Mucha, Sebastian

Strabel, Tomasz

Wolc, Anna

English

PubMed

Sebastian Mucha

Anna Wolc

Tomasz Strabel

Springer - Publisher Connector

PROCEEDINGS Open Access
Comparison of methods for estimation of genetic
covariance matrix from SNP or pedigree data
utilised to predict breeding value
Sebastian Mucha*, Anna Wolc, Tomasz Strabel
From 13th European workshop on QTL mapping and marker assisted selection
Wageningen, The Netherlands. 20-21 April 2009
Abstract
Background: The aim was to predict breeding values of non-phenotyped individuals based on a dataset prepared
for the 13th QTL-MAS Workshop in Wageningen.
Methods: Genetic co-variance matrices between animals were estimated with three methods: one using pedigree
information only and two based on SNP markers from the first chromosome. Quadratic regression of breeding
values, estimated separately in each of the five time points, was used to predict the breeding values in the
6th time point.
Results: Based on the comparison (true - estimated BV) it can be concluded that SNP based methods provided
better estimates (accuracy between 0.75 and 0.80) than pedigree (0.65).
Conclusions: Even though only SNPs from chromosome 1 were used it was still possible to achieve fairly high
accuracies. Most likely this was due to the fact that chromosome 1 contained the QTLs with the largest effects.
Background
The analysis was based on a dataset prepared for the
13th QTL-MAS Workshop in Wageningen [1]. The aim
of this paper was to predict breeding values of the 1000
non-phenotyped animals in the 6th time point, using
three different strategies based on similarity between
individuals due to common ancestry (pedigree records),
and two methods based on marker similarity. Due to
software limitations [2] only one chromosome could be
included in the analysis. The first chromosome was cho-
sen based on preliminary results of QTL mapping, per-
formed with a single QTL model with additive effects in
the GRID QTL package [3]. The most significant QTLs,
affecting the analysed trait in all five time points, were
found on chromosome 1.
Methods
Estimation of genetic relationship
Genetic covariance matrices between all animals present
in the dataset were estimated with three methods. First
approach (pedigree based method - PB) was based on
the additive relationship matrix calculated from pedi-
gree. Second method computed similarity between indi-
viduals as a correlation coefficient between allelic states
using 90 SNP markers from chromosome 1 (SNP based
method - SNPL). For this purpose the method of Loi-
selle [4] was used as implemented in software package
SPAGeDi 1.2g [2], which computes relationship as aij =
Σ1 [ Σa(ΣciΣcj(x1cia - p1a)(x1cja - p1a)/ΣciΣcj1) + Σa(p1a
(1 - p1a)/(n1 - 1)) ] / ΣlΣa (p1a(1 - p1a)) where x1cia is an
indicator variable (x1cia = 1 if the allele on chromosome
c at locus l for individual i is a, otherwise x1cia = 0), p1a
is the frequency of allele a at locus l in the reference
sample, n1 is the number of alleles defined in the sample
at locus l (the number of individuals times the ploidy
level minus the number of missing alleles), and Σci
stands for the sum over the homologous chromosomes
* Correspondence: smucha@jay.up.poznan.pl
Department of Genetics and Animal Breeding, Poznan University of Life
Sciences, Wolynska 33, 60-637 Poznan, Poland
Mucha et al. BMC Proceedings 2010, 4(Suppl 1):S7
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© 2010 Mucha et al; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
of individual i. Here, the term involving (n1 - 1) is a
sampling bias correction. The program calculates the
pair wise relationship between animals i and j (aij) leav-
ing the diagonal elements blank (aii), thus selfcoancestry
had to be estimated as: Fk = 1 + 0.5*aij, where aij is rela-
tionship between parents i and j of individual k.
The third method used MCMC (Markov Chain Monte
Carlo simulations) to estimate genetic relationship
between animals for a selected number of 39 SNP mar-
kers from chromosome 1, with minor allele frequency
above 0.1 (selected SNP method - SNPC). This limita-
tion was imposed due to time-extensive properties of
the MCMC method. Software package Citius[5,6] was
used to apply the MCMC method to calculate multilo-
cus genotype probabilities and to analyse genes shared
identical by descent (IBD). IBD matrices were calculated
in 9 points along the analysed fragment of chromosome
1. Afterwards they were averaged into one G-matrix,
that was used for further computations.
Estimation of variance components and breeding values
Variance components were estimated separately for each
time point (0, 132, 265, 397, 530), with ASREML [7]
using the following model:
yi = μ + ai + ei
Where: yi - analysed trait ai - random additive genetic
effect of animal i; ei - random residual effect.
The covariance structure was specified as:
E
a
e



 




0
0
and V
a
e
G
I
a
e



 




2
20
0

where: a2 - additive genetic variance,  e2 - residual var-
iance, G - genetic relationship matrix, I – identity matrix.
The analysis was performed with three types of
genetic covariance matrices (G) based on: pedigree (PB
method), and SNP markers (methods SNPL and SNPC).
Quadratic regression of predicted breeding values on
time, extracted from ASREML, in the first five time
points was applied to estimate least square regression
coefficients for each animal. Subsequently, the estimated
regression coefficients were used topredict the unknown
breeding values in the 6th time point (time 600) using the
following formula:
y x x xi i i i600 0 1 2
2
, , , ,      
where: y600,i is the breeding value in time point 600;
ˆ
,1 i , ˆ ,1 i , and, ˆ ,2 i are least square regression coefficients,
estimated for animal i.
Results
Variance components
Regardless of the method used, genetic and residual var-
iances increased with time (Table 1). Estimates of
Table 1 Estimates of genetic and residual variance and
heritability at five time points (T0, T132, T265, T397 and
T530) obtained with three methods: SNPL - covariance
structure from 90 SNPs on chromosome 1 (Loiselle et al.
1995), SNPC - covariance structure from 30 selected SNPs
with minor allele frequency >0.1 (Szydlowski et al. 2008),
PB - covariance structure from pedigree.
T0 T132 T265 T397 T530
Genetic variance
PB 0.05 0.33 1.81 7.49 19.23
SNPL 0.05 0.35 2.10 8.84 23.32
SNPC 0.04 0.28 1.62 6.50 16.21
Residual variance
PB 0.05 0.35 2.05 8.62 21.32
SNPL 0.04 0.27 1.53 6.35 14.98
SNPC 0.06 0.41 2.30 9.58 23.76
Heritability
PB 0.50 0.48 0.46 0.46 0.47
SNPL 0.53 0.56 0.57 0.58 0.60
SNPC 0.40 0.40 0.41 0.40 0.40
Table 2 Correlation between breeding values in five time
points (T0, T132, T265, T397 and T530) , estimated with
a genetic covariance matrix based on 90 SNPs from
chromosome 1 (SNPL method).
T0 T132 T265 T397 T530
T0
T132 0.987
T265 0.939 0.981
T397 0.862 0.929 0.982
T530 0.818 0.894 0.961 0.995
Table 3 Correlation between breeding values in five time
points (T0, T132, T265, T397 and T530) estimated with a
genetic covariance matrix based on a selected number of
SNPs from chromosome 1, with minor allele frequency
>0.1 (SNPC method).
T0 T132 T265 T397 T530
T0
T132 0.987
T265 0.940 0.981
T397 0.865 0.932 0.983
T530 0.824 0.899 0.964 0.995
Table 4 Correlation between breeding values in five time
points (T0, T132, T265, T397 and T530) estimated with a
genetic covariance matrix based on pedigree records (PB
method).
T0 T132 T265 T397 T530
T0
T132 0.986
T265 0.930 0.978
T397 0.841 0.918 0.979
T530 0.792 0.879 0.956 0.994
Mucha et al. BMC Proceedings 2010, 4(Suppl 1):S7
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genetic variance were lower for the SNPC method than
the PB or SNPL method. In case of the PB method her-
itability decreased from 0.51 (time point 0) to 0.47 (time
point 530). On the other hand the SNPL method
resulted in genetic variance increasing more than the
residual variance, which resulted in an increase of herit-
ability from 0.53 (time point 0) to 0.60 (time point 530).
Heritability estimates for the SNPC method did not dif-
fer much between the time points and were between
0.40 and 0.41. Correlations between breeding values in
the different time points were high - between 0.82 and
Table 5 Correlation and regression of true breeding
values (provided by the organizers) on breeding values
estimated with three methods: PB - relationship based
on pedigree records, SNPL - genetic similarity estimated
from 90 SNP markers from chromosome 1,
SNPC - relationship estimated from selected
SNP markers from chromosome 1 with minor allele
frequency >0.1.
PB SNPL SNPC
Correlation 0.65 0.75 0.80
Regression 0.93 0.79 0.92
Figure 1 Breeding values for members of the same 4 arbitrary selected full sib families (top diagrams - families without observations; bottom
diagrams - families with observations) estimated with genetic covariances based on 90 SNP markers from chromosome 1 (SNPL method). Similar
picture was obtained when only 30 SNPs, with minor allele frequency >0.1, from chromosome 1 (SNPC method) was used (result not shown)
Mucha et al. BMC Proceedings 2010, 4(Suppl 1):S7
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Page 3 of 5
0.99 for the SNPL and SNPC methods (Table 2 and
Table 3) and between 0.79 and 0.99 for the PB method
(Table 4) reached around 0.98.
Breeding values
The variance of predicted breeding values in the time
point 600 was the lowest for the PB method (17.44), the
highest for the SNPL method (27.94), and moderate for
the SNPC method (20.42). In contrast to the PB in case
of the SNP based methods there was considerable varia-
tion in breeding values within FS families (Figure 1). Cor-
relations between breeding values in time point 600,
estimated with the three methods were between 0.82 and
0.86. When comparing the list of top 20 nonphenotyped
animals selected with the three methods with the true list
of top 20 nonphenotyped animals from the simulation
(as provided by organizers), than the PB method had
only 30% of individuals in common. Higher agreement
was found for SNP based methods: 45% and 50% for the
SNPC and the SNPL methods, respectively. Accuracy of
breeding values (correlation between predicted and true
breeding values) for the 1000 nonphenotyped individuals
in the time point 600 was the lowest for the PB method
(0.65), higher for the SNPL method (0.75) and the highest
for the SNPC method (0.80). Regression coefficients of
true breeding values on predicted breeding values were
between 0.79 - 0.93 (Table 5).
Discussion
The genetic variance estimated with the PB method was
the closest to the true (simulated) one while variance com-
ponents obtained with SNPL method were slightly overes-
timated. Underestimation of genetic variance with the
SNPC method can be due to ignoring a part of SNPs.
Changes of heritability estimates in case of the SNPL
method could be due to overestimation of genetic variance
which was higher for higher phenotypic variance. Geno-
mic breeding values usually show bias, which is a conse-
quence of using marker instead of QTL effects [8]. This
bias exist also in our results - regression of true breeding
values on predicted breeding values is much below 1.
Rather high variation of breeding values could be
partly due to Mendelian variation and partly as a result
of method inadequacy. Both SNPL and SNPC methods
explored differences among animals within full-sib
families but it is hard to decide which one should be
preferred as one yielded higher accuracy but the second
more correctly chose the top 20 animals.
It is also worth mentioning that the method for predic-
tion of breeding values applied in this paper (quadratic
regression) does not take into account the fact that the
analysed trait will eventually reach its asymptotic value.
The restriction of using only one chromosome was
imposed partially due to the fact that SNPC method is
very computationally demanding and the SNPL method
had a software limitation for the number of markers.
This might have a drawback of our analysis as it
neglects large part of the available SNP information.
Nevertheless this simplified analysis allowed to predict
breeding values with fairly high accuracy of 0.75 - 0.80.
However because after the analysis it turned out that
the first chromosome contained QTLs with the largest
effect [1] it may be concluded that the result would
have been much worse in other, practical situations.
In our analysis we used a concept of genetic relation-
ship matrix to obtain genomic breeding values, which is
similar to the method described by Zhang et al. [9]. Van
Raden showed that reliabilities of GEBVs based on this
approach are almost as high as in the Bayes B method
[10]. The SNPL and SNPC methods, both assumed
equal effects of all markers from chromosome I.
Conclusions
Application of SNP markers enables to differentiate
breeding values within full sib families. Based on the
comparison of true (simulated by organizers) breeding
values in the time point 600 with our predictions it can
be concluded that SNP based methods provided rela-
tively good estimates. Even though only SNPs from
chromosome 1 were used it was still possible to achieve
fairly high accuracies. Most likely it was due to the fact
that chromosome 1 contained the most significant
QTLs affecting the analysed trait.
Acknowledgement
The authors would like to express their gratitude to Maciej Szydlowski for
discussion and support with the software package Citius.
This article has been published as part of BMC Proceedings Volume 4
Supplement 1, 2009: Proceedings of 13th European workshop on QTL
mapping and marker assisted selection.
The full contents of the supplement are available online at
http://www.biomedcentral.com/1753-6561/4?issue=S1.
Authors’ contributions
SM: performed the analysis and drafted the manuscript. AW: performed the
analysis and drafted the manuscript. TS: drafted the manuscript. All authors
read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Published: 31 March 2010
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Cite this article as: Mucha et al.: Comparison of methods for estimation
of genetic covariance matrix from SNP or pedigree data utilised to
predict breeding value. BMC Proceedings 2010 4(Suppl 1):S7.
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Comparison of methods for estimation of genetic covariance matrix from SNP or pedigree data utilised to predict breeding value

Citius: A program to apply Markov chain Monte Carlo method for multilocus analysis of large complex pedigrees - User Guide [http://jay.au.poznan.pl/~mcszyd/citius/citius.pdf].

Efficient Methods to Compute Genomic Predictions. Journal of Dairy Science

GRIDQTL: a grid portal for QTL mapping of compute intensive datasets.

Meuwissen T H E: Genomic selection using different marker types and densities.

R: ASReml User Guide Release

Sampling genotype configurations in a large complex pedigree.

Vekemans X: SPAGeDi: a versatile computer program to analyse spatial genetic structure at the individual or population levels. Molecular Ecology Notes

Vleck L D: Technical note: Use of marker-based relationships with multiple-trait derivative-free restricted maximal likelihood.

http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2857849

Comparison of methods for estimation of genetic covariance matrix from SNP or pedigree data utilised to predict breeding value

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