17 research outputs found
An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops
<p>Abstract</p> <p>Background</p> <p>Marginal posterior genotype probabilities need to be computed for genetic analyses such as geneticcounseling in humans and selective breeding in animal and plant species.</p> <p>Methods</p> <p>In this paper, we describe a peeling based, deterministic, exact algorithm to compute efficiently genotype probabilities for every member of a pedigree with loops without recourse to junction-tree methods from graph theory. The efficiency in computing the likelihood by peeling comes from storing intermediate results in multidimensional tables called cutsets. Computing marginal genotype probabilities for individual <it>i </it>requires recomputing the likelihood for each of the possible genotypes of individual <it>i</it>. This can be done efficiently by storing intermediate results in two types of cutsets called anterior and posterior cutsets and reusing these intermediate results to compute the likelihood.</p> <p>Examples</p> <p>A small example is used to illustrate the theoretical concepts discussed in this paper, and marginal genotype probabilities are computed at a monogenic disease locus for every member in a real cattle pedigree.</p
Improved techniques for sampling complex pedigrees with the Gibbs sampler
Markov chain Monte Carlo (MCMC) methods have been
widely used to overcome computational problems in linkage and segregation analyses.
Many variants of this approach exist and are practiced; among the most popular
is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its
simplest form) mixing and reducibility problems; furthermore in order to
initiate a Gibbs sampling chain we need a starting genotypic or allelic
configuration which is consistent with the marker data in the pedigree and which
has suitable weight in the joint distribution. We outline a procedure for finding
such a configuration in pedigrees which have too many loci to allow for exact peeling.
We also explain how this technique could be used to implement a blocking Gibbs sampler
A study on the minimum number of loci required for genetic evaluation using a finite locus model
For a finite locus model, Markov chain Monte Carlo (MCMC) methods can be used to estimate the conditional mean of genotypic values given phenotypes, which is also known as the best predictor (BP). When computationally feasible, this type of genetic prediction provides an elegant solution to the problem of genetic evaluation under non-additive inheritance, especially for crossbred data. Successful application of MCMC methods for genetic evaluation using finite locus models depends, among other factors, on the number of loci assumed in the model. The effect of the assumed number of loci on evaluations obtained by BP was investigated using data simulated with about 100 loci. For several small pedigrees, genetic evaluations obtained by best linear prediction (BLP) were compared to genetic evaluations obtained by BP. For BLP evaluation, used here as the standard of comparison, only the first and second moments of the joint distribution of the genotypic and phenotypic values must be known. These moments were calculated from the gene frequencies and genotypic effects used in the simulation model. BP evaluation requires the complete distribution to be known. For each model used for BP evaluation, the gene frequencies and genotypic effects, which completely specify the required distribution, were derived such that the genotypic mean, the additive variance, and the dominance variance were the same as in the simulation model. For lowly heritable traits, evaluations obtained by BP under models with up to three loci closely matched the evaluations obtained by BLP for both purebred and crossbred data. For highly heritable traits, models with up to six loci were needed to match the evaluations obtained by BLP
Improved techniques for sampling complex pedigrees with the Gibbs sampler
Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler
A comparison of�alternative methods to�compute conditional genotype probabilities for�genetic evaluation with�finite locus models
An increased availability of genotypes at marker loci has prompted the
development of models that include the effect of individual genes.
Selection based on these models is known as marker-assisted selection
(MAS). MAS is known to be efficient especially for traits that have
low heritability and non-additive gene action. BLUP methodology under
non-additive gene action is not feasible for large inbred or crossbred
pedigrees. It is easy to incorporate non-additive gene action in a
finite locus model. Under such a model, the unobservable genotypic
values can be predicted using the conditional mean of the genotypic
values given the data. To compute this conditional mean, conditional
genotype probabilities must be computed. In this study these
probabilities were computed using iterative peeling, and three Markov
chain Monte Carlo (MCMC) methods — scalar Gibbs, blocking Gibbs, and
a sampler that combines the Elston Stewart algorithm with iterative
peeling (ESIP). The performance of these four methods was assessed
using simulated data. For pedigrees with loops, iterative peeling
fails to provide accurate genotype probability estimates for some
pedigree members. Also, computing time is exponentially related to the
number of loci in the model. For MCMC methods, a linear relationship
can be maintained by sampling genotypes one locus at a time. Out of
the three MCMC methods considered, ESIP, performed the best while
scalar Gibbs performed the worst
Improved techniques for sampling complex pedigrees with the Gibbs sampler
Abstract Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.</p