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      Prediction of multilocus identity-by-descent.

      1 ,

      Genetics

      Genetics Society of America

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          Abstract

          Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in random-mating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X(ABC) at each of ordered loci A, B, and C can be well approximated by X(ABC) = X(AB)X(BC)/X(B) and generalizes to X(123...k) = X(12)X(23...)X(k)(-1,k)/X(k-2), where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

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          Most cited references 9

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          Novel multilocus measure of linkage disequilibrium to estimate past effective population size.

          Linkage disequilibrium (LD) between densely spaced, polymorphic genetic markers in humans and other species contains information about historical population size. Inferring past population size is of interest both from an evolutionary perspective (e.g., testing the "out of Africa" hypothesis of human evolution) and to improve models for mapping of disease and quantitative trait genes. We propose a novel multilocus measure of LD, the chromosome segment homozygosity (CSH). CSH is defined for a specific chromosome segment, up to the full length of the chromosome. In computer simulations CSH was generally less variable than the r(2) measure of LD, and variability of CSH decreased as the number of markers in the chromosome segment was increased. The essence and utility of our novel measure is that CSH over long distances reflects recent effective population size (N), whereas CSH over small distances reflects the effective size in the more distant past. We illustrate the utility of CSH by calculating CSH from human and dairy cattle SNP and microsatellite marker data, and predicting N at various times in the past for each species. Results indicated an exponentially increasing N in humans and a declining N in dairy cattle. CSH is a valuable statistic for inferring population histories from haplotype data, and has implications for mapping of disease loci.
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            Effects of genetic drift on variance components under a general model of epistasis.

            We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.
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              Prediction of identity by descent probabilities from marker-haplotypes.

              The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.
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                Author and article information

                Journal
                Genetics
                Genetics
                Genetics Society of America
                0016-6731
                0016-6731
                Aug 2007
                : 176
                : 4
                Affiliations
                [1 ] Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, W. Mains Road, Edinburgh, United Kingdom. w.g.hill@ed.ac.uk
                10.1534/genetics.107.074344
                1950633
                17507671

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