Behaviour of the additive finite locus model

Pong‐Wong, Ricardo; Haley, Chris; Woolliams, John

doi:10.1186/1297-9686-31-3-193

Cited by 13 publications

(10 citation statements)

References 20 publications

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“…Recently, a number of researchers have used finite locus models to estimate additive variance and breeding values [7,11,13,21]. The models assume a prior distribution of gene effects from which effects at individual loci are sampled.…”

Section: Discussionmentioning

confidence: 99%

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The distribution of the effects of genes affecting quantitative traits in livestock

Hayes¹,

Goddard

2001

Genet. Sel. Evol.

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Meta-analysis of information from quantitative trait loci (QTL) mapping experiments was used to derive distributions of the effects of genes affecting quantitative traits. The two limitations of such information, that QTL effects as reported include experimental error, and that mapping experiments can only detect QTL above a certain size, were accounted for. Data from pig and dairy mapping experiments were used. Gamma distributions of QTL effects were fitted with maximum likelihood. The derived distributions were moderately leptokurtic, consistent with many genes of small effect and few of large effect. Seventeen percent and 35% of the leading QTL explained 90% of the genetic variance for the dairy and pig distributions respectively. The number of segregating genes affecting a quantitative trait in dairy populations was predicted assuming genes affecting a quantitative trait were neutral with respect to fitness. Between 50 and 100 genes were predicted, depending on the effective population size assumed. As data for the analysis included no QTL of small effect, the ability to estimate the number of QTL of small effect must inevitably be weak. It may be that there are more QTL of small effect than predicted by our gamma distributions. Nevertheless, the distributions have important implications for QTL mapping experiments and Marker Assisted Selection (MAS). Powerful mapping experiments, able to detect QTL of 0.1σp, will be required to detect enough QTL to explain 90% the genetic variance for a quantitative trait.

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Section: Discussionmentioning

confidence: 99%

“…The models assume a prior distribution of gene effects from which effects at individual loci are sampled. Uniform distributions [7], Normal distributions [7,11,21], exponential distributions [21] and gamma distributions [13] have been assumed. In all cases, the parameters of the distributions were chosen arbitrarily.…”

Section: Discussionmentioning

confidence: 99%

The distribution of the effects of genes affecting quantitative traits in livestock

Hayes¹,

Goddard

2001

Genet. Sel. Evol.

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“…To estimate the development of genetic variance under various conditions, Monte Carlo simulations have been widely applied in animal breeding and conservation genetics since computers were introduced [5, 6], and they remain a valuable tool [7, 8]. Currently, two main types of genetic models are used to investigate developments in genetic variance via simulations: Fisher’s infinitesimal model [9, 10] and the finite locus models [11, 12]. The infinitesimal model assumes that quantitative traits are genetically influenced by an infinitely large number of loci, each of which has the same infinitesimally small impact.…”

Section: Introductionmentioning

confidence: 99%

Comparison of infinitesimal and finite locus models for long-term breeding simulations with direct and maternal effects at the example of honeybees

et al. 2019

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Stochastic simulation studies of animal breeding have mostly relied on either the infinitesimal genetic model or finite polygenic models. In this study, we investigated the long-term effects of the chosen model on honeybee breeding schemes. We implemented the infinitesimal model, as well as finite locus models, with 200 and 400 gene loci and simulated populations of 300 and 1000 colonies per year over the course of 100 years. The selection was of a directly and maternally influenced trait with maternal heritability of , direct heritability of , and a negative correlation between the effects of r md = − 0.18. Another set of simulations was run with parameters , , and r md = − 0.53. All models showed similar behavior for the first 20 years. Throughout the study, we observed a higher genetic gain in the direct than in the maternal effects and a smaller gain with a stronger negative covariance. In the long-term, however, only the infinitesimal model predicted sustainable linear genetic progress, while the finite locus models showed sublinear behavior and, after 100 years, only reached between 58% and 62% of the mean breeding values in the infinitesimal model. While the infinitesimal model suggested a reduction of genetic variance by 33% to 49% after 100 years, the finite locus models saw a more drastic loss of 76% to 92%. When designing sustainable breeding strategies, one should, therefore, not blindly trust the infinitesimal model as the predictions may be overly optimistic. Instead, the more conservative choice of the finite locus model should be favored.

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“…Such priors can be put either on the QTL effects themselves or on the QTL variances. For the former, possible choices include independent truncated normal (on [0, ∞]) or exponential priors (Pong-Wong et al, 1999;Du and Hoeschele, 2000a). For the latter, independent exponential priors can be placed on the additive and dominance variances of a QTL, and from this prior a prior for the additive and dominance effects can be derived.…”

Section: Prior Distributionsmentioning

confidence: 99%

“…Furthermore, FLMs differ in the number of loci, the treatment of additive, dominance and epistatic effects as constant or variable across loci, the number of two-locus interactions, and the prior distributions of the effects (Du et al, 2000;Du and Hoeschele, 2000a;Pong-Wong et al, 1999). Particularly in the presence of dominance or epistasis, estimates of the genetic variance components have been found to depend on the number of loci in the FLM, probably a small-sample problem, and this dependency is affected by the prior distribution of effects and the genotype sampling scheme (Du and Hoeschele, 2000a;Du et al, 2000;Pong-Wong et al, 1999). Modeling polygenic variation with an FLM seems more suitable in particular for linkage analysis, where an existing QTL is allowed to become unlinked and hence a member of the group of polygenic loci.…”

Section: Modeling Of Polygenic and Qtl Effectsmentioning

confidence: 99%

Mapping Quantitative Trait Loci in Outbred Pedigrees

Höschele¹

2007

Handbook of Statistical Genetics

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In this chapter, we present statistical methods for mapping quantitative-trait loci (QTLs) in outbred or complex pedigrees. Such pedigrees exist primarily in livestock populations, also in human populations, and occasionally in experimental animal or plant populations. The main focus of this chapter is on linkage mapping, but methods for linkage disequilibrium (LD) and combined linkage/LD mapping are also discussed. We describe least-squares and maximum likelihood (ML) methods for estimating QTL effects, and variance-components analysis by approximate (residual) ML for estimating QTL variance contributions. We describe Bayesian QTL mapping, its prior distributions and other distributional assumptions, its implementation via Markov chain Monte Carlo (MCMC) algorithms, its inferences, and contrast it with frequentist methodology. Genotype sampling algorithms using genotypic peeling, allelic peeling or descent graphs are described. Genotype samplers are a critical component of MCMC algorithms implementing ML and Bayesian analyses for complex pedigrees. Lastly, fine-mapping methods including chromosome dissection and LD mapping using current and historical recombinations, respectively, are outlined, and recently developed methods for joint LD and linkage mapping of disease genes and QTL are discussed. INTRODUCTIONIn this chapter, the focus is on statistical methods for mapping of quantitative-trait loci (QTLs) in populations which have not been formed recently by line crossing, and which have pedigree information available over multiple generations. Methods suitable for QTL mapping in (inbred) line crosses are described in Chapter 18. Pedigrees are used for QTL mapping in livestock and human populations, where the development and crossing of inbred lines is not feasible. Therefore, the methods discussed here have applications primarily in mapping genes for quantitative traits of economic importance in livestock and complex disease risk factors in humans. Examples include milk production in dairy 623 Handbook of Statistical Genetics, Third Edition . E dited by D . J. Balding, M . Bishop and C. Cannings.

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Behaviour of the additive finite locus model

Cited by 13 publications

References 20 publications

The distribution of the effects of genes affecting quantitative traits in livestock

The distribution of the effects of genes affecting quantitative traits in livestock

Comparison of infinitesimal and finite locus models for long-term breeding simulations with direct and maternal effects at the example of honeybees

Mapping Quantitative Trait Loci in Outbred Pedigrees

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