animal breeding applications of pedigree based mixed model
DESCRIPTION
Talk at House sparrow "lunch” meeting at NTNU, Department of Biology (http://www.ntnu.edu/biology), Trondheim, NorwayTRANSCRIPT
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Animal Breeding Applications of PedigreeBased Mixed Model
Gregor Gorjanc
University of Ljubljana, Biotechnical Faculty, Department of Animal Science, Slovenia
House sparrow "lunch” meetingTrondheim, Norway1st September 2010
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Thank you for the invitation to NTNU!!!
My department ...
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Table of Contents
1. What is the idea of animal breeding (genetic evaluation)
2. What kind of models do we use2.1 variations in the phenotype model - likelihood (data sampling
model)2.2 variations in the genetic model - prior
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Introduction
I Animal breeding= mixture(animal science, genetics, statistics, . . . )
I Many species (cattle, chicken, pig, sheep, goat, horse, dog,salmon, shrimp, honeybee, . . . )
I Many (complex) traits:I production (milk, meat, eggs, . . . )I reproduction (no. of offspring, insemination success, . . . )I conformation (body height, width, . . . )I health & longevityI . . .
I Genetic evaluation - to enhance selective breeding
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Selective BreedingI Measure phenotype in candidates and select those with the
most favourable values (= "mass” selection)I Selected candidates will bred the next (better) generation
I . . . , but phenotype is not transmitted to the next generation
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Decomposition of Phenotypic Value
Genotype Environment
Phenotype
P = G + E + G × E
I Genetic evaluation = inference of genotypic value given thedata and postulated model (= “BLUP” selection)
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Postulated Model and Data
I Postulated model
P = G + E + G × E = A + D + I + . . .
I A - additive (breeding) valueI D - dominanceI I - epistasis
I DataI phenotypes (own performance, progeny, (half)-sibs
-> in fact almost all animal "management data” from teststations & farms
I pedigrees - share of genes that relatives have due to the sameorigin (identity-by-descent = IBD)
I recently also genotype marker data (identity-by-state = IBS)
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Pedigree based Mixed ModelsI Standard example - “animal model”
y|b, c, a,R ∼ N (Xb + Zcc + Zaa,R)
R = Iσ2e
b ∼ const.c|C ∼ N (0,C)
C = Iσ2c
a|G ∼ N (0,G)
G = Aσ2a
data: y (phenotypes), X,Z∗(“covariates”), A (pedigree)
parameters: b, c, a (means)σ2
c , σ2a , σ
2e (variances)
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Multi-trait (= Multi-variate) ExampleI analyze many traits together - to estimate correlations and to
cover for possible selection on one trait
y =(yT
1 , yT2)T, X = . . .
y| . . . ∼ N (Xb + Zcc + Zaa,R)
R = R0 ⊗ I,R0 =
(σ2
e1 σe1,e2
sym. σ2e2
)c|C ∼ N (0,C)
C = C0 ⊗ I,C0 =
(σ2
c1 σc1,c2
sym. σ2c2
)a|G ∼ N (0,G)
G = G0 ⊗ A,G0 =
(σ2
ad1σad1 ,ad2
sym. σ2ad2
)I there are now 9 variance components!!!
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Phenotype Model “Variation” - Non-GaussianI Categorical (health status, calving ease score, . . . )
I threshold model = (ordered) probit model, cumulative linkmodel, . . .
I multinomial categories mostly treated separately as binarytraits
I Counts (no. of offspring, . . . )I Poisson, but rarely used - replacements: threshold and/or
Gaussian model
I Time (longevity)I survival (Weibull & Cox) models
I MixturesI Gaussian componentsI zero-inflated (no. of black spots in sheep skin -> wool, cure
model - bivariate threshold model)
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Statistical ViewI Specify the model
y|µ,θ ∼ Some − Distribution (µ,θ)
g (µ) = η = Xb + Zcc + Zaab ∼ const.
c|C ∼ N (0,C)
C = Iσ2c
a|G ∼ N (0,G)
G = Aσ2a
I Find some inference (black-box) engine (BUGS, JAGS, INLA,. . . ) to do the job of finding parameter estimates ;)
I Some multi-variate combinations have already beenimplemented
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Genotype Model “Variation”
I Standard - additive genetic modelI Some extensions
I maternal/paternal modelI dominanceI epistasisI social interactions - competitive effectsI genotype x environment interactionI genetic variation of environmental variationI genotype marker data -> genomic selectionI . . .
I Proper data structure and the amount of data is essential!!!
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Maternal/Paternal ModelI Phenotype (say growth) of animal influenced by:
I genes for growth “in animal”I genes for milk “in mother”
y|b, c, ad , am,R ∼ N (Xb + Zcc + Zadad + Zamam,R)
R = Iσ2e
b ∼ const.c|C ∼ N (0,C)
C = Iσ2c
a =(aT
d , aTm)T |G ∼ N (0,G)
G = G0 ⊗ A,G0 =
(σ2
adσad ,am
sym. σ2am
)
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Social Interactions - Competitive EffectsI Phenotype of animal influenced by:
I genes for that trait “in animal”I genes for competition (for resources) “in companions”
yi = µ+ . . .+ adi +∑
j∈c(i)
asj + ei
c (i) a set of companions of individual iy|b, c, ad , as ,R ∼ N (Xb + Zcc + Zadad + Zasas ,R)
R = Iσ2e
b ∼ const.c|C ∼ N (0,C)
C = Iσ2c
a =(aT
d , aTs)T |G ∼ N (0,G)
G = G0 ⊗ A,G0 =
(σ2
adσad ,as
sym. σ2as
)
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Thank you!