1. Using a MQTL matrix to test for pleiotropic effects of Mendelian trait loci on quantitative traits.
C. Scheper1. S. König1
1Institute of Animal Breeding and Genetics. Justus-Liebig-University Gießen Gießen
Dear Ladies and Gentleman. My name is Carsten Scheper. I am a Phd Student at the Institute of Animal Breeding and Genetics at the Justus Liebig University in Gießen. The topic i am speaking about today is an approach to test for pleiotropic effects of a Mendelian trait in cattle that is viewed as beneficial rather than detrimental. bovine polledness. However this approach could also be a feasible tool to test secondary effects of other Mendelian traits or detrimental genetic defects on other important traits as well.

2. Background | Research question
Introduction
Background | Research question
Managing a growing number of genetic characteristics (detrimental as well as beneficial) has become a major task in modern breeding programs (e.g. Cole 2015, Segelke et al 2016)
focus has shifted from asap elimination to short/mid term management and long-term elimination for detrimental recessives
negative secondary effects of recessives on other traits in breeding goals become potentially more important (e.g. Cole et al 2016), especially for beneficial characteristics (e.g. polledness (Götz et al 2015))
Are these observations due to direct pleiotropic effects or linkage to causal variants (QTL) of secondary traits?
Search for methods to estimate these direct effects of the Mendelian trait polledness on secondary quantitative traits in German Simmental cattle
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mehr Fokus auf Krankheiten

3. Variance component estimation methods to test for QTL effects
Introduction | Material and Methods
Variance component estimation methods to test for QTL effects
methods for mapping QTLs based on marker information via variance component estimation (i.e. Fernando & Grosman van Arendonk et al )
inclusion of QTL effects using special gametic ( 𝑮 𝒗 ) or numerator ( 𝑨 𝒗 ) relationship matrices derived from single- or multiple marker information
separation of polygenic (𝑨) effects and QTL-effects of the polled locus ( 𝑨 𝒗 ) for other traits
Procedure:
Variance component estimation for:
basic model with a pedigree-based animal effect -> Basic(univariate)
basic model + random QTL-effect based on 𝑨 𝒗 -> QTL (univariate)
bivariate model with the same model structure as QTL (univariate) but also modelling the Mendelian trait with a simple linear model including only the QTL-effect: 𝒚 𝒊 = 𝒗 𝒊 + 𝒆 𝒊 (numeric genotypes (0,1,2) as phenotypes) (referring to e.g. Sörensen et al 2003)
i) Validation in simulated data ii) Application to a real dataset from German Simmental
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4. Relationship Matrix 𝑨 𝒗 based on marker genotypes (MQTL-matrix)
Material and Methods
Relationship Matrix 𝑨 𝒗 based on marker genotypes (MQTL-matrix)
= gametes
calculation is based on reliably reconstructed polled genotypes in the German Simmental pedigree
calculation of transmission probabilites between gametes based on given (polled) marker genotypes using the recursive algorithm of van Arendonk et al
the relationship of polled animals among each other is enhanced compared to the numerator relationship matrix
𝑨 (𝐚𝐛𝐨𝐯𝐞 𝐝𝐢𝐚𝐠) 𝑨 𝒗 (𝒅𝒊𝒂𝒈+𝒃𝒆𝒍𝒐𝒘) P p p p P p P p
überarbeiten P P p p
2695|2694 and 2517|2516 = FS (same dam)
2695, 2694, 2517, 2516 = HS (same sire)

5. Validation using stochastic simulation (i)
Material and Methods
Validation using stochastic simulation (i)
Stochastic simulation with QMSim:
Population:3400 animals (3000 females with phenotypes. 400 males). 5 generations. random mating and selection
2 simulated quantitative traits: 1. h2 = h2 = 0.05
single QTL with a defined heritability of simulated as a Mendelian trait locus on 1 chromosome with the same size as BTA1
variance component estimation for the 3 mentioned models using DMU (Madsen et al. 2006)
𝑨 𝒗 precalculated using a self-written R function

6. Validation using stochastic simulation (i)
Results
Validation using stochastic simulation (i)
Trait
Model
σ2a
σ2v
σ2e h2
(polygenic + QTL)
QTL-h2
SE(h2)
logLik
h2 = 0.30
QTL-h2 = 0.025
Basic(univariate)
0.0030
0.0072
0.2918
0.0374
QTL (univariate)
0.0019
0.0001
0.2832
0.0944
0.0508
QTL (bivariate)
0.0025
0.0005
0.2909
0.0465
0.0464
h2 = 0.05
0.1168
2.9110
0.0386
0.0207
0.3538e-06
0.1409
2.8775
0.0467
0.0281
0.0169
0.1177
2.8755
0.0447
0.0391
0.0280
simulated QTL-effects are detected, however they are overestimated
overestimation is smaller using bivariate models (in accordance with Sörensen et al 2003)
overestimation higher in trait with h2 = 0.05

7. Material and Methods (ii) – dataset and models
Performance Traits
Traits: MY (milk yield), F% (fat percent), P% (protein percent), SCS (somatic cell score)
Dataset: test-day records from 1746 German Simmental cows (12 farms)
Model:
𝒚 𝒊𝒋𝒌𝒍 = 𝑳𝒂𝒄𝒕 𝒊 + 𝑯𝑻𝑫 𝒋 + 𝑪𝑺 𝒌 + 𝒃 𝟎 𝑷𝒓𝒆𝒈𝒅 𝒊𝒋𝒌𝒍 + 𝒃 𝑰 𝑪𝑨 𝒊𝒋𝒌𝒍 + 𝑰𝑰=𝟏 𝟑 𝒃 𝑰𝑰 𝑿 𝒊𝒋𝒌𝒍 + 𝒂 𝒍 + 𝒗 𝒍 + 𝑷𝑬 𝒍 + 𝒆 𝒍
fixed effects: lactation, herd-test-day, calving season | covariables: days pregnant, calving age, legendre polynoms 1-3
random effects in all models: animal (a), permanent environment (PE), residual error (e)
QTL-effect polled locus (v)→ Base models for comparison estimated without QTL-effects
Pedigree:
8624 animals with polled genotypes (5 generations back) -> basis for the calculation of 𝑨 𝒗
variance component estimation for the 3 mentioned models using DMU (Madsen et al. 2006)

8. Results (ii) – Performance Traits
Variance Components
Trait
Model
σ2a
σ2v
σ2PE
σ2e h2
(polygenic + QTL)
QTL-h2
SE(h2)
logLik MY
Basic (univariate)
5.771
5.504
15.482
0.216
0.030
QTL (univariate)
0.313e-03
0.117e-04
0.037
QTL (bivariate)
5.613
0.019
5.574
15.483
0.211
0.704e-03
0.014 F%
0.100
0.025
0.257
0.262
0.024
0.147e-04
0.384e-04
0.029
0.975e-04
0.261
0.255e-03
0.015 P%
0.035
0.003
0.038
0.498
0.033
0.001
0.457
0.034
0.912e-03
0.463
0.012
SCS
0.255
0.570
1.645
0.103
0.021
0.240
0.010
0.573
0.101
0.004
0.249
0.200e-03
0.612e-04
0.011
no evidence for substantial QTL-effects of the polled locus for MY, F%, SCS
small QTL effect detected for P% (~2.6% of total heritability in bivariate model)

9. Material and Methods (ii) – dataset and models
Reproduction Traits
Traits: NRR-56 (non return rate 56, cow), DFS (days to first service, cow), DO (days open, cow)
Dataset: 3834 records from 1368 German Simmental cows (12 farms)
Models: NRR-56 𝒍𝒐𝒈𝒊𝒕 𝒚 𝒊𝒋𝒌 = 𝑭𝒀 𝒊 + 𝑻𝒚𝑰𝒀 𝒋 + 𝑳𝑨𝑪𝑨 𝒌 ++ 𝒂 𝒍 + 𝒗 𝒍 + 𝑷𝑬 𝒍 + 𝒆 𝒍
DFS | DO 𝒚 𝒊𝒋𝒌𝒍 = 𝑭𝒀 𝒊 +𝑹𝒀𝑴 𝒋 + 𝒂 𝒍 + 𝒗 𝒍 + 𝑷𝑬 𝒍 + 𝒆 𝒍
fixed effects: farm-year, type of insemination-year, lactation-calving age class, region-year-month
random effects in all models: animal (a), permanent environment (PE), residual error (e)
QTL-effect polled locus (v)→ Base models for comparison estimated without QTL-effects
Pedigree:
8624 animals with polled genotypes (5 generations back) -> basis for the calculation of 𝑨 𝒗
variance component estimation for the 3 mentioned models using DMU (Madsen et al. 2006)

10. Results (ii) – Reproduction Traits
Variance Components
Trait
Model
σ2a
σ2v
σ2PE
σ2e h2
(polygenic + QTL)
QTL-h2
SE(h2)
logLik
NRR-56
Basic (univariate)
0.081
0.191
3.290
0.023
0.029
QTL (univariate)
0.063
0.011
0.196
0.021
0.003
0.050
QTL (bivariate)
0.066
0.100e-03
0.204
0.019
0.387e-04
0.036
DFS
63.636
71.755
0.026
0.027
55.629
23.449
70.368
0.033
0.010
0.022
17.784
0.800e-03
0.009
0.115e-04
0.047 DO
0.048
0.032
24.778
0.054
47.923
0.299
0.020
0.001
no evidence for substantial QTL-effects, however considering the small overall heritability they account for a higher relative fraction
bivariate models tend to underestimate the overall genetic variance in contrast to performance traits

11. Results (ii) 𝒓 𝑷 𝒓 𝒈 (𝒗) Genetic Correlations
genetic correlations from bivariate models show no unfavourable antagonistic relationships
𝒓 𝒈 (𝒗) should be interpreted in relation to the size of estimated QTL-effects
a proposed procedure could be:
estimate QTL-effects of a Mendelian trait on other traits
results: substantial QTL-effect present QTL-effect not present / very small
2. utilize 𝒓 𝒈 (𝒗) 𝒓 𝒈 (𝒗) are negligible MY F% P%
SCS
NRR56
DFS DO
𝒓 𝑷
-0.193
-0.025
-0.067
0.012
-0.041
-0.059
𝒓 𝒈 (𝒗)
-0.020
-0.005
-0.026
-0,042
-0,078
-0,035

12. Conclusions
We found evidence for a small pleiotropic or linked effect of the polled locus on P%. However the genetic correlation based on the bivariate QTL-model shows no antagonistic relationship
Given the presented results there is no evidence for substantial direct negative effects of the polled locus in German Simmental cattle on performance and reproduction traits
The presented approach could potentially be a helpful tool for the initial evaluation of (beneficial and detrimental) mendelian traits/genetic characteristics to infer their potential effects on other important traits
In presence of substantial QTL-effects of a Mendelian trait, genetic correlations based on bivariate QTL-models can be utilized in breeding plan evaluations / indexes

13. Thank you for your attention
Acknowledgments
we´d like to thank:
The present study was supported by funds of the German Government´s Special Purpose Fund held at Landwirtschaftliche Rentenbank. The authors gratefully thank the Landwirtschaftliche Rentenbank for funding this project.
Prof. Dr. Götz and Dr. Emmerling from the Institute of Animal Breeding at the Bavarian State Research Centre for Agriculture. for preparing and providing the data.
our Project Partner:
Group of Prof. Swalve at University Halle-Wittenberg/Germany
Thank you for your attention