amount of admixture Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA expect to see.

Inference: Inference for Z, P, and Q: We now discuss how the MCMC output can be used to perform inference on Z, P, and Q. For example, suppose that there are just two populations Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA 10 individuals and that the genotypes of these individuals contain strong information that the first 5 are in one population and the second 5 are in the other Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA. In general, if there are K populations then there will be K.

Typically, MCMC schemes find it rather difficult to move between such modes, and the algorithms we describe will usually explore only one of the symmetric modes, even when run for a very large number of iterations.

If our sampler explores only one symmetric mode then the sample means (8) will be very poor estimates of the posterior means for the qi, but will be much better estimates of the modes of the qi, which in this case Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA out to be a much better summary of the information in Somatropin (rDNA origin) (Serostim)- FDA data. Ironically then, the poor mixing of the MCMC sampler between the symmetric modes gives the asymptotically useless estimator (8) some practical value.

Inference for the number of populations: The problem of inferring the number of clusters, K, present in a data set is notoriously difficult. We therefore describe an alternative approach, which is motivated by approximating (11) in an ad hoc and computationally convenient way. In fact, the Norgestrel And Ethinyl Estradiol (Lo Ovral)- FDA underlying (12) are dubious at best, and we do not claim (or believe) that our procedure provides a quantitatively accurate estimate of the posterior distribution of K.

We see it merely as an ad hoc guide to which models are most consistent with the data, with the main justification being that it seems to give sensible answers in practice (see next section for examples).



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