The effect of dominance genetic parameters on rank of breeding value predictions

1
The effect of dominance genetic parameters on
rank of breeding value predictions
VD
iteration

• Jon Hallander
• Department of Forest Genetics and Plant
  Physiology, Swedish University of Agricultural
  Sciences,
• SE-901 83 Umeå, Sweden

2
Content

• introduction
• model development
• data material
• results
• conclusions

3
Introduction

• improvements
• in breeding
• accurate genetic
• parameters needed
• powerful statistical
• methods needed
• Increased production!

4
Traditional tree breeding

• breeding cycles (parent-offspring)
• time consuming
• no pedigree information
• family based models
• only additive component

5
Non-additive variance

• genetic drift situations affects genetic variance
• population bottlenecks
• founder events
• inbreeding
• directional selection
• presence of non-additive variance
• theoretical (e.g. Lopez-Fanjul et al. 2002,
  Barton and Turelli 2004, Carter et al. 2005,
  Hallander and Waldmann 2007)
• model organisms (e.g. Whitlock and Fowler 1999,
  Lindholm et al. 2005, Biggs and Goldmann 2006)

6
Why include dominance?

• better estimates of additive effects
• better ranking of selection candidates
• dominance is important to avoid inbreeding
  depression
• affects additive variance during selection

7
Statistical model
Mixed model equations
y Xb Zu e
Hendersons reformulation for one trait
(individual tree model, cf. animal model)

• inclusion of dominance term into the model
• troublesome to invert the coefficient matrix

8
Gibbs sampler

• Markov chain Monte Carlo (MCMC) method
• stochastic process
• obtain stationary
• distribution
• posterior distribution

Markov chain of additive variance
marginal posterior distribution of VA
VA
Iteration
9
Model development

• Individual tree model
• fixed effect block
• random effects additive, dominance
• polygenic model

10
Model development

• single site Gibbs sampler
• fast
• bad mixing
• blocked Gibbs sampler
• slow
• good mixing

• hybrid Gibbs sampler
• runs blocked sampler each 50th iteration
• speed
• mixing

Sorensen and Gianola 2002
11
Model development

• variable transformation

12
Model development

• equation system in MME
• sparse equation system

obtained fully conditional posteriors
13
Method summary

• model development
• estimate VA, VD, VE and breeding values in a non
  inbred population
• Bayesian approach
• model verification
• real data 2 traits (diameter, height)
• model comparison

14
Data material

• Scots pine (Pinus Sylvestris L.)
• partial diallel design
• 5022 individuals
• 26 years old
• two traits
• height
• stem diameter

15
Results

• trait diameter

Posterior dist. for VA
Posterior dist. for VD
Posterior dist. for VE
Density
VA mode 54.7 mean 62.5 HPD
2.5 27.7 HPD 97.5 103.7
VD mode 82.8 mean 88.5 HPD
2.5 39.7 HPD 97.5 142.1
VE mode 722.2 mean 721.7 HPD
2.5 665.3 HPD 97.5 776.8
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Results
Posterior dist. for h2 for both A and AD models
AD
A
Density
Density
A mode 0.0798 mean 0.0890 HPD
2.5 0.0484 HPD 97.5 0.1363
d2 mode 0.0939 mean 0.1014 HPD
2.5 0.0457 HPD 97.5 0.1616
AD mode 0.0630 mean 0.0714 HPD
2.5 0.0327 HPD 97.5 0.1170
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Results

• stem diameter
• breeding value (EBV)
• dominance value

MCMC of additive value (EBV)
MCMC of dominance value
Position
Position
Iteration
Iteration
18
Results
ranking of clones based on mean of posterior
distribution of EBV
19
Results

• position of some individuals for diameter (mean,
  EBV)

20
Results
21
Conclusions

• new model implemented and tested
• hybrid Gibbs sampler works smooth
• variable transformation successful
• relatively high levels of dominance in Swedish
  pine breeding population
• more accurate ranking of individuals in breeding
  populations

22
Future work

• implement model on a cluster network
• increased sample size possible
• extended study on EBV
• selection index EBV - d values
• overview of non-additive variance in tree
  literature
• implications to breeding
• using marker information

23
Acknowledgements
Patrik Waldmann1, Fabian Hoti2,3, Mikko J.
Sillanpää2 1 Department of Forest Genetics and
Plant Physiology, SLU, SE-901 83 Umeå,
Sweden 2Department of Mathematics and
Statistics, P.O. Box 68, FIN-00014 University of
Helsinki, Finland 3National Public Health
Institute, Department of Vaccines, FIN-00300
Helsinki, Finland