ESTIMATION AND EXPLOITATION OF LINKAGE DISEQUILIBRIUM IN PIGS
By
Yvonne Martina Badke

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
Animal Science - Doctor of Philosophy
2013

ABSTRACT
ESTIMATION AND EXPLOITATION OF LINKAGE DISEQUILIBRIUM IN
PIGS
By
Yvonne Martina Badke
The United States Pork Industry is an important source of income in rural America, and
its continued proﬁtability and success can be facilitated through genetic improvement for
a variety of production and health traits. Prediction of genomic breeding values (GEBV)
based on high density genotypes has the potential to increase genetic progress. The overall
objective of this dissertation was to describe the structure of linkage disequilibrium (LD)
across the pig genome, assess the potential of genotype imputation from low to high density
genotypes, and estimate accuracy of genomic prediction in pure-bred pig populations using
either observed or imputed high density genotypes.
The ﬁrst study focused on the estimation of LD and pairwise persistence of phase across
the genome of four US pig populations. Observed LD was high between adjacent SNP
(0.36-0.46) and persisted at high levels as pairwise distance between SNP increased to 1
Mb (0.20-0.25). Persistence of phase is a measure of prediction reliability of markers in
one population by those in another and ranged between 0.87 and 0.92 for pairwise SNP
distance <10 kb. We concluded that high estimates of LD between adjacent SNP in this
study are promising for the implementation of genomic selection, especially in conjunction
with genotype imputation to increase cost eﬃciency. However, persistence of phase appears
to be too low to indicate that the use of combined training panels would be advantageous
for accuracy of genomic prediction at the current marker density.
The second study focused on the accuracy of genotype imputation and variables aﬀecting

imputation accuracy. Using a commercially available 10K tagSNP panel and a small reference
panel of 128 haplotypes average accuracy of imputation was 0.95. Increasing the size of the
haplotype reference panel led to an overall increase in imputation accuracy (IA = 0.97 with
512 haplotypes), but was especially useful in increasing imputation accuracy of SNP with
MAF below 0.1 and for SNP located in the chromosomal extremes. In addition, our results
show that randomly sampling individuals to genotype for the construction of a reference
haplotype panel is more cost eﬃcient than speciﬁcally sampling older animals or trios with
no observed loss in imputation accuracy. From these results, we expected that losses in
accuracy of genomic prediction using imputed genotypes would be minimal.
In the third study we assessed the loss of prediction accuracy of GEBV obtained for
Yorkshire pigs using imputed instead of observed genotypes. Accuracy of genomic evaluation
using observed genotypes was high for three traits (0.65-0.68). Using genotypes imputed with
high accuracy (R2 = 0.95) for genomic evaluation did not signiﬁcantly decrease accuracy of
prediction. The decrease in accuracy of genomic evaluation was signiﬁcant when imputation
accuracy dropped to R2 = 0.88. Genomic evaluation based on imputed genotypes in selection
candidates is a cost eﬃcient alternative for implementation of genomic selection in pigs.
Furthermore, genotyping animals at lower cost and low density, followed by imputation, can
result in increased accuracy by allowing more animals into the training panel.
In conclusion, we showed that accurate prediction of GEBV in a US Yorkshire population
is possible, and cost eﬃciency can be increased through the use of genotype imputation in
selection candidates. Furthermore, our results of LD for three other US pig populations
indicate that similar or high accuracy of prediction can be expected within each of these
populations. In addition, we brieﬂy discuss how our results can be extended to prediction
of breed composition, and GEBV prediction and GWAS using whole genome sequence.

To my parents, Jutta and Ruediger for their love and support, and my grandmother for
her persistent insistence that I ﬁnish my education.
Meinen Eltern, Jutta und Rueder, fuer ihre Liebe und Unterstuetzung, und meiner Oma
fuer Ihre durchgehende Motivation meine Ausbildung abzuschliessen.

iv

ACKNOWLEDGMENTS

First I would like to acknowledge and express my deepest gratitude to my family, especially
my parents and my brother Alexander. Without your support, encouragement, understanding, and humor the completion of this program would not have been possible. You were
there for me when I had good news and more importantly you were always there for the
bad news. Knowing that you trusted me to ﬁnish this program was an incredible source of
strength for me and a huge motivation to not disappoint you.
Secondly, I would like to thank my advisor Juan P Steibel for his encouragement, guidance, and support during the last 4 years. Coming from a background with little knowledge
of animal breeding and very limited recollection of Mendelian genetics learned in high-school
I would have been lost in this ﬁeld without his continued assistance and academic mentoring.
Thanks to his support and patience in getting through the trials and triumphs of my PhD
program I feel that I have grown as a scientist and as a person.
I would also like to thank the members of my guidance committee Drs Cathy Ernst, Ron
Bates, Rob Tempelman, and Yuehua Cui for their patience and encouragement, helping me
to navigate my dissertation research, each oﬀering their unique perspective and knowledge
on the topics I worked on. Especially Drs Cathy Ernst and Ron Bates for their insights,
suggestions, and kind revisions of my publications as well as their constant availability to
answer any questions I had. I would also like to thank Drs. Rob Tempelman and Dennis
Banks for giving me the opportunity to teach in their classes. It has been a unique experience
and I realized that I really enjoy teaching and I hope I will be able to integrate some of
teaching into my future career.
Finally I would like to thank many of my good friends and fellow graduate students: Maria
v

Arceo, Pablo Parraga, Elodie Hablot, Oscar Arreola, Emily McKinney, Marcos Oliveira,
Jacqueline Reit, and many others. Coming to MSU has given me the opportunity to meet so
many diﬀerent and amazing people and I am grateful for every one of you and I hope I will
keep in touch with all of you. Your kindness, support, encouragement, and example have
been a vital part of my strength and motivation over the last years. We have shared many of
the unique experience of aspiring to a PhD degree, and comforted each other through failed
experiments and long weekends with the knowledge that it will work out in the end, and
it will be worth it. I knew I could come to you when I needed someone to lift me up and
tell me that will get better, and you were always right about that, and you were there to
celebrate whenever I had something to celebrate.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Chapter 2 Estimation of linkage disequilibrium in four US pig breeds .
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Estimation of Linkage Disequilibrium . . . . . . . . . . . . . . . .
2.2.2 Persistence of Phase . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Extent of Linkage Disequilibrium . . . . . . . . . . . . . . . . . .
2.3.2 Persistence of Phase . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Implications of estimated levels of LD for GEBV implementation
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Sample Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Estimation of average LD and persistence of phase . . . . . . . .

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25
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Chapter 3 Methods of tagSNP selection and other variables aﬀecting imputation accuracy in swine . . . . . . . . . . . . . . . . . . . . . . .
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Genotypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Genotype imputation and estimation of imputation accuracy . . . . .
3.2.3 Methods of tagSNP selection . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Increasing reference panel size . . . . . . . . . . . . . . . . . . . . . .
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Comparison of methods for tagSNP selection . . . . . . . . . . . . . .
3.3.2 Imputation accuracy using the commercial 9K tagSNP set . . . . . .
3.3.3 Eﬀect of numbers of reference haplotypes on imputation accuracy . .
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Methods for tagSNP selection . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Factors aﬀecting imputation accuracy . . . . . . . . . . . . . . . . . .
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Supplementary Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33
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40
42
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47
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vii

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Chapter 4 Accuracy of estimation of genomic breeding values in pigs using
low density genotypes and imputation . . . . . . . . . . . . . . . .
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1.1 Animals and Genotypes . . . . . . . . . . . . . . . . . . . .
4.2.1.2 Phenotypes . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2.1 De-regression of breeding values . . . . . . . . . . . . . . . .
4.2.2.2 Estimation of genomic relationship matrix . . . . . . . . . .
4.2.2.3 Implementation of prediction model . . . . . . . . . . . . .
4.2.3 Genomic prediction under cross-validation . . . . . . . . . . . . . . .
4.2.3.1 Estimation of accuracy . . . . . . . . . . . . . . . . . . . . .
4.2.3.2 Genotype imputation . . . . . . . . . . . . . . . . . . . . . .
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Accuracy of genomic evaluation and GEBV using observed genotypes
4.3.2 Eﬀect of genotype imputation on accuracy of genomic evaluation and
GEBV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Accuracy of genomic evaluation and GEBV using observed genotypes
4.4.2 Eﬀect of genotype imputation on accuracy of genomic evaluation and
GEBV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Supplementary Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68
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93

Chapter 5 General Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1 Objectives revisited and their impact on genomic selection in swine breeding
96
5.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

viii

LIST OF TABLES

Table 2.1

Average r2 at various distances in four breeds . . . . . . . . . . . .

13

Table 2.2

Average r2 between adjacent SNP for sparse marker panels . . . . .

15

Table 2.3

Pairwise breed comparison of correlation of phase and proportion of
phase agreement at various distances . . . . . . . . . . . . . . . . .

19

Table 2.3

(cont’d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

Table 4.1

Descriptive statistics of EBV . . . . . . . . . . . . . . . . . . . . . .

73

Table 4.2

Estimates of accuracy for genomic evaluation and individual GEBV
across imputation scenarios . . . . . . . . . . . . . . . . . . . . . . .

81

Signiﬁcance of variables aﬀecting accuracy of genomic evaluation . .

82

Table 4.3

ix

LIST OF FIGURES

Figure 2.1

Decay of average r2 over distance . . . . . . . . . . . . . . . . . . .

14

Figure 2.2

Correlation of gametic phase compared across breeds over distance .

18

Figure 3.1

Imputation accuracy based on tagSNP selected using 3 diﬀerent methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

Figure 3.2

Imputation accuracy using evenly spaced or statistically selected tagSNP 46

Figure 3.3

SNP-wise imputation accuracy by chromosomal location . . . . . . .

48

Figure 3.4

Three measures of SNP-wise imputation accuracy by MAF . . . . .

51

Figure 3.5

Eﬀect of number of reference haplotypes on imputation accuracy . .

53

Figure 3.6

Eﬀect of reference panel size on imputation accuracy of SNP as a
function of their MAF . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Eﬀect of reference panel size on imputation accuracy of SNP as a
function of scaled physical location . . . . . . . . . . . . . . . . . . .

67

Accuracy of GEBV by observed accuracy of EBV for a) BF, b) D250,
and c) LEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Accuracy of GEBV by average top 10 relatedness between the individual and training panel for (A) BF, (B) D250, and (C) LEA rGEBV
in relation to the animals rel10, a loess smoother (red line), which is
a local weighted mean of the rGEBV . . . . . . . . . . . . . . . . .

85

Distribution of genomic heritability across 10 folds for a) BF, b) D250,
and c) LEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

Average accuracy of genotype imputation for imputation from a small
(blue) or large (red) reference panel as a function of (A) chromosomal
location of SNP and (B) MAF . . . . . . . . . . . . . . . . . . . . .

94

Figure 3.7

Figure 4.1
Figure 4.2

Figure 4.3
Figure 4.4

x

Chapter 1
Introduction

1

Pigs are an important livestock species in the United States producing total sales of more
than $97 billion and directly employing almost 35.000 people around the country according
to 2011 estimates from the National Pork Producers Council. Genetic improvement through
breeding for meat quality, reproductive performance, and health traits is an important tool
to assure the pork industries competitiveness and continued success. There has been an increase in lean percentage of roughly 0.1% per year since 2001 (USDA, 2009a) and the number
of piglets per litter has increased from 8.8 to 9.5 (USDA, 2009b). This progress in animal
performance and productivity can be attributed to a number of factors such as improvements
in overall herd health and housing, improved feeding, and genetic improvement through traditional breeding schemes. Traditional breeding describes the estimation of breeding values
(EBV) for all animals based on the performance of their relatives. Linear mixed models are
ﬁtted to obtain predictions of performance of animals through their expected relationship
matrix combining information across all available relatives (Henderson, 1984). Favorably
ranking animals are further evaluated based on the information of their oﬀspring to obtain
highly accurate EBV to be used in predictions for future generations. It has been conservatively estimated that improvement from traditional genetic selection programs increases
revenue to the pork industry by more than $42 million annually (C. Schwab, personal communication). A large number of studies to date have aimed to identify quantitative trait loci
(QTL) associated with economically important traits, such that the pig QTL database currently documents 8402 QTL from 356 publications (http://www.animalgenome.org/pigs/).
Certain traits, i. e. halothane sensitivity, could be traced back to the gene and the corresponding mutation directly aﬀecting the phenotype, allowing these loci to be directly used
in gene assisted selection (Meuwissen et al., 2013). However, the majority of phenotypes appears to be associated with a large number of loci with comparably small individual eﬀects
2

across the genome (Meuwissen et al., 2001) making selection based on single loci impossible
for most economic traits. A related attempt to utilize genetic information, mostly single nucleotide polymorphisms (SNP), for breeding was marker assisted selection, where SNP were
tested for association with the phenotype and subsequent selection was based signiﬁcantly
associated SNP (Meuwissen et al., 2013). However, due to imperfect linkage disequilibrium (LD) between the SNP used for selection and the underlying QTL (Meuwissen et al.,
2013) and ascertainment bias in selecting signiﬁcantly related SNP (Meuwissen et al., 2001),
accuracy from this approach was generally unsatisfactory.
An alternative to traditional breeding schemes, and gene- or marker-assisted selection
has been proposed by Meuwissen et al. (2001). Based on the assumption that phenotypes
are associated with a large number of loci with small eﬀects, many of which will fail to
reach statistical signiﬁcance when QTL are mapped, they proposed a method of genomic
evaluation ﬁtting a prediction equation to thousands of genetic markers in parallel to obtain
predicted genomic breeding values (GEBV; Meuwissen et al., 2001). As initially proposed,
genomic selection models were based on a two-stage design. In the ﬁrst stage, a prediction
equation was ﬁt to a training panel of animals with highly accurate EBV to estimate SNP
eﬀects for all markers. In the second stage, the estimated SNP eﬀects and observed genotypes
of selection candidates were used to calculate GEBV. GEBV, especially for young animals,
are expected to be more accurate than EBV due to the inclusion of both close and distantly
related animals, as well as the use of actual proportions of identity shared by descent (IBD)
between animals vs. the expected proportion of IBD that is used to estimate EBV. In
addition, GEBV are expected to increase the accuracy of selection for traits that are diﬃcult
to measure such as health traits, life-time productivity, or those only available post-mortem.
Also, since this method allows selection of animals at a very young age it is expected to
3

shorten generation intervals (Meuwissen et al., 2001; VanRaden et al., 2009).
Research and implementation of this method has been facilitated in several livestock
species through the recent availability of high density genotyping platforms for bovine
(Matukumalli et al., 2009), ovine (Archibald et al., 2010), chicken (Groenen et al., 2009), and
pig (Ramos et al., 2009). An impressive body of research including simulation experiments
and studies on real populations over the last few years have furthered our understanding
of variables aﬀecting the accuracy of genomic evaluation and possible designs which can be
used to implement GEBV in the livestock industry (Daetwyler et al., 2013).
Among variables aﬀecting the accuracy of genomic selection are the level of LD across
the genome, the composition and size of the training population, the statistical models used
for prediction (Meuwissen et al., 2013), the genetic architecture and heritability of the trait
(Hayes et al., 2009a), and in case genotype imputation is utilized the accuracy of imputation
(Weigel et al., 2010a). Interactions between these variables, like the genetic architecture of
the trait deﬁning the optimal statistical model (Meuwissen et al., 2013) increase the diﬃculty
of choosing an optimal design.
When the Illumina PorcineSNP60 Genotyping BeadChip (Illumina Inc.; Ramos et al.,
2009) was ﬁrst released in 2008 it introduced the possibility of enabling genomic selection
in swine breeding. It was the goal of this dissertation research to use this newly available
platform to assess the potential of genomic selection to be implemented into commercial
swine breeding.
Our initial step was to assess the extent of LD across the genome in four breeds of pigs and
estimate persistence of phase between the breeds. Extent of LD is an important precursor
for genomic selection (Hayes et al., 2009a), since the average LD between SNP is indicative
of the LD that can be expected between a QTL and neighboring SNP. We compared aver4

age LD between both neighboring SNP and also SNP at an increasing distance, to assess
whether or not reducing the number of markers necessary to implement genomic selection
could potentially be reduced to increase cost eﬃciency (Badke et al., 2012). Persistence of
phase between populations is informative to assess the usability of training panels combining
animals across populations for genomic selection (Goddard et al., 2006; de Roos et al., 2009).
If phase is conserved between breeds to a large extent, then combining animals across breeds
to form a training panel will likely lead to an increase in selection accuracy (de Roos et al.,
2009). However, if persistence of phase between two populations is low then combining them
to form a training panel would have a negative impact on the resulting accuracy of genomic
selection (de Roos et al., 2009). Due to the relatively small size of pure-bred swine populations combining animals across populations to form a training panel for genomic selection
could decrease the initial investment necessary.
After assessing that LD in swine is comparably high between both neighboring SNP and
SNP at an increasing distance we considered options to implement low density genotyping
and genotype imputation to potentially increase cost eﬃciency of genomic selection (Badke
et al., 2012). Cost eﬃciency is critical in swine breeding to allow a widespread implementation of genomic methods, but accuracy of genomic prediction based on imputed instead of
observed genotypes depends on the accuracy of genotype imputation Weigel et al. (2010a).
Though overall cost of genotyping has decreased dramatically over the last few years it is
still not feasible for pig breeding operations to genotype young animals or selection candidates using high density genotypes on the PorcineSNP60. We proposed to select a small
panel of maximally informative tagSNP (Qin et al., 2006) that could subsequently be used
to impute genotypes from low density back to the original high density array. Genotype
imputation from low density panels using a reference panel of haplotypes is computationally
5

eﬃcient and imputed genotypes can reach almost perfect accuracy at a much reduced cost
(Browning and Browning, 2009; Dassonneville et al., 2011; Gualdr´n Duarte et al., 2013;
o
Huang et al., 2012; Wiggans et al., 2012). Accuracy of imputation mainly depends on the
amount of information available for imputation, such that a large reference panel of haplotypes (Dassonneville et al., 2011) and the inclusion of linkage and LD information positively
impact the resulting accuracy (Gualdr´n Duarte et al., 2013; Huang et al., 2012). It was
o
our second objective to select a maximally informative panel of low density SNP in four US
pig breeds using several selection strategies such as the physical distance between SNP, a
minimum threshold of LD between tagSNP (Qin et al., 2006), or the ability of each SNP to
accurately predict the genotypes of markers not included in the panel (Badke et al., 2013).
Since low density to high density genotype imputation necessitates the use of a reference
panel of haplotypes we also sought to investigate the eﬀect of reference panel composition.
Parallel to our work on designing low density SNP panels the GeneSeek Genomic Proﬁler
for Porcine LD (GGP Porcine), a low density platform comprising roughly 10K, assembled
using the SNPspace software (C.P. Van Tassell, unpublished data) was released by GeneSeek
(Lincoln, NE). Recognizing the potential of a non breed-speciﬁc general low density panel for
industrial application in pig breeding we changed our focus from the design of breed-speciﬁc
low density platforms to perform a detailed assessment of genotype imputation accuracy
using the GGP Porcine to impute high density genotypes in Yorkshire pigs.
Finally, we combined the results obtained in our previous publications (Badke et al.,
2013, 2012) to investigate the accuracy of genomic evaluation in a US Yorkshire population
using both observed and imputed genotypes. Imputation accuracy observed in this Yorkshire
population was comparable to previous reports in dairy cattle (Dassonneville et al., 2011;
Wiggans et al., 2012) and we expect it can be further increased through the use of algorithms
6

that combine information on linkage and LD to obtain imputed genotypes (Gualdr´n Duarte
o
et al., 2013; Huang et al., 2012; Wiggans et al., 2012). Therefore, the loss of accuracy
in genomic evaluation when imputed instead of observed genotypes are used in selection
candidates is expected to be minimal, which would concur with previous results in dairy
cattle breeding (Dassonneville et al., 2011; Wiggans et al., 2012). We used a cross validation
design to implement genomic evaluation using a computationally eﬃcient model and assessed
the accuracy of this evaluation for both observed genotypes, and genotypes imputed using
diﬀerent size reference panels. In addition, we assessed the eﬀect of several variables that
have previously been shown to inﬂuence accuracy of genomic evaluation such as relatedness
between training and prediction (Clark et al., 2012), and the accuracy of EBV used for
validation (Hayes et al., 2009a).
In conclusion, the overarching goal of this dissertation was to implement a scheme for
the adoption of genomic selection techniques into swine breeding, that would be optimally
ﬁt to the structure and requirements of this population. We aimed to present a solution that
would yield highly accurate predictions while maintaining cost eﬃciency with respect to
initial and long-term investment. In addition, by releasing all data and code used to obtain
these results we hope to facilitate further research addressing issues within this speciﬁc
population, but also the translation of our approach to designing a genomic selection scheme
for other populations and species not currently employing these techniques.
Speciﬁcally the objectives of this dissertation were:
1. Estimate LD in the Duroc, Hampshire, Landrace and Yorkshire pig breeds using SNP
genotypes obtained using the Illumina PorcineSNP60 Genotyping BeadChip. Determine persistence of phase between breeds to assess the potential of mixed breed reference panels for both imputation and genomic selection in the future.
7

2. Assess tagSNP selection strategies to obtain a maximally informative subsets of tagSNP
that eﬀectively span the genome for each breed. In addition, report on imputation
accuracy of the recently released GeneSeek Genomic Proﬁler for Porcine LD (GGPPorcine, GeneSeek a Neogen Company, Lincoln, NE), a commercially available 10K
tagSNP panel.
3. Perform GEBV prediction for economically important production traits using high
density SNP genotypes for the Yorkshire breed, as well as genotypes imputed from the
GGP-Porcine. Assess the loss in accuracy when genotypes in selection candidates were
imputed from low to high density.

8

Chapter 2
Estimation of linkage disequilibrium
in four US pig breeds
Badke, Y. M., Bates, R. O., Ernst, C. W., Schwab, C., & Steibel, J. P. (2012). Estimation
of linkage disequilibrium in four US pig breeds. BMC genomics, 13(1), 24.

9

2.1

Background

The extent of non-random association of gametes at diﬀerent loci, or linkage disequilibrium
(LD), has become the focus of many recent studies in both humans and animals (Amaral
et al., 2008; Conrad et al., 2006; Reich et al., 2001; Corbin et al., 2010). Gaining knowledge
of the distribution of LD in livestock populations is important for genetic mapping of economically important traits such as disease resistance (Pritchard and Donnelly, 2001), and it
can reveal population history and breed development (Nordborg and Tavare, 2002; Tenesa
et al., 2007). Moreover, genome wide association (GWAs) studies as well as genomic selection in livestock rely on the existence of LD between causative variants and genetic markers
(Hayes et al., 2009a; Goddard and Hayes, 2009). Recent advances in genotyping technology
allow high density genotyping of single nucleotide polymorphisms (SNP) for several livestock
species such as cattle (Matukumalli et al., 2009), chicken (Groenen et al., 2009), and pigs
(Ramos et al., 2009) Obtaining high density genotypes from a sample of individuals allows
for the estimation of genome-wide LD and persistence of phase among breeds (Goddard
et al., 2006). Previous studies have shown that the extent and persistence of LD in livestock
(de Roos et al., 2008; Sargolzaei et al., 2008; Uimari and Tapio, 2011) is much larger than
that found in human populations (Reich et al., 2001), due to selection and smaller eﬀective
population size in livestock species (Amaral et al., 2008; Harmegnies et al., 2006). Using
dense markers to cover the genome increases the likelihood of SNP markers to be in high LD
with causative genes altering important production phenotypes (Goddard, 2008). Meuwissen and Goddard (2001) proposed that the merit of these markers in livestock would be in
the parallel use of all markers to derive genomic breeding values (GEBV) as a composite
score of all individual SNP eﬀects rather than improving mapping of quantitative trait loci

10

(QTL). The implementation of genomic selection using GEBV has been successful in dairy
cattle (Hayes et al., 2009a; VanRaden et al., 2009; Goddard and Hayes, 2007), and is currently being tested in laying chickens (Wolc et al., 2011) and pigs (Cleveland et al., 2010).
The reliability of GEBV prediction relies on the level of LD between markers and QTL, the
origin of such LD (either within family or population-wise), the number of animals used in
the training population as well as heritability of the trait (Hayes et al., 2009a). In this study
it is our objective to estimate and describe genome wide levels of LD in four pig breeds using
high density genotypes. We also estimate population-wise LD for a variety of panels with
lower marker density in order to estimate the number of markers needed to reach a given
level of LD. We estimate persistence of phase between the four breeds in this study as a
measure of relationship between these populations.

2.2
2.2.1

Results
Estimation of Linkage Disequilibrium

To estimate LD, we genotyped 351 animals in 117 sire/dam/oﬀspring trios across four breeds
of pigs (Duroc, Hampshire, Landrace and Yorkshire) using the Illumina Porcine SNP60
BeadChip (Ramos et al., 2009). We used BEAGLE (Browning and Browning, 2009) to build
haplotypes and estimated pairwise r2 for all SNP on the same chromosome using equation
(2.1). Average r2 between adjacent markers within breed was estimated using equation (2.2).
Average r2 at various distances was computed by grouping all SNP combinations by their
pairwise distance in classes of 100 kb of length starting at 0 to 10 Mb. Figure 2.1 displays
an overview of the decline of r2 over distance in each breed. In addition, Table 2.1 displays
average r2 for adjacent markers and at 0.5, 1 and 5 Mb. The average r2 between adjacent
11

SNP was largest in the Duroc animals (r2 =0.46), followed by Hampshire (r2 =0.44), whereas
Yorkshire and Landrace exhibited the smallest average r2 (0.39 and 0.36 respectively; Table
2.1). Marker pairs with an average distance of 1 Mb had an average r2 of 0.20 for Hampshire,
0.19 for Duroc, 0.16 for Yorkshire and 0.15 for Landrace. For all breeds, at least 54% of the
adjacent SNP had an r2 ≥ 0.2 and 44% r2 ≥ 0.3. For most chromosomes, average r2 between
adjacent SNP in Duroc and Hampshire was larger than average r2 in Landrace or Yorkshire.
In addition to estimating average r2 within distance classes, we also computed average r2
between adjacent markers for diﬀerent marker densities. To obtain marker sets with various
SNP densities we sequentially removed markers from the current map using every second,
fourth, 10th, 50th, 100th and 200th marker (Table 2.2). Average r2 decreased between 6%
for Yorkshire to 15% for Hampshire when only 50% of the markers were used, with highest
average r2 for Duroc (r2 =0.40) followed by Hampshire (r2 =0.37), Yorkshire (r2 =0.34) and
the lowest for Landrace (r2 =0.30). Using only every 10th marker, average r2 decreased
to around 50% of the original r2 (r2 =0.20-0.25), and using every 100th marker average r2
ranged from 0.05-0.07 at an average marker distance of 6.5 Mb, which was comparable to
the results found for average r2 at 5 Mb.

12

Table 2.1: Average r2 at various distances in four breeds

Breed

Adjacent

0.5Mb2

1Mb2

5Mb2

Duroc

0.46

0.26

0.19

0.06

Hampshire

0.44

0.25

0.20

0.08

Landrace

0.36

0.19

0.15

0.06

Yorkshire

0.39

0.21

0.16

0.05

1 Average r2 for SNP with adjacent map positions (exact spacing: 70 kb for Duroc, 74 kb
for Hampshire, 60 kb for Landrace, and 61kb Yorkshire).
2 Average r2 for SNP spaced 0.5 Mb, 1 Mb and 5 Mb apart

13

Figure 2.1: Decay of average r2 over distance
Average r2 between markers in Duroc, Hampshire, Landrace and Yorkshire at various
distances in base pairs ranging from 0 to 10 Mb.
For interpretation of the references to color in this and all other ﬁgures, the reader is
referred to the electronic version of this dissertation.

14

Table 2.2: Average r2 between adjacent SNP for sparse marker panels
Duroc

% of SNP kept 1

Hampshire

Landrace

Yorkshire

average

average

average

average

average

average

average

average

r2 2

distance

r2 2

distance

r2 2

distance

r2 2

distance

in kb 3

in kb 3

in kb 3

in kb 3

50%

0.4

141

0.37

148

0.3

120

0.34

123

25%

0.34

281

0.31

296

0.25

239

0.28

246

10%

0.25

703

0.23

740

0.2

597

0.21

613

2%

0.1

3,507

0.11

3,693

0.09

2,978

0.09

3,056

1%

0.05

7,026

0.06

7,399

0.05

5,963

0.05

6,127

0.50%

0.02

14,120

0.04

14,872

0.03

11,977

0.02

12,313

1 Percentage of SNP included in the current set of markers
2 Average r2 for SNP with adjacent map positions for the current set of markers
3 Average distance in kb for SNP with adjacent map positions in the current set of markers

15

2.2.2

Persistence of Phase

Persistence of phase is a measure of the degree of agreement of LD phase for pairs of SNP
between two populations. To estimate persistence of phase, we calculated rij as the square
2
root of rij in equation (2.1) between all possible combinations of SNP i and j respectively,
using the sign of the non-squared numerator. If r2 between two markers is equal in two
populations, but their corresponding r has opposite sign, the gametic phase is reversed
(Uimari and Tapio, 2011). Persistence of phase over a certain genomic distance interval
can be estimated as the pairwise Pearson correlation coeﬃcient (R
) of inter-marker rij
k,k
between two populations k and k (Equation 2.3). For all pairwise comparisons of breeds
we estimated R
and the percentage of SNP with reversed sign of r. Similar to our
k,k
computation of average r2 , we grouped SNP pairs in classes of inter-marker distances 100
kb long and computed persistence of phase within each class starting at 0 up to 10 Mb
(Figure 2.2). In theory, the Pearson correlation coeﬃcient ranges between -1 and 1. Large
negative values are a result of high LD (r2 ) in both breeds but phase is reversed between
them. High positive values are a result of high r2 and equal phase in both breeds (Uimari
and Tapio, 2011). Correlation of phase between SNP less than 100 kb apart ranged from 0.73
for Duroc with Hampshire and Yorkshire to 0.82 for Landrace with Yorkshire. Considering
SNP pairs with an average distance of 0.9 to 1 Mb, correlation of phase decreased to 0.41 for
Duroc with Hampshire and to 0.57 for Yorkshire with Landrace (Table 2.3). Persistence of
phase decreased with increasing marker distance at a rate comparable to that observed for the
decrease in average r2 with increasing marker spacing. The slope of the decline was lower for
the correlation between Landrace and Yorkshire when compared to other breed comparisons.
Applying a z-test with Fishers transformation (Cohen et al., 2003) to the correlation of phase

16

at <10 kb, the correlation of phase between Landrace and Yorkshire was signiﬁcantly larger
(p < 0.001, n = 1520) than all other breed combinations. Results for the correlation of
phase were not signiﬁcantly diﬀerent (p > 0.05, n = 1520) in the Duroc-Hampshire, DurocLandrace, Duroc-Yorkshire, Hampshire-Yorkshire, and Hampshire-Landrace pairings (Table
2.3). For these ﬁve population comparisons, the average proportion of SNP with r having
opposite sign ranged between 9-11% for SNP spaced within 10 kb and up to 45-49% for SNP
spaced between 4.9 and 5 Mb (Table 2.3). In general, the estimates of r with reversed sign
for the Landrace-Yorkshire were lower ranging from 9% to 45%. These results suggested a
closer population relationship between the Landrace and Yorkshire populations than among
all other populations.

17

Figure 2.2: Correlation of gametic phase compared across breeds over distance
Correlation of Phase between breeds for SNP pairs grouped by distance in intervals 100 kb
long covering 0 to 5 Mb across the genome.

18

Table 2.3: Pairwise breed comparison of correlation of phase and proportion of phase agreement at various distances
Breeds Compared

Distance1

Proportion

of

r

Correlation

of

with opposite sign2
0-10kb

0.762

50-100kb

0.246

0.668

0.391

0.408

0.469

0.21

0-10kb

0.108

0.872

10-50kb

0.186

0.773

50-100kb

0.251

0.681

0.9-1Mb

0.395

0.438

4.9-5Mb

0.485

0.19

0-10kb

0.104

0.87

10-50kb

0.195

0.761

50-100kb

0.252

0.67

0.9-1Mb

0.396

0.422

4.9-5Mb

0.468

0.201

0-10kb

0.099

0.882

10-50kb
Hampshire - Landrace

0.184

4.9-5Mb

Duroc - Yorkshire

0.875

0.9-1Mb

Duroc Landrace

0.107

10-50kb
Duroc Hampshire

rij(k) and rij(k) 3

0.184

0.776

50-100kb

0.242

0.697

0.9-1Mb

0.392

0.441

4.9-5Mb

0.475

0.189

19

Table 2.3: (cont’d)
Breeds Compared

Distance1

Proportion

of

r

Correlation

of

with opposite sign2
0-10kb

0.871

0.189

0.771

50-100kb

0.249

0.686

0.9-1Mb

0.389

0.439

4.9-5Mb

0.459

0.245

0-10kb

0.087

0.921

10-50kb

0.16

0.842

50-100kb

0.204

0.783

0.9-1Mb

0.353

0.571

4.9-5Mb

Landrace - Yorkshire

0.113

10-50kb
Hampshire - Yorkshire

rij(k) and rij(k) 3

0.448

0.297

1 Interval length in kb
2 Proportion of SNP pairs having r with reversed sign within the interval
3 Correlation of phase between two breeds (k and k) within the given interval

2.3
2.3.1

Discussion
Extent of Linkage Disequilibrium

Current eﬀective population size of the breeds used in this study was previously estimated,
using pedigree information, to be between 74 (Landrace) and 113 (Duroc, Yorkshire, (Welsh
et al., 2010)). Consistent with having the largest current eﬀective population size, we ﬁnd
that long range r2 (10 Mb, Fig. 2.1) estimated from our data was smallest for Duroc and
Yorkshire (0.035, 0.03). In Hampshire, a smaller eﬀective population of 109 corresponded to

20

higher r2 at 10 Mb (0.046). Due to the similar long range r2 (0.035) at 10 Mb we would
have expected the Landrace population to have an eﬀective population size comparable to
that of Duroc and Yorkshire. However, using pedigree data Welsh et al. (2010) estimated
the current eﬀective population size of Landrace to be 74. The reason for this discrepancy
remains unknown. Several previous studies investigated LD in pigs using reduced numbers
of microsatellite markers and fewer animals from commercial populations (Harmegnies et al.,
2006; Nsengimana et al., 2004). Nsengimana et al. (2004) found relatively large estimates of
LD (D) from 0.29 to 0.41 using 15 microsatellite markers. In contrast, using r2 instead of D
and thereby correcting for minor allele frequency, Harmegnies et al. (2006) found r2 ranging
from 0.15 to 0.19 for marker distance < 1 cM and 0.10-0.12 for markers spaced between 1 cM
and 5 cM, using 29 microsatellite markers on SSC15, comparable to our results of r2 between
0.16-0.22 for marker spaced between 1 and 5 Mb. Du et al. (2007) estimated r2 from 4,500
SNP markers in six commercial lines of pigs and found estimates of average r2 = 0.51 for
markers less than 0.1 cM apart, and estimates of 0.21 and 0.07 at marker distances of 1 cM
and 5 cM respectively. Similarly, our populations had average r2 of 0.15 to 0.20 and 0.05
to 0.08 at marker distances of 1 Mb and 5 Mb, respectively. A recent study conducted by
Uimari and Tapio (2011) used the same genotyping platform as our study to estimate r2 and
eﬀective population size in Finnish Landrace and Yorkshire populations. Uimari and Tapio
(2011) found average r2 of 0.43 and 0.46 for adjacent markers in the Finnish Landrace and
Yorkshire populations, respectively, which was higher than our results of 0.36 for Landrace
and 0.39 for Yorkshire. In addition, Uimari and Tapio (2011) reported that the r2 for markers
spaced at 5 Mb decreased to 0.09 and 0.12 in the Finnish Landrace and Yorkshire breeds,
respectively. In the present study, r2 declined further to 0.05-0.06 at 5 Mb marker spacing
for Landrace and Yorkshire (Table 2.1). The higher average r2 for distant (r2 > 0.2 for 1
21

Mb) markers in the Finnish populations could be explained by smaller eﬀective population
size of the Finnish populations, causing higher r2 on average. This is partially conﬁrmed by
comparing the estimated eﬀective size of the Finnish populations (Ne = 91, 61 for Landrace
and Yorkshire, respectively) (Uimari and Tapio, 2011), to estimated eﬀective population
sizes of the populations used in the current study reported by Welsh et al. (2010) (N e = 74,
113 for Landrace and Yorkshire, respectively), where the current eﬀective population size
for Finnish Yorkshire is approximately half that of our Yorkshire population. Compared to
recent estimates from Canadian populations we found estimates of average r2 for markers
with pairwise distance below 100kb to be consistent in Landrace (US: 0.34, Canadian: 0.31)
and Yorkshire (US: 0.37, Canadian: 0.32; Jafarikia et al., 2010). However, in Duroc estimates
of average r2 for markers with pairwise distance below 100kb were considerably higher in
the US population (0.42) compared to the Canadian population (0.31, Jafarikia et al., 2010).

2.3.2

Persistence of Phase

Persistence of phase can be used to infer upon the history of a species and relatedness of
breeds within that species as well as on reliability of across population GWA and GEVB
prediction (de Roos et al., 2008). Persistence of phase was previously reported for three
Canadian swine breeds (Duroc, Landrace, Yorkshire, Jafarikia et al., 2010). For SNP with
pairwise distance below 50kb we estimated persistence phase to be 0.88 between Landrace
and Yorkshire and 0.82 for both Landrace and Yorkshire with Duroc. In the Canadian breeds
persistence of phase also indicates a closer relationship between Landrace and Yorkshire
(0.82) and a more distant relationship between Landrace/Yorkshire and Duroc (Jafarikia
et al., 2010). We found correlation of phase of 0.82 for Landrace/Yorkshire with Duroc,
while the Canadian breeds had 0.66/0.65, indicating less agreement of phase even at short
22

pairwise distance (Jafarikia et al., 2010). Our results showed that correlation of phase for
the pig breeds in this study ranged between 0.87 for Duroc-Yorkshire and 0.92 for LandraceYorkshire for markers with pairwise distance <10 kb. Previous research in Australian cattle
breeds (de Roos et al., 2008) showed correlation of phase between 0.68 for Australian AngusNew Zealand Jersey to 0.97 for Dutch Holstein-Black and White. At increasing marker
distance, correlation of phase for the pig breeds in this study decreased (range in r: 0.41 to
0.57) at an average pairwise marker distance of 1 Mb. This decrease however was less than the
decrease de Roos et al. (2008) observed in all but two of the cattle breeds they considered
(< 0.4 for markers spaced 1 Mb). While correlation of phase was similar between these
pig breeds and dairy cattle at short range (<10kb), the pig breeds showed generally larger
correlation of phase than the dairy cattle de Roos et al. (2008) at increasing marker distances.
If two populations diverged from a common ancestral population, their correlation of phase
2
2
can be expressed as r0 (1 − c)2T , where r0 is a measure of LD in the common ancestral
population, c is the recombination distance between markers, and T is time since breed
divergence in generations (Sved et al., 2008). For markers as close as 10 kb the recombination
distance c will be almost 0, so that correlation of phase at those short distances can serve
2
as an estimation of r0 in the common ancestral population. Since correlation of phase was
comparable in the pig populations (0.87-0.92) for markers with pairwise distance below 10
kb to that reported in Australian cattle (0.80-0.97, de Roos et al., 2008), LD in the common
ancestral pig population is likely to be similar to that in the common ancestral population
of Australian cattle breeds. Larger correlation of phase at increasing marker distance (1
Mb) in the pig populations used in this study (0.41-0.57) compared to Australian cattle
breeds (< 0.40) suggests that T is smaller in our pig breeds than it is in the cattle breeds.
The expected correlation of r between two breeds can be expressed as e−2cT (de Roos
23

et al., 2008). To estimate the time since breed divergence for the pig breeds in this study
we used SNP with pairwise distance between 10kb and 300kb, and estimated correlation of
phase for each 2.5kb interval. We calculated the linear regression of the natural logarithm
of the estimated correlation of phase onto the average pairwise distance c. The slope of
this regression is an estimate of −2T . Consequently, the slope divided by -2 is the number
of generations (T ) since these two breeds have diverged (de Roos et al., 2008). Results
suggest that the pig breeds in this study diverged approximately 40-66 generations ago. The
expected correlation of phase would decrease to 0.41 and 0.02 at 1 cM and 5 cM distance
2
respectively in the Yorkshire-Landrace comparison, assuming T of 40 and r0 of 0.92. We
observed a correlation of phase of 0.57 and 0.30 at 1 Mb and 5 Mb, respectively, between
these two breeds, indicating that a T of 40 may overestimate the actual time since breed
divergence. One possible cause of this observation is admixture between these two breeds,
causing more common LD between them than what would be expected from fully diverged
breeds (de Roos et al., 2008). We obtained the date of herd book closure for each of the
breeds in this study, and assuming a generation interval of approximately 2 years (Welsh
et al., 2010), Duroc, Hampshire, Landrace, and Yorkshire have existed as distinct breeds for
at least 38.5, 44.5, 31.5, and 30.5 generations, respectively. The time of herd book closure
does not directly indicate the time since breed divergence, since distinguishable breeds must
have existed before herd book closure. Nevertheless, the time of herd book closure further
supports our observation that Landrace and Yorkshire have developed as separate breeds
later than Duroc and Hampshire.

24

2.3.3

Implications of estimated levels of LD for GEBV implementation

Our results have several important implications for future implementation of genomic selection in swine. Accuracy of prediction of genome wide marker assisted selection can be
directly aﬀected by the chosen marker density (resulting in average r2 between markers
and QTL), and the size of the training population (Hayes et al., 2009a). The currently
used marker panel, containing approximately 40,000 usable markers, had average r2 of approximately 0.4 between adjacent markers for all four breeds. That exceeds the level of
r2 = 0.2 simulated by Meuwissen et al. (2001) to reach prediction GEBV accuracy around
0.85. Furthermore, our results indicated that reducing the original marker panel to 10% of
the markers (3,000-4,000 SNP) still resulted in average r2 for adjacent markers exceeding
0.2 in all four breeds. On the other hand, recent research in Australian Holstein Friesian
cattle has shown (Moser et al., 2010) that using subsets of 3000-5000 SNP to estimate direct
genomic breeding values (DGV) could only reach 80% of the prediction accuracy previously
estimated using approximately 42,000 SNP. Such a reduction in prediction accuracy will be
unacceptable for most practical implementations. However, the accuracy of GEBV predicted
by low density panels can be increased through the use of genotype imputation (Weigel et al.,
2010a), where high density genotypes are imputed using low density SNP genotypes and a
high density reference panel of haplotypes (Browning and Browning, 2009). Weigel et al.
(2010b) used approximately 10% of 2,693 SNP from Bos Taurus chromosome 1 to impute
the full SNP set in a Jersey population. They found that using a high density reference
genotype panel (n = 2, 542 animals), the imputation accuracy of the non-typed markers was
between 0.86 and 0.94. Average r2 in our populations ranged from 0.36 to 0.48 for markers

25

less than 100 kb apart, comparable to average r2 = 0.38 for markers spaced at <100 kb
in the Jersey population (Villa-Angulo et al., 2009). Assuming a comparable decline of LD
for increasing marker distance between the Jersey population and our pig populations, we
would expect to accurately impute approximately 90% of the high density genotypes, using a low density panel containing 10% of the markers. More recent results reported even
higher average accuracy of imputation (approximately 95%) when imputing 42,000 SNP in
the Bovine 50K using the 3K subset in Holstein cattle (Johnston et al., 2011). To assess
the accuracy of GEBV estimated from imputed genotypes Weigel et al. (2010a), used the
same Jersey population from their previous study (Weigel et al., 2010b), and they found that
the accuracy of GEBV based on imputed markers was 95% of the accuracy of the GEBV
estimated using the observed genotypes (Weigel et al., 2010a). As noted above average r2
is similar between the American Jersey population and our pig populations, suggesting that
future research in genomic selection in swine should explore the use of imputed low density
genotypes to increase cost eﬃciency. Previous research in humans (Huang et al., 2009), and
European Holstein cattle (Dassonneville et al., 2011) indicated that combining haplotypes
from closely related populations can increase the accuracy of genotype imputation, while research in sheep suggests that breed speciﬁc reference haplotypes would yield better accuracy
(Hayes et al., 2012). The success of combined haplotypes for genotype imputation depends
on the relatedness between the populations. Further research is necessary to determine if
persistence of phase is large enough in our pig populations to increase imputation accuracy
when combining reference haplotypes across breeds. As noted by Goddard (2008), the accuracy of GEBV prediction can be expressed as a function of the LD of between marker and
QTL and the accuracy of estimated SNP eﬀects. The loss in accuracy of GEBV prediction
caused by imputing instead of observing genotypes could be compensated by increasing the
26

number of animals used to estimate SNP eﬀects. If not enough animals are available for
the estimation of SNP eﬀects, animals from diﬀerent, but closely related, populations could
be combined to estimate SNP eﬀects for GEBV prediction in both populations (Goddard
et al., 2006; Ib´nez-Escriche et al., 2009). The squared short-range (<10 kb) correlation of
a
phase can also serve as the accuracy with which we can predict a marker-QTL association in
one population using known marker-QTL associations from another population. For the pig
breeds reported in this study the squared correlation of phase for close markers (0-100kb)
ranged from 0.53 to 0.67. To evaluate whether these accuracies would warrant the use of
a combined training population to estimate SNP eﬀects accurately for both populations we
refer to a simulation study conducted by de Roos et al. (2009) estimating the accuracy of
GEBV prediction for combined training populations of highly, moderately and lowly related
populations. Correlation of phase for populations diverged approximately T = 30 generations ago was reported to be below 0.80 for markers with pairwise distance below 0.055 cM
(de Roos et al., 2009). We found correlation of phase between Landrace-Yorkshire of around
0.80 at a corresponding marker distance. de Roos et al. (2009) concluded that reliability
of GEBV prediction could be increased between 0.05-0.10 points in two populations, when
approximately 40,000 marker genotypes are available, heritability is h2 = 0.3 or higher, 1000
animals from each population were used to estimate SNP eﬀects, and under the assumption
that QTL eﬀects are the same for both populations (de Roos et al., 2009). In addition,
they found that for genetically distant populations, at least 1,000 animals with genotypes
and phenotypes available in each population were needed to avoid a decrease in the reliability of prediction (de Roos et al., 2009). When SNP eﬀects estimated in one population
are used to calculate GEBV for another population which diverged approximately T = 30
generations ago, the reliability of the predicted GEBV was 0.65 assuming both high marker
27

density (M = 40, 000) and heritability h2 = 1 (de Roos et al., 2009). Consequently, combining animals into a multi-breed panel to estimate SNP eﬀects is likely to be only marginally
beneﬁcial for the pig breeds in this study, given the estimated correlation of phase and the
large number of animals and markers required (de Roos et al., 2009).

2.4

Conclusions

We used the PorcineSNP60 chip (Ramos et al., 2009) to obtain high density genotypes
(34,000-40,000 SNP) from pig trios in four breeds. From this data we estimated r2 as a
measure of LD across the genome as well as correlation of r, which measures phase agreement
between breeds. We found r2 of approximately 0.4 for markers less than 100 kb apart, which
is higher than comparable estimates reported for North American Holstein cattle (Sargolzaei
et al., 2008) as well as various Australian cattle breeds (de Roos et al., 2008). The same was
true for average r2 between markers with pairwise distance larger than 1 Mb, indicating a
smaller past eﬀective population size of these pig breeds. We also report a relatively slow rate
of decay of LD over distance, observing r2 around 0.2 at 1 Mb. The comparably high long
range LD is an indicator that good accuracy can be expected for future implementations of
GEBV in pigs using 10% (3,000-4,000) of SNP used in the current assay or less, along with
genotype imputation. We would encourage future research in genomic selection in swine
to especially focus on the possible beneﬁts of the combined use of reduced marker panels
and genotype imputation. To successfully promote the use of genomic selection in swine it
will be necessary to increase cost eﬃciency while maintaining high accuracy of prediction.
Currently no low density panels for SNP genotyping are publicly available for swine, but
the presented results will be available to aid in the development of eﬃcient SNP platforms.

28

Relatively low persistence of phase reported here implies that the use of multi-breed panels
estimating SNP eﬀects for genomic selection will likely be limited, especially when using low
density genotypes, but the merit of combining reference haplotypes for genotype imputation
should be further investigated.

2.5
2.5.1

Methods
Sample Design

For this study sire/dam/oﬀspring trios of the Duroc, Hampshire, Landrace and Yorkshire
breeds were selected from the National Swine Registry (NSR) pedigree. Selected parents
were unrelated for at least two generations. All animals were genotyped using the Illumina
PorcineSNP60 (Number of markers M = 62, 163) Genotyping BeadChip (Illumina Inc.)
(Ramos et al., 2009) at a commercial laboratory (GeneSeek, a Neogen Company, Lincoln,
NE). All SNP showing Mendelian inconsistencies for a trio were set missing in that particular
trio. If one or more animals within a trio had missing genotypes in more than 10% of the
SNP that trio was eliminated from further analysis. Similarly, SNP were removed if they did
not have genotypes available for at least 90% of the samples across all breeds (MCallRate <
0.9 = 5080). Only autosomal SNP were considered in this study, leading to the exclusion
of all SNP with an uncertain map position on build 10 of the pig genome sequence, as well
as SNP on the sex chromosomes (Mnon−autosomal = 9308). To exclude non-segregating
SNP from the analysis we removed markers with minor allele frequency (MAF) below 5%
within each breed separately. The number of ﬁxed SNP varied substantially between breeds:
we excluded MM AF < 5% = 13, 646 SNP in Duroc, MM AF < 5% = 15, 405 SNP in
Hampshire, MM AF < 5% = 7, 631 SNP in Landrace, and MM AF < 5% = 8, 665 SNP in
29

Yorkshire. Additionally, SNP were excluded for failure to meet Hardy Weinberg Equilibrium
(p < 0.001) within breeds causing MHW E < 0.001 = 117, 85, 146, and 176 SNP to be
discarded in Duroc, Hampshire, Landrace, and Yorkshire respectively. After applying the
described ﬁltering criteria, a total of 30, 26, 29, and 32 trios were included for the Duroc,
Hampshire, Landrace and Yorkshire breeds, respectively. And a total of 34,129, 32,370,
40,144 and 39,110 SNP spaced at an average distance of 70, 74, 60 and 61 kb satisﬁed the
SNP selection criteria for Duroc, Hampshire, Landrace and Yorkshire, respectively.

2.5.2

Estimation of average LD and persistence of phase

Haplotypes were obtained for the founder animals using the trio option of BEAGLE (Browning and Browning, 2009), phasing the genotypes by chromosome. Sampling animals in trios
was shown to yield improved accuracy of estimated haplotypes (Marchini et al., 2006). To
further increase haplotype accuracy, BEAGLE was set to run 100 iterations of the phasing
algorithm and sample 100 haplotype pairs for each individual per iteration. Additionally,
a short simulation experiment was conducted showing that for MAF above 5% average r2
can be reliably estimated from the current sample size (results not shown). Alleles for each
SNP were re-coded as 0/1, keeping the reference allele constant across all four populations,
allowing for later determination of phase agreement. Haplotypes and code needed to reproduce these results are publicly available at https://www.msu.edu/~steibelj/JP_files/
LD_estimate.html. For all pairs of SNP r2 was estimated, using allelic frequencies of the
founding animals, according to the following equation:
(pij − pi pj )2
2 =
rij
pi (1 − pi )pj (1 − pj )

30

(2.1)

where pi , pj are the marginal allelic frequencies at the ith and j th SNP respectively and
pij is the frequency of the two-marker haplotype (Devlin and Risch, 1995), using the freely
available software R (Team, 2011). Marker pairs were grouped by their pairwise physical
distance into intervals of 100 kb starting from 0 up to 10 Mb. Average r2 for SNP pairs in
each interval was estimated as the arithmetic mean of all (Equation 1), with the pairwise
distance between the ith and j th element of the currently considered interval:

r2 =
¯

Ml −1

1

18 (M − 1)
i=2
i=1 l

2
ri,i+1

(2.2)

where r2 is the average of all adjacent SNP across 18 autosomes (l), with Ml SNP per
¯
chromosome. To estimate average r2 between adjacent markers for diﬀerent marker densities
a certain percentage of markers (50%, 75%, 90%, 95%, 99%, and 99.5%) were removed before
average r2 was estimated using equation 2. To select markers, an increasing proportion of
SNP were sequentially removed solely considering their map position, so that for instance:
to reduce a panel to 50%, every second marker was kept for analysis, for 25% every fourth
was kept and so on. To estimate persistence of phase only markers with minimum MAF of
5% in all breeds were included in the analysis, resulting in 22,340 common SNP across all
breeds. Correlation of phase was estimated for intervals of 100 kb (from 0 to 10 Mb). We
excluded markers with pairwise distance above 10 Mb to decrease the computational load.
Estimates of average r2 at larger distances are close to zero, which would cause correlation
of phase to be close to zero as well. Persistence of phase was then estimated as:

Rk,k =

¯
¯
(i,j)∈p (rij(k) − r(k) )((rij(k ) − r(k ) )
s(k) s
(k )

31

(2.3)

where R
is the correlation of phase between rij(k) in population k and rij(k) in popk,k
ulation k, s(k) and s(k) are the standard deviation of rij(k) and rij(k) respectively, and
r(k) /¯
¯
r
are the average ri j across all SNP i and j within interval p for population k and
(k )
k respectively.

32

Chapter 3
Methods of tagSNP selection and
other variables aﬀecting imputation
accuracy in swine
Badke, Y. M., Bates, R. O., Ernst, C. W., Schwab, C., Fix, J., Van Tassell, C. P., & Steibel,
J. P. (2013). Methods of tagSNP selection and other variables aﬀecting imputation accuracy
in swine. BMC genetics, 14(1), 8.

33

3.1

Background

Recent advances in genotyping technology have facilitated the availability of high density
genotyping platforms in many livestock species. High density platforms including several
thousand single nucleotide polymorphisms (SNP) are available for cattle (Boichard et al.,
2012; Matukumalli et al., 2009; VanRaden et al., 2011), chicken (Groenen et al., 2009), sheep
(Archibald et al., 2010), and pig (Ramos et al., 2009).
These platforms can be used to increase the eﬃciency and accuracy of breeding programs
by implementing genomic selection (Hayes et al., 2009a; Meuwissen et al., 2001). Using SNP
data to inform breeding decisions allows animal breeders to select breeding stock prior to the
animals having progeny of their own, thereby accelerating genetic progress through shortened
generation intervals (Hayes et al., 2009a; Meuwissen et al., 2001).
Currently, genomic selection has been successfully implemented in dairy cattle based
on genotypes from the Illumina BovineSNP50 chip (Hayes et al., 2009a). In an eﬀort to
increase cost eﬃciency, the use of low density (tagSNP) genotyping platforms was exploited
for dairy cattle (Dassonneville et al., 2011; Weigel et al., 2010a). If high density genotypes
are imputed from tagSNP with high accuracy, the loss of reliability of predicted genomic
breeding values is minimal (Berry and Kearney, 2011; Dassonneville et al., 2011; Weigel
et al., 2010a). High accuracy of imputed genotypes depends on the selection of tagSNP, as
well as the composition and size of the reference panel of haplotypes used for imputation.
If close relatives of all imputation candidates are genotyped at high density, untyped
markers can be recovered through linkage and segregation analysis (Habier et al., 2009),
where haplotypes can be traced through generations of directly related individuals using the
rules of Mendelian inheritance. However, in some species it may not be feasible to genotype

34

a large proportion of the pedigree at high density. In that case a small panel of reference
haplotypes can be used to impute all untyped markers by exploiting population-wide linkage disequilibrium (LD) (Browning and Browning, 2009; Scheet and Stephens, 2006). This
approach was initially proposed in human genome-wide association studies (GWAS) and has
recently found application in plant (Hickey et al., 2012) and animal breeding (Berry and
Kearney, 2011; Hayes et al., 2012; Weigel et al., 2010a). A combination of imputation based
on segregation analysis and population-wide LD is currently being used in dairy breeding
(Dassonneville et al., 2011). While combining both approaches will increase accuracy of
imputation, eventually becoming the default method, cost-eﬀective implementation of genomic selection in novel populations is likely to initially rely more on LD based imputation.
Consequently, in this paper we will concentrate on LD based imputation by investigating
tagSNP selection and haplotype reference panel construction.
Human geneticists have proposed a variety of approaches to select an optimal low density
set of tagSNP to achieve cost eﬃcient imputation in GWAS (He and Zelikovsky, 2007).
These approaches include statistical criteria based on a pairwise threshold of LD between
SNP (e.g. Qin et al., 2006) and predictive ability, selecting tagSNP that provide the most
accurate prediction of all non-typed markers (He and Zelikovsky, 2006). On the other hand,
tagSNP sets used in livestock are mainly selected for equidistant spacing based on physical
position along the genome, and high minor allele frequency (MAF) to ensure segregation
(e.g. Boichard et al., 2012).
Crucial to successful implementation of genotype imputation using population wide LD
is the availability of a representative panel of reference haplotypes (Howie et al., 2011; Huang
et al., 2009). These panels are commonly built by genotyping a small number of trios or
a larger number of relatively unrelated individuals. The overall goal in either case is to
35

collect genotypes that can be accurately phased (Marchini et al., 2006) into haplotypes
representative of population frequencies. As a result, we began our study by genotyping and
phasing a small number of trios in four US pig breeds (Badke et al., 2012, NT rios ∼ 30)
and further enriching this panel for the Yorkshire breed with a set of high density genotypes
from largely unrelated individuals (Nsamples = 889).
The objective of this study was to develop guidelines for the implementation of genotype
imputation in livestock populations having little or no prior use of genome-wide markerassisted-selection. First, we compared imputation accuracy resulting from three methods
of tagSNP selection using Yorkshire pigs genotyped with a high density SNP set (Illumina
PorcineSNP60). This includes a report on imputation accuracy of the recently developed
commercially available 9K tagSNP set referred to as the GeneSeek Genomic Proﬁler for
Porcine LD (GGP-Porcine, GeneSeek a Neogen Company, Lincoln, NE). Second, we assess
accuracy of imputation based on an increasing number of reference haplotypes to inform
the selection of an optimal reference panel of haplotypes. Finally, we discuss imputation
accuracy as a function of chromosomal location and MAF of non-observed SNP.

3.2
3.2.1

Methods
Genotypes

High density genotypes for approximately 30 sire/dam/oﬀspring trios were obtained and
phased for each of four breeds of pigs (Duroc, Hampshire, Landrace, Yorkshire) in a previous
study (Badke et al., 2012). To ensure accurate phasing, the reference panel for imputation
used in this study was the 128 haplotypes from the Yorkshire sire/dam pairs previously
genotyped as parents in those trios. Animal protocols were approved by the Michigan State
36

University All University Committee on Animal Use and Care (AUF# 03/09-046-00). The
haplotypes of these animals are freely available at https://www.msu.edu/~steibelj/JP_
files/LD_estimate.html.
Detailed information about data cleaning procedures, descriptive statistics of LD, and
correlation of phase between Yorkshire and other US pig breeds can be found in Badke et al.
(2012). In addition, DNA samples were collected from 920 Yorkshire pigs and sent to a
commercial laboratory (GeneSeek, a Neogen Company, Lincoln, NE) to be genotyped on the
Illumina PorcineSNP60 (Number of markers M=62,163) Genotyping BeadChip (Illumina
Inc.) (Ramos et al., 2009). Only animals with more than 90% genotype call rate were
considered for analysis, resulting in 889 animals used as the testing panel for this study. All
SNP included in the 128 haplotype Yorkshire reference panel were used for analysis. All data
from this study is available at https://www.msu.edu/~steibelj/JP_files/imputation.
html.
In our previous study (Badke et al., 2012) we reported breed speciﬁc LD and persistence
of phase among breeds for Duroc, Hampshire, Landrace, and Yorkshire pigs. We found that
persistence of phase between Yorkshire and the other breeds ranged between 0.42 and 0.57
for SNP spaced approximately 1MB apart (Badke et al., 2012). As a result the amount of LD
within the Yorkshire breed that could be recovered through haplotypes from another breed
ranges between 0.18 and 0.33, such that adding haplotypes of a second breed to impute
Yorkshire genotypes did not appear to be beneﬁcial. For genomic selection, a simulation
study conducted by de Roos et al. (2009) found that persistence of phase between breeds
needs to be much larger than the reported value between Yorkshire and any of the other
three breeds to implicate any advantage for the use of mixed breed training panels. For this
reason we decided to use only Yorkshire haplotypes in the reference panel for imputation in
37

this paper.

3.2.2

Genotype imputation and estimation of imputation accuracy

All imputations in this study were done using BEAGLE version 3.3.1 (Browning and Browning, 2009), a genotype imputation software that uses a reference panel of haplotypes to estimate phase and impute missing genotypes in a set of unrelated individuals. Beagle was run
separately for each chromosome using 128 reference haplotypes from the trio design (Badke
et al., 2012, phased ﬁle) to phase and impute genotypes of the 889 un-phased testing animals. All SNP, except tagSNP, were masked as missing in the testing set. Beagle was run
for ten iterations of the phasing algorithm, drawing four samples per iteration. Previous
results from another study (Hayes et al., 2012), as well as a short experiment conducted
in this study (data not shown) found no increase in imputation accuracy when the number
of iterations or samples per iteration were increased. The output ﬁles from BEAGLE contained the most likely imputed genotypes (AA, AB, BB), posterior genotype probabilities
(P (AA), P (AB), P (BB)), and posterior expected allelic dosage of the B allele derived from
the posterior genotype probabilities (i.e. 0 ∗ P (AA) + 1 ∗ P (AB) + 2 ∗ P (BB)) (Browning,
2011).
Imputation accuracy was estimated using three diﬀerent measures that reﬂect diﬀerent
inﬂuences of MAF and error counting. The proportion of correctly imputed alleles was
computed as
M Ni
IA = 1 −

i=1 j=1
2∗

|gij − gij |
ˆ
M

i=1
38

(3.1)
Ni

where gij is the observed allelic dosage of SNP i in individual j, gij is the corresponding
ˆ
posterior expected allelic dosage obtained from BEAGLE output, M is the total number of
imputed SNP, and Ni is the number of individuals with called genotypes for SNP i. This
overall measure of imputation accuracy can be further decomposed into SNP-speciﬁc accuMj
Ni
|gij −ˆij |
g
|gij −ˆij |
g
j=1
i=1
) and animal speciﬁc accuracy (IA.j = 1 −
).
racy (IAi. = 1 −
2∗Ni
2∗Mj
This measure of imputation accuracy will be biased upwards, especially for SNP with low
MAF, because even if imputation ignores LD information and is based solely on allele frequency, the major allele would be correctly imputed for a large proportion of genotypes
(Hayes et al., 2012; Hickey et al., 2012). As tagSNP density decreases, imputation accuracy
of rare alleles further decreases as rare haplotypes become harder to identify due to longer
sequences of SNP missing (Hickey et al., 2012). Estimating the total percentage of correctly
imputed alleles for SNP with low MAF will be biased due to the large number of correctly
imputed major alleles masking the small number of misspeciﬁed minor alleles, which can be
overcome through the use of a more sensitive measure of accuracy for these SNP (Hickey
et al., 2012). In addition, if individuals carrying the minor allele are not correctly identiﬁed and their phenotype cannot be matched for GWAS this relatively small proportion
of incorrectly imputed alleles will further decrease power. A variety of measures have been
introduced to obtain estimates of imputation accuracy unbiased by MAF (Hayes et al., 2012;
Hickey et al., 2012; Zheng et al., 2011). We estimated the proportion of correctly imputed
alleles adjusted for MAF using the formula presented by Hayes et al. (2012):
IA − IAF req
IAM AF =
1 − IAF req

39

(3.2)

where IA is computed as described in equation (3.1) and IAF req is the accuracy of imputation based on genotypic frequencies estimated as:

IAF req = p(AA)ref ∗ p(AA)val + p(AB)ref ∗ p(AB)val + p(BB)ref ∗ p(BB)val (3.3)

where p(AA)ref , p(AB)ref , and p(BB)ref are the observed frequencies for genotypes
i
i
i
AA, AB, and BB for SNP i in the reference haplotypes and p(AA)val , p(AB)val , and
i
i
p(BB)val are the predicted genotypic frequencies in the testing population for SNP i.
i
IAF req can be interpreted as the expected probability of correctly imputing a genotype in
the testing population by assigning a randomly sampled genotype from the haplotypes in
the reference panel. This measure was computed on a SNP-wise basis and averaged across
all SNP. To account for a slightly diﬀerent number of genotypes observed within each SNP
(due to missing at random) the average was obtained by weighting the accuracy of each SNP
by the number of individuals with observed genotypes within each SNP.
Alternatively, another measure of imputation accuracy robust to MAF is the squared
correlation between the observed and imputed allelic dosage (Hickey et al., 2012). The
correlation was obtained on a SNP by SNP basis using the correlation function in R (Becker
et al., 1988). SNP wise correlation measures were weighted by the number of available
observations within the SNP to obtain an overall average imputation accuracy.

3.2.3

Methods of tagSNP selection

TagSNP were selected using three approaches: 1) evenly spaced based on physical position,
2) based on minimum pairwise LD with non-tagSNP (statistical selection), and 3) based
on marker predictive ability to accurately impute non-observed SNP genotypes (predictive
40

selection).
To select evenly spaced SNP the total length of each chromosome was partitioned into
segments corresponding to the total number of tagSNP to be selected. Then, within each
segment the SNP closest to the segment center was identiﬁed and added as a tagSNP. If a
given segment was empty, no tagSNP was selected in that segment.
To implement a statistical search for tagSNP (He and Zelikovsky, 2006) we used the
freely available software package FESTA (Qin et al., 2006). FESTA performed a greedy
search, where each SNP i was either an element of the tagSNP set or in LD higher than a
2
threshold (rt ) with an existing element of the tagSNP set. FESTA was run repeatedly for
2
increasing rt ranging from 0.1 to 0.9 in 0.1 increments using estimates of LD based on 128
reference haplotypes.
To implement predictive tagSNP selection, we applied the following forward search algorithm: First, we split the 64 Yorkshire reference animals into a randomly sampled set
of 10 individuals (training set) and 54 individuals (reference haplotypes). Second, all SNP
except one tagSNP in the training set were masked and imputed using the reference haplotypes. Third, accuracy of all imputed SNP was estimated and saved. Steps two and three
were then repeated until all estimates of imputation accuracy were available for all potential
tagSNP (at ﬁrst, the potential tagSNP are all SNP on the chromosome). Fourth, the SNP
that yielded the highest average accuracy of imputation among those not already chosen
as tagSNP was selected as a new tagSNP. Steps two through four were repeated until the
maximum number of tagSNP or a target imputation accuracy were reached. Because of
the high computational demand of this methodology, this approach was only applied to the
smallest available chromosome (SSC18), selecting tagSNP from 786 candidate SNP.
Concurrent to this research, a set of 9390 tagSNP (Release Date: April 2012) was as41

sembled by GeneSeek (Lincoln, NE) for the development of a commercial platform for low
density genotyping in swine. This assay has been marketed as the GeneSeek Genomic Proﬁler
for Porcine LD (GGP-Porcine; GeneSeek, Lincoln, NE). After production, the GGP-Porcine
contains approximately 8500 tagSNP (Jeremy Walker, personal communication). TagSNP
covering the entire genome were selected based on MAF in 13 commercial lines of pigs represented by four breeding companies and four purebred populations. The MAF were provided
by the breeding companies (identiﬁed simply as company A, B, C, and D). The number of
lines provided by these companies were 1, 1, 4, and 7. Additional estimates of MAF used
to identify tagSNP were obtained from our previous study (Badke et al., 2012) of four pure
breeds: Duroc, Hampshire, Landrace, and Yorkshire. The freely available SNPspace software (C.P. Van Tassell, unpublished data) was used to select tagSNP. SNPspace was initially
developed to select SNP for the Illumina BovineSNP50 beadchip (Matukumalli et al., 2009).
The conceptual framework of SNPspace is brieﬂy described in that study (Matukumalli et al.,
2009), but additional features have been added since that time. Relative weights on lines
or breeds of pigs ranged from 0.00625 to 0.25. SNPspace is based on a greedy algorithm,
where SNP scores account for breed or line speciﬁc MAF, region of the genome, and position of SNP relative to previously selected tagSNP. Density of tagSNP was doubled within
5 Mbp of the chromosomal extremes, which has been shown to improve average accuracy
of imputation compared to tagSNP evenly spaced across the entire chromosome (Boichard
et al., 2012; Dassonneville et al., 2012).

3.2.4

Increasing reference panel size

To assess the eﬀect of the number of reference haplotypes on imputation accuracy, we split
the available sample of 889 Yorkshire pigs into two groups: 1) a 200 animal testing panel,
42

and 2) a 689 animal set of supplemental reference sires. Assignment to the two panels was
random.
To obtain imputation accuracy for a decreased set of reference haplotypes, we split the
original 128 reference haplotypes obtained from 64 Yorkshire animals into two groups of
64 reference haplotypes (corresponding to 32 animals) and estimated average imputation
accuracy in the 200 animal testing set. Then, we split the two groups of 64 reference
haplotypes further into two groups of 32 reference haplotypes and obtained four estimates
of imputation accuracy that were averaged into a single measure.
Subsequently, we compared imputation accuracy using trio based reference panels to
imputation accuracy based on randomly sampled reference panels. To this end, we randomly
sampled 16 animals from the 689 animal supplemental reference set and continued to add
individuals at random to obtain reference sets of 24, 32, 48, 64, 96, 128, 256, and 512 animals.
Each of these sets was phased individually using BEAGLE (Browning and Browning, 2009)
and then those haplotypes were used as reference panel to impute the 200 testing animals.
Finally, we assembled reference panels of haplotypes combining the original 128 haplotypes from trios, with an increasing number of supplemental reference sires. To form these
reference panels 64, 128, 192, and 448 supplemental reference sires were randomly selected
and phased using the trio haplotypes as a reference panel. Both, the trio reference haplotypes and an increasing number of supplementary reference haplotypes were then used to
impute the 200 animal testing set.
Because imputation accuracy was constant across chromosomes (see Results, section 3.1)
we conducted this experiment on chromosome SSC14, a medium sized chromosome that has
uniform coverage of SNP across its length. We expect results to extrapolate to all other
chromosomes.
43

3.3
3.3.1

Results
Comparison of methods for tagSNP selection

Due to the high computational demand, we initially performed a comparison of methods
for tagSNP selection only on the smallest chromosome (SSC18). Statistical tagSNP selec2
2
tion requires ﬁxing an r2 threshold (rt ). Setting rt = 0.2 resulted in the selection of 165
2
tagSNP, which produced imputation accuracy of 0.936. Increasing rt to 0.3, led to a panel
of 235 tagSNP and an increased imputation accuracy of 0.956. In comparison, imputation
accuracy based on 165 and 235 tagSNP selected for predictive ability was 0.93 and 0.945,
respectively. Direct comparison to tagSNP sets selected for even spacing is more diﬃcult
because of empty intervals, for which no tagSNP were selected, resulting in smaller than targeted tagSNP sets. The evenly spaced tagSNP sets closest in size to 165 and 235 tagSNP were
as expected slightly smaller (161 and 224 tagSNP), and the resulting imputation accuracies
were slightly lower than those obtained using the other sets (0.92 and 0.941, respectively).
As expected, imputation accuracy increased with increasing densities of tagSNP regardless
of the selection method (Figure 3.1). Statistically selected tagSNP performed slightly better
than both, predictive and evenly spaced tagSNP (Figure 3.1), but all three methods resulted
in similar imputation accuracy. Selection of tagSNP using predictive ability required an at
least 500-fold increase in computation time for SSC18 compared to statistical and evenly
spaced selection. However, results of imputation accuracy indicate that predictive tagSNP
did not yield signiﬁcantly higher imputation accuracy compared to tagSNP selected by other
methods. Therefore, only statistical and evenly spaced tagSNP were selected in an exhaustive evaluation of imputation accuracy across all autosomes (Figure 3.1).

44

Figure 3.1: Imputation accuracy based on tagSNP selected using 3 diﬀerent methods
Average imputation accuracy (IA) as a function of the number of tagSNP selected using
three methods of tagSNP selection for SSC18: 1) evenly spaced (red square), 2) statistical
selection (black circle), or 3) predictive selection (green line).
When imputing across all autosomes, as observed on SSC18, imputation accuracy using
statistically selected tagSNP was slightly higher than that using evenly spaced tagSNP (Figure 3.2). In particular, to attain imputation accuracy of 0.95, 7036 statistically selected
2
tagSNP were necessary (rt = 0.3). In comparison, 10540 evenly spaced tagSNP were necessary to reach similar imputation accuracy. Imputation accuracy was virtually uniform across
45

2
2
chromosomes ranging from 0.92 to 0.94 for rt = 0.2 and from 0.94 to 0.96 for rt = 0.3.

Figure 3.2: Imputation accuracy using evenly spaced or statistically selected tagSNP
Average imputation accuracy (IA) as a function of the number of tagSNP selected for: 1)
even spacing (red square), or 2) statistical selection (black circle) across all autosomes.
Imputation accuracy for 7323 tagSNP from the commercial 9K tagSNP set (green triangle)
with 95% highest posterior density interval.
We computed imputation accuracy based on 7323 tagSNP from the original list of 9K
tagSNP provided by GeneSeek that passed quality control in this study (M AF > 0.05,
CallRate > 0.9, assembled to an autosome under map build10) resulting in imputation

46

accuracy of 0.951 with a SNP-wise 95% highest posterior density interval equal to [0.84, 1]
(Figure 3.2). Accuracy of imputation using the commercial tagSNP was similar to that ob2
tained using statistically selected SNP, at comparable density (rt = 0.3, MtagSN P = 7036).
The advantage of the proposed commercial platform is that it is not based on population
speciﬁc LD, thereby making it applicable across swine populations. For this reason all subsequent results of imputation accuracy will be based on the tagSNP element of the Genomic
Proﬁler for Porcine LD.

3.3.2

Imputation accuracy using the commercial 9K tagSNP set

To assess accuracy of imputation as a function of chromosomal location we plotted imputation accuracy of each individual SNP versus chromosomal position (Figure 3.3). SNP within
5% of the chromosomal extremes had on average slightly lower imputation accuracy (0.949)
than the 10% in the center of the chromosome (0.972). As mentioned before, this property of
imputation accuracy has previously been observed for other low density sets (Boichard et al.,
2012; Dassonneville et al., 2012) and was anticipated during the tagSNP set design. Based
on these reports (Boichard et al., 2012; Dassonneville et al., 2012), the density of tagSNP
was approximately doubled within 5 Mbp of the chromosomal ends in the commercial 9K
tagSNP set.

47

Figure 3.3: SNP-wise imputation accuracy by chromosomal location
SNP-wise imputation accuracy (IAi. ) vs. the scaled chromosomal location of the SNP. The
red line is the weighted mean average estimated using a loess smoother (Cleveland et al.,
1992), and the green line represents average imputation accuracy (IA = 0.951).
Animal-wise imputation accuracy (IAi. ) averaged 0.951 but the corresponding highest
posterior density interval ([0.917, 0.978]) was shorter than that observed for SNP-wise accuracy. Overall, all but 12 animals had imputation accuracy > 0.90 and 551 animals (62%) had
imputation accuracy above 0.95. Also, seven of the animals had a dam, sire, or grand-sire
in the reference panel (Badke et al., 2012), which resulted in on average higher accuracy of
48

imputation in these animals (0.959). A group of 15 animals was identiﬁed with consistently
low imputation accuracy (i.e. < 0.91 for 9K tagSNP) across all sets of tagSNP selected.
An ongoing research project in our laboratory investigating breed composition, identiﬁed
all of the 15 low accuracy individuals as potentially having mixed breed ancestry (YiJian
Huang, unpublished data). Further assessing the pedigree of these 15 animals, we found that
nine of them were imported to the US, which could result in a slightly diﬀerent haplotype
composition and the observed low accuracy of imputation, when only American Yorkshire
pigs had been used as reference. Another three animals of the remaining six US Yorkshires
with low imputation accuracy were identiﬁed as a family (sire, two oﬀspring), such that the
observed low accuracy in the oﬀspring is likely a result of the mixed breed ancestry of their
sire.
As noted before, to assess the eﬀect of MAF of imputed SNP on imputation accuracy
required adjusting estimates of imputation accuracy for MAF. Imputation accuracy as a
function of MAF is presented in Figure 3.4, where imputation accuracy was estimated as
a) proportion of alleles correctly imputed, b) coeﬃcient of determination (R2 ) between observed and imputed allelic dosage (Hickey et al., 2012; Zheng et al., 2011), and c) proportion
of alleles correctly imputed adjusted for MAF (Hayes et al., 2012). The red line in all plots
represents the weighted mean average estimated using a loess smoother (Cleveland et al.,
1992). Loess consists of ﬁtting smooth piecewise polynomial regressions to local subsets
of data and it is widely used in normalization of micro-array experiments (Steibel et al.,
2009). At ﬁrst inspection, it can be seen that accuracy estimated as the proportion of correctly imputed alleles (Figure 3.4a) is highest for low frequency alleles and exhibits a small
decrease as MAF increases. However, the observed high proportion of correctly imputed
alleles in SNP with low MAF is based on the fact that high frequency alleles can be im49

puted with high accuracy even if imputation is solely based on allele frequency (Hayes et al.,
2012; Hickey et al., 2012). For this reason, we computed R2 and the proportion of correctly
imputed alleles adjusted for MAF that provide estimates of imputation accuracy unbiased
by allele frequency. In other words, these measures are indicative of the performance of the
imputation algorithm in comparison to a baseline imputation based on genotypic frequencies
(Hayes et al., 2012; Hickey et al., 2012). When imputation accuracy is adjusted for MAF,
estimated accuracy is generally higher for intermediate allele frequencies (M AF ∼ 0.5) and
declines as MAF decreases (Figure 3.4 b/c). Average imputation accuracy considering only
the added beneﬁt of the imputation algorithm was lower (IAM AF = 0.91, R2 = 0.81) than
the total proportion of correctly imputed alleles (IA = 0.951). The diﬀerence between the
proportion of correctly imputed alleles adjusted for MAF (Figure 3.4c) and estimates of R2
(Figure 3.4b) can be explained by the diﬀerence in error counting between these measures.
While the proportion of correctly imputed alleles adjusted for MAF is obtained by counting
the total number of wrongly imputed alleles, R2 is obtained from the squared diﬀerence
in imputed and observed alleles, thereby more heavily penalizing large diﬀerences between
observed and imputed allelic dosage.

50

Figure 3.4: Three measures of SNP-wise imputation accuracy by MAF
SNP-wise imputation accuracy computed as A) the proportion of correctly imputed alleles (IAi. ), B) the correlation between
imputed and observed allelic dosage (R2 ), and C) the proportion of correctly imputed alleles adjusted for MAF (IAM AF ),
i.
as a function of MAF of the SNP. The red line is the weighted mean average estimated using a loess smoother.

51

3.3.3

Eﬀect of numbers of reference haplotypes on imputation accuracy

For all previous analyses in this paper we imputed genotypes of 889 individuals across all autosomes using a reference panel of 128 Yorkshire haplotypes obtained from a sire/dam/oﬀspring
genotyping design (Badke et al., 2012), phased with higher accuracy (Marchini et al., 2006).
Reducing the number of imputation animals from 889 to 200 had no impact on the observed
imputation accuracy. Imputation accuracy using all 128 haplotypes from the original reference panel was 0.959 on SSC14, which reduced to 0.939 when 64 haplotypes were used,
and further to 0.904 when imputation was based on 32 haplotypes (Figure 3.5). Therefore,
imputation accuracy larger than 0.90 can be obtained using the commercial 9K tagSNP set
with a reference panel of only 32 haplotypes, given that these haplotypes were phased at
high accuracy.

52

Figure 3.5: Eﬀect of number of reference haplotypes on imputation accuracy
Average imputation accuracy (IA) as a function of the number of haplotypes in the
reference panel used for imputation. Imputation accuracy was estimated for reference
panels composed of haplotypes from a trio design (blue triangle), reference panels
composed of haplotypes from randomly sampled sires (red circle), and reference panels
composed of both haplotypes from a trio design and haplotypes from randomly sampled
sires (black circle).
We further investigated if it is necessary to obtain reference haplotypes from a trio design,
or if accuracy can be replicated using a reference panel of randomly sampled individuals
genotyped at high density. In comparison to imputation accuracy obtained using a trio

53

reference panel, imputation accuracy based on 32 and 64 reference haplotypes derived from
selected sires was slightly lower (0.875 and 0.926, respectively). However, accuracy from 128
reference haplotypes obtained from 64 randomly sampled individuals was 0.955, which is
practically identical to results obtained using 128 reference haplotypes from trios. Therefore,
if the reference panel of haplotypes is composed of more than 128 haplotypes, there is
no longer an advantage in using haplotypes obtained from a trio design. Alternatively,
the cost of assembling panels of 32, 64, and 128 reference haplotypes obtained from a trio
design involves the same genotyping cost as assembling panels of 48, 96, and 192 haplotypes
obtained from randomly sampled individuals. This is due to the fact that in a trio design
the oﬀspring haplotypes are not used as part of the reference panel, since they are identical
to the parents transmitted haplotypes. Imputation accuracies for 48, 96, and 192 reference
haplotype panels from randomly sampled individuals were estimated to be 0.906, 0.947, and
0.965, respectively, which is either equivalent or higher than accuracy of imputation obtained
using the cost equivalent trio based reference panels (Figure 3.5). In addition, we compared
imputation accuracy from reference haplotypes of either 64 randomly selected individuals
or the 64 oldest individuals and found no diﬀerence in imputation accuracy (0.956, 0.953
respectively). Consequently, if no reference panel of haplotypes is available for a population,
according to the results of this study, it would be most cost eﬃcient to assemble high density
haplotypes of randomly sampled individuals.
Previous research has indicated an increase in imputation accuracy can be expected
as the number of available reference haplotypes increases to a certain point (Howie et al.,
2011; Huang et al., 2009). We added randomly selected individuals to the reference panel
and obtained 256, 512, and 1024 reference haplotypes. These panels resulted in average
accuracy of imputation of 0.971, 0.978, and 0.985 respectively (Figure 3.5). Imputation
54

accuracy only marginally increased when more than 256 haplotypes were used as reference
panel for imputation (up to 1.4% gain). Additionally, we assessed accuracy of imputation
from reference panels composed of the original 128 reference haplotypes from a trio design
and an increasing number of randomly sampled individuals added to that panel. In this
case, imputation accuracy based on reference panels with 256 and 512 haplotypes was 0.969
and 0.978 respectively, which is virtually identical to results obtained using reference panels
solely from randomly sampled individuals (Figure 3.5).
In addition to assessing the eﬀect of an increased number of reference haplotypes on
average accuracy, we also investigated how it aﬀects individual SNP with diﬀerent MAF and
physical location. We found that as the size of the reference panel increases, imputation
accuracy (quantiﬁed as R2 ) improved more markedly for SNP with MAF below 0.1, such
that when the size of the reference panel is increased from 256 haplotypes to 512 haplotypes
the increase in accuracy for SNP with MAF below 0.1 was on average 0.06 points, while for all
other SNP the increase was only 0.02 points (Additional ﬁle 1: Figure 3.6). When imputation
was based on 1024 reference haplotypes imputation accuracy appears to be uniform across
allele frequencies. Similarly, we observed that imputation accuracy (proportion of correctly
imputed alleles) for SNP located in the 10% chromosomal extremes (5% on either side) could
be improved through an increase in the number of reference haplotypes (Additional ﬁle 2:
Figure 3.7). A reference panel containing 512 haplotypes was necessary to obtain maximal
imputation accuracy (IA = 0.99) for SNP located in the chromosomal center, while SNP in
the chromosomal extremes were imputed with accuracy of only 0.97, even when the number of
reference haplotypes was doubled (1024 reference haplotypes). Imputation accuracy observed
in SNP located in the chromosomal extremes was more than 0.02 accuracy units lower than
the average imputation accuracy of all remaining SNP irrespective of the reference panel
55

size.

3.4
3.4.1

Discussion
Methods for tagSNP selection

Current algorithms for genotype imputation exploit population-wise LD (Browning and
Browning, 2009; Scheet and Stephens, 2006), familial LD from identity by descent (Abecasis
et al., 2002), or a combination of both (Hickey et al., 2011) to infer unobserved genotypes
conditional on tagSNP information. Virtually all methods for tagSNP selection aim at
identifying tagSNP that carry the maximum amount of information to impute unobserved
markers. This is attained by either directly quantifying the tagSNP ability to predict nontyped SNP (predictive tagSNP selection) or indirectly by selecting tagSNP in high pairwise
LD with non-tagSNP (statistical tagSNP selection) (He and Zelikovsky, 2007).
A goal of this study was to select a minimal set of tagSNP that would yield acceptable
accuracy of imputation of non-tagSNP (Dassonneville et al., 2012; Weigel et al., 2010a). Since
genotype imputation utilizes information about the structure of LD to infer non-observed
SNP, we expected that tagSNP sets selected based on LD information, such as statistical and
predictive tagSNP selection, would yield higher accuracy of imputation than tagSNP selected
based solely on their physical location. In addition, we expected that directly assessing the
ability of each tagSNP to predict non-observed SNP (predictive selection) would yield an
improvement in imputation accuracy compared to tagSNP selected purely based on pairwise
thresholds of LD (statistical selection).
We found that at the lowest examined tagSNP density (1 tagSNP per Mb) accuracy of
imputation was below 0.87 irrespective of the method of tagSNP selection and that at least 2
56

tagSNP per Mb were necessary to increase accuracy to at least 0.91. Accuracy of imputation
increased as tagSNP density increased, reaching a plateau accuracy of approximately 0.98
when tagSNP were spaced at an average distance of less than 125kb with negligible increases
beyond such density. Our results compare well to those of Weigel et al. (2010b), where
randomly selected tagSNP at an approximate density of 300kb were necessary to obtain accuracy larger than 0.90 in the US Jersey cattle population using a similar type of imputation.
In our study, imputation accuracy of approximately 0.95 was obtained using between 7000
(average tagSNP spacing of 340kb) and 10000 tagSNP (average tagSNP spacing of 230kb),
depending on the method of tagSNP selection.
As expected, predictively and statistically selected tagSNP did yield higher accuracy of
imputation than evenly spaced tagSNP, but we found no diﬀerence in imputation accuracy
between tagSNP sets selected statistically or based on predictive ability. Comparing 300
tagSNP selected using predictive ability to 317 tagSNP obtained using statistical selection
2
(rt = 0.4) on SSC18, we observed the same imputation accuracy (IA = 0.95). However, the
two sets are qualitatively diﬀerent. For instance, the 300 predictive tagSNP only provide
statistical coverage (r2 ≤ 0.4) to 37% of non-tagSNP. The tagSNP sets also have on average
diﬀerent MAF (M AFpredictive = 0.30, M AFstatistical = 0.27). We attribute the equivalence in imputation accuracy of two diﬀerent tagSNP sets to the extent of LD observed
across the genome in Yorkshire pigs (r2 = 0.16 at 1 Mb, Badke et al., 2012). Under these
conditions, precision of estimates of individual tagSNP imputation accuracy is likely compromised by collinearity, making selection of a single best predictive tagSNP at each step
of the forward search complicated (Vittinghoﬀ et al., 2005). For example, the initial step of
the forward search for predictive tagSNP resulted in six SNP with predictive ability within
0.002 accuracy units of each other. Each of these SNP could have been selected as a starting
57

point of the greedy search, resulting in diﬀerent sets of tagSNP selected. Furthermore, the
implemented predictive forward search requires

Mti (2Mi −Mti +1)
imputation operations
2

per iteration step compared to only two with statistical selection, where Mi is the number
of SNP per chromosome and Mti is the number of selected tagSNP on that chromosome.
Consequently, even though both methods result in diﬀerent tagSNP sets, statistical selection is a computationally eﬃcient proxy for predictive tagSNP selection when moderate LD
between consecutive markers is present.
We show that tagSNP sets strictly selected for even spacing are slightly outperformed by
statistical or predictive tagSNP selection. However, it is possible to enhance the performance
of evenly spaced tagSNP through a few simple measures. TagSNP with high MAF seem to be
advantageous for genotype imputation (predictive tagSNP selection seemed to favor tagSNP
with high MAF) and their likelihood to segregate across populations will ensure that they
carry information for imputation in various populations. This has been exploited previously
in cattle for the assembly of the 3K platform (Dassonneville et al., 2012), as well as in
newer tagSNP sets aimed to further increase imputation accuracy (Boichard et al., 2012). In
addition to selecting evenly spaced tagSNP with high MAF, an increase in accuracy can be
obtained by increasing tagSNP density in the chromosomal extremes (Boichard et al., 2012).
The success of these enhancements of evenly spaced tagSNP is evident in the imputation
accuracy we report using the commercial 9K set (MtagSN P = 7323, IA = 0.951), which is
2
similar to results we found for statistical tagSNP sets for thresholds rt = 0.3 (MtagSN P =
7036, IA = 0.952). In addition, although the recently released commercially available chip
has approximately 10% fewer tagSNP than the original 9K tagSNP list that was used for
this analysis, our conclusions regarding imputation accuracy are likely to uphold, due to the
fact that we based our analysis on a set of only 7323 tagSNP, which should be representative
58

of the number of commercial tagSNP that will pass quality control in future study samples.
In summary, eﬃcient tagSNP selection based on MAF and physical location is feasible
and more ﬂexible than statistical tagSNP selection. Selecting evenly spaced tagSNP with
high MAF requires knowledge of the physical location of the SNP and the MAF across
populations of interest, while statistical tagSNP selection requires knowledge of the LD
structure, and would be population speciﬁc. As a result, selecting a tagSNP set with high
MAF and an increased density in the chromosomal extremes is more versatile than tagSNP
sets selected for predictive ability or based on statistical criteria while yielding the same
accuracy of imputation. In addition, the tagSNP set selected based on physical location
and MAF is expected to be useful for imputation as long as the 60K chip is being used
for genomic selection, because we do not expect selection to alter LD or MAF of selected
SNP in any particular way. If such tagSNP sets will be used across multiple closely related
populations it will be necessary to include a number of SNP that will be speciﬁc to a subset
of populations. In the case of the 9K tagSNP set more than 9000 tagSNP were selected
based on MAF across several populations and physical location of the SNP, but only 7323
of these SNP passed quality editing for the Yorkshire data in this study.

3.4.2

Factors aﬀecting imputation accuracy

Accuracy of imputation is aﬀected by several factors including the selection and density of
tagSNP as detailed above, the MAF and the physical location of the imputed SNP, as well
as the size and composition of the reference panel.
When evaluating imputation accuracy as a function of the tagSNP selection method and
density we have focused on average accuracy as a measure of overall performance. Assessing the average accuracy of imputation is a good indicator of the performance of imputed
59

genotypes, when all genotypes are used simultaneously to obtain a global measure. Such a
measure could be prediction of GEBV, which would be based on all SNP simultaneously,
such that a small number of wrongly imputed SNP is unlikely to greatly aﬀect the accuracy of prediction. Alternatively, some applications of imputed high density genotypes
may require high accuracy across all SNP. One example would be GWAS based on imputed
genotypes. For GWAS, SNP associations are assessed on a SNP by SNP basis, such that
wrongly imputed alleles for low frequency SNP are more likely to cause bias in the estimated
association, especially since phenotypes of interest are suspected to be associated with low
frequency alleles (Howie et al., 2011).
One of the factors directly related to the individual SNP imputation accuracy, is the
allele frequency of that particular SNP. To investigate imputation accuracy as a function
of MAF we used two measures of imputation accuracy that were unbiased by MAF (i.e.
IAM AF , R2 ). The adjusted proportion of correctly imputed alleles (IAM AF ) and the
correlation between observed and imputed allelic dosage (R2 ) are scaled diﬀerently, such
that the observed accuracy diﬀers as a function of scale, but the comparative diﬀerence in
imputation accuracy as a function of MAF can be observed using either of the two accuracy
measures. We found that estimates of imputation accuracy adjusted for MAF (R2 , IAM AF )
are lower (R2 = 0.73, IAM AF = 0.89) for SNP with MAF below 0.1, compared to SNP
with MAF above 0.1 (R2 = 0.82, IAM AF = 0.91), which has been previously noted by
Hayes et al. (2012) reporting results of genotype imputation in sheep and Hickey et al. (2012)
in lines of maize.
Another factor relating to individual SNP imputation accuracy is the physical location
of the SNP. Previous studies designing low density genotyping platforms have pointed out
the need to increase coverage of tagSNP in the chromosomal extremes due to diﬃculties
60

in correctly imputing SNP located in those regions (Boichard et al., 2012; Dassonneville
et al., 2012). In the commercial 9K tagSNP set the density of tagSNP within 5Mbp of
the chromosomal extremes was approximately doubled to aid imputation accuracy. We
found that imputation accuracy using the 9K commercial tagSNP was still slightly lower in
the extreme regions (0.949) when compared to the chromosome center (0.972). The eﬀect
however was alleviated in comparison to an equally spaced tagSNP set of comparable density,
where the average imputation accuracy in the chromosomal extremes was only 0.89.
We found a group of 15 animals that produced consistently low imputation accuracy
(IA ≤ 0.90), compared to all remaining animals (IA = 0.951). Nine of these animals were
identiﬁed as imports, such that the observed low accuracy of imputation is likely a result of
diﬀerences in haplotype frequencies between the US Yorkshire population that was used as
reference for imputation, and the population(s) from which these animals originated. The
remaining six animals were all identiﬁed as having potentially mixed breed ancestry based on
results of a concurrent research project in our laboratory (YiJian Huang, unpublished data).
In addition, we can infer from these results that if a population contains heterogeneous
sub-populations, such as a large number of imported animals or animals with cross-bred
ancestry, imputation accuracy will be decreased if this sub-structure is not accounted for
when sampling reference haplotypes.
We found that increasing the number of reference haplotypes led to an increase in average imputation accuracy. In addition to the number of reference haplotypes, their average
relatedness to the imputation candidates (Gualdron Duarte et al., 2012; Hayes et al., 2012;
Hickey et al., 2012; Huang et al., 2012), as well as accurate phasing of these haplotypes
(Browning and Browning, 2011) directly aﬀect the resulting accuracy of imputation. In this
paper, we assessed the eﬀect of phasing accuracy and the number of reference haplotypes.
61

Previous research comparing phasing accuracy of unrelated or randomly sampled individuals
and trio designs (sire/dam/oﬀspring), found that genotypes from trios can be phased with
higher accuracy (Marchini et al., 2006). The initial reference panel available in this study
was composed of the haplotypes of sire/dam pairs from a previous sample of trios that were
unrelated for at least two generations and therefore sampled to eﬃciently cover the Yorkshire
population (Badke et al., 2012). We found that for haplotype panels composed of 64 or less
haplotypes, imputation accuracy was higher when these haplotypes were obtained from the
trio design rather than a random sample of individuals (Figure 3.5). This advantage of the
trio design is likely due to the superior phasing accuracy as well as the sampling strategy
used to obtain these samples. However, adjusting sample size for the increased genotyping
cost in a trio design, we observed that imputation accuracy was equal or higher when imputation was based on haplotypes obtained from randomly sampled individuals instead of
trio reference haplotypes (Figure 3.5). Therefore, we conclude that if no reference panel is
available in a population the most cost eﬃcient method for reference panel construction is
genotyping a random sample of individuals across the population.
Next we assessed imputation accuracy as a function of increasing reference panel size.
We found that a reference panel of 256 to 512 reference haplotypes is suﬃcient to obtain
imputation accuracy of IA = 0.97. If the size of the reference panel is increased beyond
1024 haplotypes (IA = 0.985) any further gain in imputation accuracy appears to be very
small. A similar type of response has been observed in human genotype imputation (Huang
et al., 2009). This relatively small number of reference haplotypes necessary to obtain high
imputation accuracy (IA = 0.97) is likely due to the relatively small eﬀective population
size of the Yorkshire population (Ne = 113, (Welsh et al., 2010)), and consequently high
average LD even at decreased tagSNP density.
62

After determining that increasing the size of the reference panel would increase accuracy
of imputation, we assessed whether accuracy would diﬀer as a function of reference panel
composition. In general, when imputation experiments are conducted the older animals are
used as reference panel, while the younger animals serve as imputation candidates (Weigel
et al., 2010b; Zhang and Druet, 2010). We assessed whether imputation accuracy would
diﬀer depending on the reference panel being composed of randomly selected individuals or
older individuals and found no advantage in imputation accuracy when selecting a reference
panel composed of older animals.
In addition to the observed increase in overall imputation accuracy, we found that increasing the size of the reference panel is especially eﬃcient at increasing the individual imputation accuracy of SNP that exhibited below average imputation accuracy (Howie et al.,
2011). SNP with MAF below 0.1 were imputed poorly in comparison to SNP with MAF
above 0.1 (accuracy measure R2 , IAM AF ), but as reference panel size increased imputation accuracy of these SNP improved, and for imputation based on 1024 haplotypes we
observed a uniform distribution of imputation accuracy (quantiﬁed as R2 ) across levels of
MAF (Additional ﬁle 1: Figure 3.6). An increase in the size of the reference panel increases
the precision of estimated frequencies of haplotypes containing rare alleles, which appears to
more eﬃciently boost imputation accuracy for the corresponding SNP (Howie et al., 2011).
SNP located in the 10% chromosomal extremes (5% on either side) also had on average
lower imputation accuracy than the remaining SNP. As reference panel size was increased
very little improvement could be observed in imputation accuracy of SNP located in the
center of the chromosome, due to these SNP already being imputed with accuracy close to 1.
However, imputation accuracy of SNP in the chromosome ends improved as reference haplotypes were added to the panel, until reaching accuracy within 0.02 points of the average
63

imputation accuracy of SNP in the remainder of the chromosome for imputation based on a
reference panel containing 1024 haplotypes (Additional ﬁle 2: Figure 3.7).
Although, we did not assess the accuracy of GEBV prediction based on imputed genotypes in this paper, we can use results from dairy cattle breeding that show the promise of
imputed genotypes to predict GEBV. Based on the average imputation accuracy we observed
for Yorkshire pigs and previous results for GEBV prediction based on imputed genotypes
in dairy cattle we could expect that losses in accuracy of GEBV prediction as a result of
genotype imputation will be negligible. Wiggans et al. (2012) and Dassonneville et al. (2011)
reported correlation of GEBV from imputed genotypes (IA ≥ 0.96) with GEBV estimated
from high density genotypes larger than 0.93. Moreover, Weigel et al. (2010a), reported a
loss in accuracy of GEBV, estimated as the correlation between GEBV and direct genomic
value, between 0 and 5% when using genotypes imputed with low accuracy (IA = 0.91).
Since our estimates of imputation accuracy in the Yorkshire population are within the range
of those reported in dairy cattle (Dassonneville et al., 2011; Weigel et al., 2010a,b; Wiggans
et al., 2012), we expect GEBV estimated from imputed genotypes in Yorkshire pigs to be as
accurate as those currently used in the dairy breeding industry. Furthermore, these results
are expected to hold in other swine breeds with similar levels of LD (Badke et al., 2012).

3.5

Conclusion

In conclusion, high (IA ≥ 0.95) genotype imputation accuracy can be achieved in pigs
combining the newly available commercial 9K tagSNP set and a relatively small reference
haplotype panel (128 haplotypes), even when imputation is based only on population-wide
LD. Further improvements in imputation accuracy could be achieved through the inclusion

64

of additional reference animals (IA = 0.97 with 512 reference haplotypes) and the use of
pedigree relations between reference and imputation animals in the imputation algorithm
(Gualdron Duarte et al., 2012; Huang et al., 2012; Wiggans et al., 2012). An important
result from this study is that an eﬃcient design for reference panel construction is randomly
sampling individuals instead of speciﬁcally sampling older animals or trios. In addition, a
relatively small panel of reference haplotypes (≥ 128) can eﬃciently serve as a reference
panel for genotype imputation, such that any available high density genotypes in a livestock
population could potentially serve this purpose. For the pig species such panels are already
available for several populations (Badke et al., 2012). Finally, prospects for the use of
imputed genotypes in GEBV prediction are very positive based on the results from dairy
breeding that routinely use similarly accurately imputed genotypes for genomic evaluation
(Dassonneville et al., 2011; Weigel et al., 2010a; Wiggans et al., 2012). The methodology
used in this paper for construction of tagSNP sets and reference haplotype panels can be
easily applied in any future study population. Code and data to obtain and reproduce
the results presented is publicly available at https://www.msu.edu/~steibelj/JP_files/
imputation.html.

65

3.6

Supplementary Materials

Figure 3.6: Eﬀect of reference panel size on imputation accuracy of SNP as a function of
their MAF
Weighted mean average imputation accuracy (quantiﬁed as R2 ) as a function of MAF
depicted for imputation based on haplotype reference panels of increasing size.

66

Figure 3.7: Eﬀect of reference panel size on imputation accuracy of SNP as a function of
scaled physical location
Weighted mean average imputation accuracy (quantiﬁed as IA) as a function of the scaled
chromosomal location for imputation based on haplotype reference panels of increasing size.

67

Chapter 4
Accuracy of estimation of genomic
breeding values in pigs using low
density genotypes and imputation
Badke, Y. M., Bates, R. O., Ernst, C. W., Fix, J., & Steibel, J. P. (2013). Accuracy of
estimation of genomic breeding values in pigs using low density genotypes and imputation.
submitted to G3

68

4.1

Introduction

Genetic improvement through breeding for lean growth, reproductive performance, meat
quality, and health traits is an important tool in the pig breeding industry to assure its continued competitiveness and success. The use of traditional estimated breeding values (EBV)
derived from pedigree information has lead to important advances in genetic improvement
but has several limitations (Dekkers et al., 2010). A number of important phenotypes, such
as disease resistance or lifetime productivity traits are diﬃcult and expensive to observe or
can only be measured later in life, which impairs the estimation of highly accurate EBV.
Furthermore, EBV estimated from performance records of close relatives are based on the
expected instead of observed proportions of identity by descent between the animals.
The use of genomic breeding values (GEBV), estimated using a large number of genetic
markers across the genome is expected to overcome a number of these limitations (Meuwissen
et al., 2001; Dekkers et al., 2010). Genomic prediction is expected to improve the accuracy of
breeding values, especially for lowly heritable and complex traits and allow for the selection
of animals at a young age thereby shortening generation intervals (Hayes et al., 2009a;
VanRaden et al., 2009; Wiggans et al., 2011). A number of review papers have reported the
progress and success of genomic selection in dairy cattle (Hayes et al., 2009a; VanRaden et al.,
2009; Wiggans et al., 2011), and it is expected to be equally useful in pigs (Tribout et al.,
2012). High density genotypes in pigs can be obtained from the PorcineSNP60 BeadChip
(Illumina, San Diego, CA) containing roughly 62K SNP (Ramos et al., 2009). Previous
research based on this chip has reported on extent of linkage disequilibrium (LD) (Uimari
and Tapio, 2011; Badke et al., 2012), eﬀective population size (Uimari and Tapio, 2011), the
correlation of phase between populations (Badke et al., 2012), and genome wide association

69

studies (GWAS) performed for various traits e.g. boar taint (Duijvesteijn et al., 2010).
First implementations of genomic prediction in pigs included evaluations for total number
of pigs born in a litter and percent stillborn (Cleveland et al., 2010). Results of this study
indicated that GEBV in pigs can reach accuracies comparable to those observed in dairy
cattle if the training population is large enough (Cleveland et al., 2010). In addition, several
strategies to increase cost eﬃciency through the use of low density genotypes have been
explored but accuracy of GEBV was reasonable only for certain traits, likely due to diﬀerences
in the genetic architecture of the traits (Cleveland et al., 2010). However, when genotypes
were imputed with high accuracy results for genomic evaluation were promising for several
traits in a commercial pig population (Cleveland and Hickey, 2013).
The relatively high genotyping cost per animal currently limits the widespread commercial use of high density genotypes for genomic selection purposes in pigs. One strategy to
improve the cost eﬃciency of genotyping schemes is the use of genotype imputation for a
portion of the population. In the interest of cost eﬃciency it is likely that selection candidates will not be genotyped using a high density array such as the PorcineSNP60, but
rather will be genotyped on a low density array like the recently released GeneSeek Genomic
Proﬁler for Porcine LD (GGP-Porcine: GeneSeek Inc., a Neogen Co., Lincoln, NE), a subset of the PorcineSNP60 containing roughly 10K SNP. We showed (Badke et al., 2013) that
genotypes in pigs can be imputed from the GGP-Porcine to the PorcineSNP60 with accuracy
of R2 = 0.88 using LD based imputation algorithms with a reference panel of haplotypes as
small as 128 haplotypes. Imputation accuracy can be further improved by adding animals
to the reference panel (Badke et al., 2013), or in case of a pedigreed population exploiting
Mendelian segregation and population wide LD (Huang et al., 2012; Gualdr´n Duarte et al.,
o
2013). We use genotypes imputed based on population wide LD, oﬀering a strategy that
70

can be applied universally in any population, for which a suitable reference panel can be
assembled.
Our objective was to assess how using imputed instead of observed genotypes would
aﬀect the accuracy of genomic evaluations using an eﬃcient G-BLUP ﬁtting the prediction
equation to the realized genomic relationship matrix (Hayes et al., 2009b). We used two sets
of reference haplotype panels, small (N = 128) or a large (N ∼ 1800), to evaluate how an
increase in imputation accuracy aﬀects the accuracy of genomic predictions.

4.2

Materials & Methods

4.2.1

Materials

4.2.1.1

Animals and Genotypes

Data used in this study was collected from 983 Yorkshire sires. High density genotypes for
these animals were obtained from samples provided by the National Swine Registry (NSR).
Genotyping was performed at a commercial laboratory (GeneSeek, a Neogen Company, Lincoln, NE) using the Illumina PorcineSNP60 BeadChip. The same dataset was previously
used to assess the eﬀect of genotype imputation (Badke et al., 2013) and is publicly available
at:
https://www.msu.edu/~steibelj/JP_files/imputation.html. Animal protocols were approved by the Michigan State University All University Committee on Animal Use and Care
(AUF# 03/09-046-00). Genotyping rate of at least 90% of both animals and SNP and a
minor allele frequency of at least 5% were required for genotypes to be included in the analysis, leaving a total of 41248 markers in 983 animals. SNP that were not assigned to an

71

autosomal position in map build 10.2 were excluded from the analysis. It was our goal to
estimate the genomic breeding value (GEBV) of male oﬀspring of a sire and since sires will
not pass an X chromosome to their male oﬀspring, these SNP do not contribute to the sons
GEBV (VanRaden et al., 2009). In addition to genotypes for 983 Yorkshire sires, a set of
128 Yorkshire haplotypes was available as a reference panel for genotype imputation from a
previous study (Badke et al., 2012). These haplotypes are also freely available at
https://www.msu.edu/~steibelj/JP_files/LD_estimate.html and details on the design
and phasing can be found in Badke et al. (2012).

4.2.1.2

Phenotypes

For every animal and their parents, estimated breeding values (EBV) and accuracies were
obtained for three traits from NSR through their traditional genetic evaluation. These
traits were: backfat thickness (BF), number of days to 250lb (D250), and loin muscle area
(LEA). Descriptive statistics of EBV and accuracies are presented in Table 4.1. All code
and data used in this paper has been assembled into an R package, accessible at: http:
//tinyurl.com/MSURGEBV.

4.2.2

Methods

4.2.2.1

De-regression of breeding values

De-regressed breeding values (dEBV) were used as response variables throughout the analysis. We computed individual animal dEBV and their weights (wi ) with the parent average
removed following the procedure outlined by Garrick et al. (2009). After de-regression and
ﬁltering a total of 965, 936, and 938 animals remained for the traits BF, D250, and LEA

72

respectively (Table 4.1).
Table 4.1: Descriptive statistics of EBV
BF

D250

LEA

¯
EBV

-0.03

4.57

0.61

rEBV ×
¯2

0.74

0.67

0.75

N

965

936

938

h2

0.45

0.26

0.47

× average reliability of EBV
number of animals with usable EBV
4.2.2.2

Estimation of genomic relationship matrix

The genomic relationship matrix was estimated from observed or imputed high density (∼
41K) SNP genotypes. Genotypes were expressed as allelic dosage, which is the number of
copies of the minor allele, such that genotypes were entered into a marker matrix M as a
decimal number in the interval [0, 2]. We obtained matrix Z by subtracting twice the allelic
frequency of the minor allele (pi ), from columns of M (VanRaden, 2008). The genomic
relationship matrix was then calculated as:

ZZ

G=
2

where 2

M p (1 − p )
i
i=1 i

(4.1)

M p (1 − p ) is a normalizing constant (Wang et al., 2012) summing expected
i
i=1 i

variances across markers scaling G towards the numerator relationship matrix (VanRaden,
2008). The allele frequency pi was obtained using all available animals (N=983). Average
relatedness between animals was obtained from the row/column vectors of G. We quantiﬁed
relatedness in this study as the average of the top 10 relationships observed within the G

73

matrix (rel10).

4.2.2.3

Implementation of prediction model

Using the genomic relationship matrix from equation (4.1) an animal-centric model for genomic evaluations can be written as:

y = 1n µ + a + e

(4.2)

where y is the vector of dEBV, µ is the overall mean, a is the vector of n animal eﬀects
2
2
(a ∼ N (0, Gσa )), and e is a vector of random residuals (e ∼ N (0, Rσe )). The variance of
2
2
the dEBV is var(y) = Gσa + Rσe , where R is a diagonal matrix with diagonal elements
1
Rii = w , the inverse of the weights of the dEBV (VanRaden et al., 2011). Equivalently,
i
the information in G can also be included in the incidence matrix of the animal eﬀects a as
follows (Vazquez et al., 2010):
y = 1n µ + Ca∗ + e

(4.3)

where C is the Cholesky decomposition of G, such that G = CC , µ is the overall mean,
a∗ is the vector of animal eﬀects with a∗ ∼ N (0, Iσ 2∗ ) noticing that a = Ca∗ , and e is a
a
2
2
2
vector of residual eﬀects e ∼ N (0, Rσe ) such that var(y) = CC σ 2∗ + Rσe = Gσ 2∗ + Rσe .
a
a
The variance terms for models (4.2) and (4.3) are equal, such that the two models are in
fact equivalent if variance components are assumed known. Likewise, when estimating the
parameters under these two models we found virtually identical results, but model (4.3) was
computationally more eﬃcient resulting in a two fold reduction in compute time (results not
shown). The BLR package (P´rez et al., 2010) in R (Team, 2011) was used to ﬁt the mixed
e
2
2
model equations. Model parameters σe and σa∗ were sampled from their corresponding full
74

conditional distribution using a Gibbs sampler. Prior distributions were elicited based on
2
2
equations presented by P´rez et al. (2010). The prior distribution of σe and σa∗ were an
e
inverse χ2 distribution with degrees of freedom df and scale S. To ensure proper priors with
ﬁnite expectations we set df = 3. The scale parameters were obtained as a function of the
df and assuming values of the genetic variance (Va ) and error variance (Ve ) (P´rez et al.,
e
2010):
2
σe ∼ χ−2 (dfe = 3, Se = Ve (dfe + 2))
2
σa∗ ∼ χ−2 (dfa = 3, Sa =

Va (dfa + 2)
)
¯
Aii

¯
where Aii , is the average inbreeding coeﬃcient, set equal to 1 in this case, assuming no
inbreeding. Heritability was assumed to be h2 = 0.5, such that after the value for Ve was
2
arbitrarily set to 0.4, Va was estimated Va = Ve h 2 . The Gibbs sampler implemented in
1−h
BLR (P´rez et al., 2010) was used to obtain a total of 100,000 samples, 10,000 of which were
e
2 2
discarded as burn-in. The reported estimates of σe , σa∗ , animal eﬀects (a∗ ), and GEBV
(ˆ) were based on the posterior means of the remaining 90,000 iterations. We assessed
y
convergence of the MCMC chain as well as sensitivity to priors to ensure robustness of
estimates to priors (results not shown).

4.2.3

Genomic prediction under cross-validation

Accuracy of genomic evaluation was estimated in a 10 fold cross-validation design. Approximately 10 % of the animals were randomly assigned to a validation panel (V ) in which
predictions would be made, while the remaining 90% were used as the training panel (T )
to estimate the parameters necessary for prediction. A total of 10 separate datasets were
created such that each animal would be used for validation once. Across cross-validation
75

datasets we ﬁt model (4.3) to the training animals, we refer to that subset by adding a
subindex T :
yT = 1nT µ + CT a∗ + eT
T

(4.4)

to estimate the BLUP of ˆ∗ (VanRaden et al., 2011):
aT
σ2
ˆ
ˆ∗ = CT (GT + RT e )−1 (yT − 1nT µ)
aT
2
σa

(4.5)

where the matrices G and C are partitioned into block structure such that








GT
GT V





GT V   CT


=


GV
CT V



0   CT


CV



0





CT V   CT CT


=


CT V CT
CV

CT CT V
CT V CT V + CV CV
(4.6)

The relation between the BLUP for a based on model (4.2) and ˆ∗ based on model (4.3)
a
can be expressed as:








aT 

aV







=





CT
CT V

0 


CV



a∗
T
a∗
V







(4.7)

The genomic breeding value of training animals in model (4.2) were computed as:
σ2
σ2
ˆT = CT ˆ∗ = CT CT (GT +RT e )−1 (yT −1nT µ) = GT (GT +RT e )−1 (yT −1nT µ)
a
aT
ˆ
ˆ
2
2
σa
σa
Subsequently, the genomic breeding values of the validation animals ˆV were estimated from
a
ˆT using the following equation:
a
σ2
ˆV = GT V G−1 ˆT = CT V CT (GT + RT e )−1 (yT − 1nT µ)
a
a
ˆ
T
2
σa

76

(4.8)






2 2
ˆ
where σe , σa , and µ are estimated using model (4.4) which is equivalent to applying model
(4.3) to the training animals.

4.2.3.1

Estimation of accuracy

Accuracy of genomic evaluation is the correlation between the estimated GEBV and the
unknown true breeding values (TBV) (Hayes et al., 2009a). However, the TBV are unknown.
Consequently, the accuracy of genomic evaluation has to be approximated using the available
information. Hayes et al. (2009a) proposed to express the correlation between GEBV and
TBV as a function of the correlation between GEBV and EBV:

cor(GEBV, EBV )
cor(GEBV, EBV )
=
r(GEBV,T BV ) =
cor(EBV, T BV )
2
rEBV

(4.9)

2
2
where rEBV is the estimated reliability of the EBV. VanRaden et al. (2009) replaced rEBV
with the arithmetic mean of the reliability of the EBV. Daetwyler et al. (2013) proposed to
report a simple Pearson correlation coeﬃcient between GEBV and EBV to allow for comparability of results across studies. We estimate accuracy of genomic evaluation as the Pearson
correlation coeﬃcient between GEBV and EBV (r(GEBV,EBV ) ) and the Pearson correlation coeﬃcient adjusted for the average accuracy of the EBV to facilitate such comparison
r(GEBV,EBV )
(
).
rEBV
¯
Accuracies of individual GEBV were obtained analogous to the accuracy of EBV in
an animal model (Goddard et al., 2011) through inversion of the mixed model equations
(Mrode, 2005; VanRaden, 2008; VanRaden et al., 2009; Strand´n and Garrick, 2009; Clark
e
et al., 2012). The accuracy of ˆ of the model (4.2) can be expressed as (Mrode, 2005;
a

77

Strand´n and Garrick, 2009; Clark et al., 2012):
e

ra =
ˆ

2
1 − (P EV /σa )

(4.10)

where P EV is the prediction error variance of ˆ:
a

ˆ
P EV = var(a − a) = (R−1

1
1
+ G−1 )−1
2
2
σe
σa

(4.11)

2
and σa is the genetic variance such that:

2
var(a) = Gσa

(4.12)

Strand´n and Garrick (2009) showed, that ra for all animals can be obtained from the
e
ˆ
diagonals of:

ra =
ˆ

σ2
G(G + R e )−1 G
2
σa
ii
{G}ii

(4.13)

and VanRaden (2008) showed that the accuracy of GEBV of the validation animals can be
obtained from the diagonals of:

rˆ =
aV

σ2
GT V (GT + RT e )−1 GT V
2
σa
ii
GV
ii

(4.14)

This equation was used to estimate the accuracy of individual GEBV for validation animals.

78

4.2.3.2

Genotype imputation

Linkage disequilibrium (LD) based genotype imputation was performed with BEAGLE version 3.3.1 (Browning and Browning, 2009). We used the standard settings for BEAGLE:
ten iterations of the phasing algorithm, drawing four samples per iteration. Previous results
from our group (Badke et al., 2013) and other studies (Hayes et al., 2012) showed negligible
improvement in imputation accuracy as a result of an increase in iterations or samples per
iteration.
A matrix of ‘observed’ genotypes was created by imputing randomly missing genotypes
in the 983 Yorkshire sires (≤ 0.05%) supplementing the data with a reference panel of
128 Yorkshire haplotypes to improve imputation accuracy. Due to the small (≤ 0.05%)
percentage of randomly missing genotypes we expected accuracy of imputation very close
to 100%, and consequently treated these genotypes as ‘observed’ genotypes for all further
analysis.
We implemented two separate imputation experiments, which diﬀer in the size of the high
density reference panel used for imputation: 1) a reference panel of 128 Yorkshire haplotypes
or 2) a reference panel combining the 128 Yorkshire haplotypes with the haplotypes of all
animals that are part of the training panel (∼ 1700 additional haplotypes) in the respective
cross-validation dataset. To assess the eﬀect of genotype imputation on genomic prediction we considered the following four scenarios: 1) the reference scenario where genomic
evaluation was based on observed genotypes in training and validation animals, 2) genomic
evaluation based on observed genotypes in the training animals and genotypes imputed from
a large reference panel (∼ 1800 haplotypes) in the validation animals, 3) genomic evaluation
based on observed genotypes in the training animals and genotypes imputed from a small

79

reference panel (128 haplotypes) in the validation animals, and 4) genomic evaluation based
on imputed genotypes in training and validation animals using a small (128 haplotypes)
but representative reference panel for imputation. All genotype imputation and subsequent
estimation of imputation accuracy was implemented using the R package impute.R (Badke
et al., 2013). To compare average accuracy of genomic evaluation across these four scenarios
we ﬁtted a linear model with the average accuracy of genomic evaluation as response variable and the genotype imputation scenario as independent variable, adding the eﬀect of the
random cross-validation dataset in which accuracy of genomic evaluation was estimated as
a random blocking factor.

4.3
4.3.1

Results
Accuracy of genomic evaluation and GEBV using observed
genotypes

When genotypes were observed in both training and prediction animals, accuracy of genomic
evaluation, measured as the weighted mean of the Pearson correlation coeﬃcient between
EBV and predicted GEBV across 10 cross-validation datasets, was 0.68, 0.66, and 0.65 for
BF, D250, and LEA respectively (Table 4.2). When the measure of accuracy was adjusted for
the average reliability of the EBV of the training animals the observed accuracy of genomic
evaluation was 0.80, 0.82, and 0.76 for BF, D250, and LEA respectively (Table 4.2).

80

Table 4.2: Estimates of accuracy for genomic evaluation and individual GEBV across imputation scenarios
rEBV,GEBV
rEBV
¯

rGEBV
¯

0.7998

0.6852

[0.5395, 0.8211]

0.6795a

0.7981

0.6861

[0.5467, 0.8164]

(1, 0.88)

0.6585b

0.7734

0.6684

[0.5498, 0.7909]

4

(0.88, 0.88)

0.6598b

0.7749

0.7014

[0.5727, 0.8267]

1

(1, 1)

0.6603a

0.8229

0.6575

[0.5073, 0.7948]

2

(1, 0.95)

0.6555ab

0.8170

0.6585

[0.5187, 0.7962]

3

(1, 0.88)

0.6521ab

0.8127

0.6412

[0.5213, 0.7771]

4

(0.88, 0.88)

0.6463b

0.8054

0.6750

[0.5345, 0.7985]

1

(1, 1)

0.6516a

0.7639

0.6859

[0.5386, 0.8325]

2

(1, 0.95)

0.6491a

0.7610

0.6868

[0.5377, 0.8214]

3

(1, 0.88)

0.6278c

0.7360

0.6684

[0.5519, 0.8054]

4

(0.88, 0.88)

0.6364d

0.7461

0.7040

[0.5667, 0.8330]

trait

scenario ×

BF

1

(1, 1)

0.6810a

2

(1, 0.95)

3

D250

LEA

imputation accuracy

rEBV,GEBV

rEBV
¯
0.8510

0.8020

0.8529

HP D

× scenarios 1: no imputation, 2: imputation in prediction panel (R2 = 0.95), 3: imputation in prediction panel (R2 = 0.88),
and 4: imputation in all animals (R2 = 0.95)
2 2
accuracy of genotype imputation R2 for training and validation animals: (RT , RV )
Tukey HSD post-hoc comparison of accuracy of genomic evaluation across imputation scenarios
average accuracy of EBV in the validation panel
95% highest posterior density (HPD) interval of GEBV accuracy across validation animals
81

We observed a signiﬁcant diﬀerence between the estimates of accuracy of genomic evaluation across ten randomly assigned cross-validation datasets for three traits (Table 4.3).
That variation across cross-validation datasets was partially explained by a signiﬁcant eﬀect
of the average EBV accuracy of validation animals on accuracy of genomic evaluation (Table 4.3) in three traits and a signiﬁcant eﬀect of top 10 relatedness on accuracy of genomic
evaluation in D250. Another source of diﬀerence of accuracy of genomic evaluation across
cross-validation datasets could be the population structure. This would be revealed through
diﬀerences in estimated variance components. We did not expected diﬀerences in variance
components estimated from randomly assigned validation datasets. We conﬁrmed this asσ2
sumption by studying the distribution of estimated heritability ( 2 a 2 ) and included the
σa +σe
obtained results in Supplementary Figure 4.3.
Table 4.3: Signiﬁcance of variables aﬀecting accuracy of genomic evaluation
folds ×

rel10

rEBV
¯

p

F †

p

F †

p

258

< 0.001

2.83

0.1013

11.73

0.0016

D250

229

< 0.001

5.18

0.0291

7.238

0.0109

LEA

311

< 0.001

2.06

0.1605

3.430

0.0725

trait

F

BF

× accuracy of genomic evaluation by randomly assigned folds of the cross-validation
accuracy of genomic evaluation by average of the top 10 genomic relationship estimates of
animals in the validation set
accuracy of genomic evaluation by average accuracy of EBV of validation animals by fold
df = c(9, 27)
† df = c(1, 35)
The average accuracy of the genomic evaluation and the assessment of the accuracy of
individual GEBV using equation 4.14 is equally important in a practical implementation of

82

genomic selection. Average accuracy of individual GEBV was 0.69, 0.66, and 0.69 for BF,
D250, and LEA respectively with a 95% highest posterior density (HPD) interval ranging
from roughly 0.51 to 0.80 across all traits (Table 4.2).
As can be seen in Figure 4.1 accuracy of GEBV (rGEBV ) and accuracy of EBV (rEBV )
are not linearly related. accuracy of GEBV (rGEBV ) and accuracy of EBV (rEBV ) are
not linearly related. Accuracy of EBV was higher than the estimated accuracy of GEBV for
most animals in three traits, especially when rEBV > 0.8. For a few animals with rEBV
between 0.4 and 0.8 accuracy of GEBV was higher than their respective EBV accuracy. We
observed there was an almost linear increase (Figure 4.2) in rGEBV as top 10 relatedness
increased, which we found was statistically signiﬁcant (p < 0.01).

83

Figure 4.1: Accuracy of GEBV by observed accuracy of EBV for a) BF, b) D250, and c) LEA
rGEBV in relation to the animals rEBV , with the 1-1 line of the regression (green line) and a loess smoother (red line), which
is a local weighted mean of the rGEBV

84

Figure 4.2: Accuracy of GEBV by average top 10 relatedness between the individual and training panel for (A) BF, (B) D250,
and (C) LEA
rGEBV in relation to the animals rel10, a loess smoother (red line), which is a local weighted mean of the rGEBV

85

4.3.2

Eﬀect of genotype imputation on accuracy of genomic evaluation and GEBV

Accuracy of imputation (R2 ) for each animal was measured as the squared correlation between the observed and imputed allelic dosage across all SNP (Badke et al., 2013). Average
accuracy of imputation was R2 = 0.88 for the ﬁrst scenario using a small (128) haplotype
reference panel, and it increased to R2 = 0.95, when a larger reference panel (∼ 1800 haplotypes) was utilized. In our previous study (Badke et al., 2013) we found that increasing
the size of the reference panel led to an improved imputation especially of SNP that appear
diﬃcult to impute, such as SNP with low (≤ 0.1) MAF and those located in the chromosomal
extremes. These results were replicated in this study (Supplementary Figure 4.4).
For BF we found that the average accuracy of genomic evaluation under scenario 2
(rGEBV,EBV = 0.6795), where genotypes in the validation animals were imputed with
high accuracy (R2 = 0.95), was not signiﬁcantly diﬀerent from the accuracy observed in the
reference scenario (rGEBV,EBV = 0.681), where all genotypes were observed. However
average accuracy of genomic evaluation was signiﬁcantly lower (rGEBV,EBV = 0.6585,
rGEBV,EBV = 0.6598), when genotypes were imputed with lower accuracy (R2 = 0.88)
when using a small reference panel of haplotypes (scenarios 3 & 4). For D250 there was
no signiﬁcant diﬀerence in accuracy of genomic evaluation between the reference design
(rGEBV,EBV = 0.6603) and the two scenarios where genotypes were imputed in the validation animals (Table 2). However, when genotypes were imputed in both training and validation (scenario 4) accuracy of genomic selection was signiﬁcantly lower (rGEBV,EBV =
0.6463). For LEA there was also no diﬀerence in accuracy of genomic evaluation between
the reference scenario (rGEBV,EBV = 0.6516) and scenario 2 (rGEBV,EBV = 0.6491).

86

There was a signiﬁcant decrease in accuracy of genomic evaluation when genotypes were
imputed with lower accuracy (R2 = 0.88) in scenarios 3 (rGEBV,EBV = 0.6278) and 4
(rGEBV,EBV = 0.6364).
To assess the eﬀect of genotype imputation on the results of a genomic evaluation we
compared the top 5% sires (n = 46), ranked by their estimated GEBV across imputation
scenarios. Again, scenario 1 was used as a reference design to compare how many of the
top 5% ranked animals were also top ranked under the imputation scenarios (2-4). The
proportion of top 5% ranked sires that were conserved when genotypes were imputed in
validation animals with high accuracy (scenario 2) was 0.96 for BF and 0.98 for D250 and
LEA. When genotypes were imputed in validation animals with lower accuracy (scenario 3)
the proportion of top 5% ranked sires decreased to 0.86, 0.92, and 0.87 for BF, D250, and
LEA respectively. When genotypes were imputed in training and validation the proportion
of top 5% sires conserved in comparison to the reference design showed a small increase
compared to the design with only validation animals imputed for BF (0.88), a small decrease
for D250 (0.89), and a more substantial decrease for LEA (0.81).
Accuracy of individual GEBV is estimated using the genomic relatedness between training and validation animals. Using genotypes imputed with high accuracy (R2 = 0.95) the
estimated rGEBV remained constant in all traits, compared to estimates obtained from
observed genotypes. When genotypes were imputed with less accuracy (R2 = 0.88) rGEBV
slightly decreased. However, when the genomic relationship matrix was obtained from imputed genotypes in both training and prediction animals (R2 = 0.88) the observed accuracy
of GEBV was higher than even the reference scenario across traits. Examining the estimation procedure for rGEBV we found that this diﬀerence was due to smaller estimates of
the diagonal elements of the genomic relationship matrix between the validation elements
87

(GV ) in the scenario with all imputed genotypes. These diagonal elements were used to
scale values of rGEBV (equation 4.14), and smaller values in the denominator resulted in
the larger estimates of rGEBV we saw for animals in scenario 4. Comparing unscaled values
of rGEBV individual accuracy was higher in the reference scenario for all animals.

4.4
4.4.1

Discussion
Accuracy of genomic evaluation and GEBV using observed
genotypes

The size of the training population used to train the prediction equation in this study was
small compared to previous genomic evaluations published in swine (Cleveland et al., 2010,
2012), and especially compared to studies applying genomic evaluation in European (Dassonneville et al., 2011) or US dairy cattle (Weigel et al., 2010a; Wiggans et al., 2012). Observed
accuracy of genomic evaluation in this study was in good agreement with previously published results for genomic evaluation in pigs, assessing ﬁve unspeciﬁed commercial traits
with comparable heritability (Cleveland et al., 2012) and earlier results for two reproductive
traits (Cleveland et al., 2010). Accuracy of genomic evaluation was high across three traits
(BF: rGEBV = 0.6810 D250: rGEBV = 0.6603, LEA: rGEBV = 0.6516). In addition,
we report accuracy adjusted for the fact that the Pearson correlation between EBV and
GEBV will underestimate the true quantity of interest (Luan et al., 2009). Assessing the
variation in accuracy of genomic evaluation across datasets of the cross-validation, we found
that the rEBV of the validation animals and their relatedness to the training animals were
¯
signiﬁcantly associated to the average accuracy of genomic evaluation. Higher accuracy of

88

genomic evaluation of prediction animals with close relatives in the training population (Habier et al., 2010; Clark et al., 2012) and within closely related populations, with relatively
small eﬀective population size, has been previously reported (Daetwyler et al., 2013). Accuracy of genomic evaluation in this study was high in spite of the limited number of animals
available for training and the inclusion of animals with relatively low EBV accuracy. Furthermore, we obtained accurate genomic predictions using an equivalent model ﬁtting the
genomic relationship matrix instead of a marker based matrix (Hayes et al., 2009b), thereby
greatly reducing the computational load. We expect that accuracy of genomic evaluation in
this population, and other US swine populations with comparable population structure and
LD (Badke et al., 2012), will be feasible for commercial implementation and could be further
increased through the inclusion of additional training animals with highly accurate EBV.
Besides assessing the accuracy of genomic evaluation we also reported accuracies for individual GEBV. The accuracy of GEBV will be important to inﬂuence selection decisions, but
as proposed by Goddard et al. (2011), can also be approximated prior to the implementation
of genomic evaluation and used to inform the design of genomic selection in a population. As
expected, we observed that accuracy of GEBV increased with increased relatedness between
the animal and the training panel. Several previous studies in other populations and simulation experiments also showed the importance of relatedness for the prediction of accurate
GEBV (Habier et al., 2010; Clark et al., 2012), especially when the training population was
small (Wientjes et al., 2013) as was the case in our study. In addition, we observed that accuracy of GEBV was higher than accuracy of EBV for only a few animals that had mostly low
accuracy of EBV. This ﬁnding is further supported by previous reports that implementation
of genomic evaluation would be most beneﬁcial for young animals with little information on
their own and subsequently low accuracy of traditional EBV (VanRaden, 2008).
89

4.4.2

Eﬀect of genotype imputation on accuracy of genomic evaluation and GEBV

Genotype imputation is an eﬃcient tool to decrease the cost of obtaining high density genotypes for selection candidates. It was the goal of this study to quantify the loss on accuracy
of genomic evaluation if GEBV were estimated from imputed rather than observed genotypes
in selection candidates. Comparing accuracy of genomic evaluation across four scenarios of
genotype imputation we found that for three traits there was no signiﬁcant diﬀerence between genomic evaluation as a function of genotypes in validation animals being observed
or imputed with high accuracy (R2 = 0.95). Accuracy of genomic evaluation decreased in
comparison to the reference scenario when genotypes in selection candidates were imputed
with lower overall accuracy (R2 = 0.88). Especially when imputation was applied in training
and prediction animals we observed a decrease in accuracy of genomic evaluation, such that
while this would be the most cost eﬃcient scenario, it would not be feasible as practical
implementation to obtain maximally accurate results of genomic evaluation. Accuracy of
genotype imputation is a function of the SNP density, the size of the reference panel, the
level of LD between adjacent SNP, and the SNP chromosomal location and MAF (Badke
et al., 2013). Combined with the results from this study that a minimum accuracy of imputed genotypes was necessary to conserve accuracy of genomic evaluation, these variables
can be used to design an optimally cost eﬃcient scheme of genomic selection with genotype
imputation in a population without any current use of molecular markers to estimate genetic
merit. Once genomic selection has been successfully implemented, the constant inﬂux of additional animals with high density genotypes and accurate EBV will only serve to increase
the accuracy of both imputation and subsequent genomic evaluation. Previously published

90

results support that while it is not feasibly to implement genomic prediction based on low
density genotypes (Habier et al., 2009; Cleveland et al., 2010), even if SNP were preselected
for association with the phenotype, accuracy of genomic evaluation is still feasible for practical implementation when genotypes in selection candidates are accurately imputed to high
density (Weigel et al., 2010a; Cleveland and Hickey, 2013). In addition, several studies also
support that an increase in imputation accuracy will facilitate results of genomic evaluation
nearly indistinguishable from those obtained from observed genotypes (Dassonneville et al.,
2011; Wiggans et al., 2012; Cleveland and Hickey, 2013) while the cost eﬃciency of low
density genotypes allows a much larger proportion of the population to be included in the
genomic evaluation procedure (Wiggans et al., 2012). In conclusion, an implementation of
genomic selection based on observed genotypes for training of the prediction equation and
GEBV predictions obtained from genotypes imputed with high accuracy appears to be a
promising approach to provide the swine breeding industry with a cost eﬃcient procedure to
obtain GEBV for animals at a young age. A recent study assessing the accuracy of genomic
evaluation using high density genotypes and various imputation schemes in a commercial
pig population further supports these ﬁndings (Cleveland and Hickey, 2013).
We found that accuracy of individual GEBV was a linear function of the relatedness
between a validation animal and the respective training set. As has been previously shown
in the literature, animals that are highly related to the training population will have higher
rGEBV (Habier et al., 2010; Clark et al., 2012). For scenarios with observed genotypes used
in training animals the average rGEBV was in good agreement with the overall accuracy
of genomic evaluation. However, when genotypes were imputed in training and prediction
animals, the average rGEBV was notably larger than the accuracy of genomic evaluation,
which we found was an artifact of lower estimates of the diagonal elements of the G matrix.
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This was caused by a decrease in the variance of the allelic dosage of imputed genotypes
due to the relatively small number of reference haplotypes available. When the variance of
imputed allelic dosages was decreased, the deviation from the expected value estimated from
MAF (2p) also decreased, causing overall smaller estimates of Z and the resulting diagonal
elements of the G matrix. This increase in the homogeneity of allelic dosages in the imputed
genotypes causes the observed inﬂation in accuracy of estimated GEBV, such that in any
case when GEBV are obtained from imputed genotypes the estimated accuracy of GEBV
should be used with caution. The average GEBV accuracy notably exceeded the expected
accuracy of genomic evaluation in that scenario.
In conclusion, we found that results for accuracy of GEBV further support the notion that
genomic evaluation using high density genotypes imputed with high accuracy for selection
candidates is a feasible method to implement a cost eﬃcient design for genomic selection
in swine. When genotypes were imputed with lower accuracy in training and prediction
animals accuracy of genomic evaluation was signiﬁcantly decreased and estimates of accuracy
of GEBV were inﬂated. As mentioned before, all code and data used in this paper has been
made available through an R package, accessible at: http://tinyurl.com/MSURGEBV

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4.5

Supplementary Materials

Figure 4.3: Distribution of genomic heritability across 10 folds for a) BF, b) D250, and c) LEA

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Figure 4.4: Average accuracy of genotype imputation for imputation from a small (blue) or large (red) reference panel as a
function of (A) chromosomal location of SNP and (B) MAF

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Chapter 5
General Discussion
Genomic selection is a valuable tool to genetically improve livestock and plant species
(Daetwyler et al., 2013). Direct use of genome wide marker information allows for accurate selection of superior animals for breeding at a very young age, even if the phenotype
under selection is diﬃcult to measure (Daetwyler et al., 2013). Furthermore, results from
dairy cattle breeding show that implementation of genomic selection can shorten generation
intervals while increasing the rate of genetic gain (VanRaden et al., 2009). Through the
availability of the PorcineSNP60 BeadChip (Ramos et al., 2009) implementation of genomic
selection for swine breeding has become a probable development (Cleveland and Hickey,
2013). It was the objective of this dissertation to assess variables aﬀecting accuracy and
cost eﬃciency of genomic selection programs in four US pure-breed pig populations. We
intended to show how genomic selection could be optimally implemented meeting the swine
breeding industry’s requirements of high prediction accuracy and cost eﬃciency. In addition, we released computer algorithms and data to facilitate further research in these speciﬁc
populations and allow researchers working with other species to implement a similar set of
steps to investigate the usability and optimal design of genomic prediction.

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5.1

Objectives revisited and their impact on genomic
selection in swine breeding

1. Estimate LD and in the Duroc, Hampshire, Landrace and Yorkshire pig breeds using SNP genotypes obtained using the Illumina PorcineSNP60 Genotyping BeadChip.
Determine persistence of phase between breeds to assess the potential of mixed breed
reference panels for both imputation and genomic selection in the future.
LD describes the non-random association between gametes at diﬀerent loci across the genome.
High genome wide pair-wise estimates of LD are an important precursor for genome wide
association studies (GWAS) and accurate genomic prediction. The level of LD in pigs was
previously measured using low density markers (Du et al., 2007; Harmegnies et al., 2006;
Nsengimana et al., 2004), but our study of LD in four US pig breeds (Badke et al., 2012) was
among the ﬁrst to report genome wide levels of LD using a high density SNP panel (Jafarikia
et al., 2010; Uimari and Tapio, 2011). Indicative of a relatively small eﬀective population
size we found average LD of approximately 0.4 for markers within 100kb of each other, and
0.2 when average distance between SNP was 1 Mb. Due to these relatively high estimates
of pairwise LD, even at increasing distance we projected that implementation of genomic
selection has the potential to achieve accuracy of prediction comparable to that observed in
dairy cattle populations. We based this projection on the fact that pairwise LD between
SNP is an important prerequisite for accurate prediction (i. e. Hayes et al., 2009a), and
that LD in these pig breeds was higher than reported estimates for dairy cattle populations
(de Roos et al., 2008). Since persistence of LD at increasing distances was high, genotype
imputation from a more cost eﬃcient low density SNP panel should be considered in the
design of a genomic selection scheme.
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Implementation of genomic selection requires a large sample of training individuals with
highly accurate EBV to estimate SNP eﬀects. Especially in small populations obtaining
a large number of adequate training animals is often cost-prohibitive. Combining training
animals across populations to reduce cost has previously been proposed and is based on the
assumption that the extent and phase of LD, and the eﬀect of the QTL are conserved across
populations. We obtained estimates of correlation of phase, as a measure of persistence of
phase, for all pairwise comparisons among four US pig breeds. Our results suggest, that
persistence of phase between Duroc, Landrace, Hampshire, and Yorkshire is not suﬃcient to
support the hypothesis that combining any of these populations to train a prediction equation for genomic selection would be beneﬁcial. Persistence of phase will generally increase
with increasing marker density, such that this recommendation should be reevaluated as the
density of the available SNP chip increases (Goddard et al., 2006). In conclusion, we found
promising levels of genome wide LD in these pig populations, but implementation of genomic
selection should remain breed speciﬁc as marker phase is not suﬃciently conserved at the
current marker density.
2. Assess tagSNP selection strategies to obtain maximally informative subsets of tagSNP
that eﬀectively span the genome for each breed. In addition, report on imputation
accuracy of the recently released GeneSeek Genomic Proﬁler for Porcine LD (GGPPorcine, GeneSeek a Neogen Company, Lincoln, NE), a commercially available 10K
tagSNP panel.
Although results presented in the previous chapter indicate that genome wide LD is suﬃcient
to support the expectation of accurate genomic prediction, implementation based on high
density SNP remained unlikely due to cost concerns. A common approach to decrease
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genotyping costs used in human (i. e. Howie et al., 2011), plant (Hickey et al., 2012), and
animal research (i.e. Wiggans et al., 2012) is genotype imputation. Accuracy of genotype
imputation depends on the eﬀective size of the population, the size and composition of
the reference panel (Howie et al., 2011; Hayes et al., 2012), the proportion of tagSNP, the
location and MAF of untyped SNP (Badke et al., 2013; Hickey et al., 2012), and the type
of information used for imputation (Marchini and Howie, 2008). To establish a baseline for
imputation accuracy, we applied a population LD based imputation algorithm, mimicking
the case of a population with no pedigree available. In case linkage information is available
and utilized imputation accuracy is expected to further increase (Huang et al., 2012). Low
density SNP panels (tagSNP) selected exploiting population wide LD generally outperformed
tagSNP set selected for even spacing along the genome. However, if pairwise LD is exploited
the resulting panels are population speciﬁc. Therefore, when the GGP-Porcine was released
parallel to our eﬀorts of tagSNP selection, we decided to refocus our attention and assess
genotype imputation accuracy based on this commercially available 10K platform.
Imputation accuracy (IA), measured as the proportion of correctly imputed alleles, was
high (0.95) when imputation was based on the GGP Porcine and a small reference panel
of 128 haplotypes. Relatedness to the reference panel had a positive impact on accuracy
of imputation even if it was not directly exploited through the imputation algorithm. SNP
within the chromosomal extremes or low MAF had on average lower accuracy of imputation
(Badke et al., 2013; Hickey et al., 2012). Increased density of tagSNP in the chromosomal
extremes was implemented to improve imputation accuracy of SNP located in these areas.
In the GGP Porcine tagSNP density is approximately doubled in the 10% extreme locations.
Secondly, increasing the size of the reference population did increase overall accuracy of
imputation, but especially imputation accuracy of SNP with low MAF or those located in
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the chromosomal extremes beneﬁted from adding haplotypes. In our population an ideal
number of reference haplotypes to ranged between 1000-1200, beyond which any increase in
accuracy was marginal. This information can be utilized to optimize the allocation of funds
available to implement genomic selection between genotyping reference animals, genotyping
of selection candidates at low density, and phenotype collection. In conclusion, genotype
imputation from the commercially available GGP-Porcine is suﬃciently high (IA = 0.95) to
expect that genomic prediction obtained from imputed genotypes will suﬀer only marginal
losses in accuracy compared to those obtained from observed genotypes. The design of
the GGP Porcine (Curtis P. Van Tassell, SNPSpace), selecting tagSNP evenly covering
the genome with maximal MAF to ensure segregation, can serve as an example for other
populations. Our results on individual and SNP speciﬁc accuracy can be used to design an
optimal reference panel of haplotypes and select individuals for imputation who are expected
to yield imputed genotypes with high accuracy.
3. Perform GEBV prediction for economically important production traits using high
density SNP genotypes for the Yorkshire breed, as well as genotypes imputed from the
GGP-Porcine. We assessed the loss in accuracy when genotypes in selection candidates
were obtained through a more cost eﬃcient low density panel (GPP-Porcine) instead
of observed high density genotypes (PorcineSNP60).
Results from chapters 2 and 3 indicated that genomic selection in the Yorkshire pig population has the potential to be highly accurate, even if genotypes in selection candidates
are imputed. We implemented a ten-fold cross validation study to assess the accuracy of
genomic evaluation from observed genotypes, and the loss in accuracy of genomic evaluation
if genotypes were imputed. Genomic selection was implemented using a computationally
99

eﬃcient animal model, and accuracy of individual GEBV was calculated through inversion
of the mixed model equations. As expected, we found that accuracy of genomic evaluation
for three traits (back-fat thickness, loin muscle area, and # days till 250lb) were in good
agreement with the few available results from pig populations (Cleveland et al., 2010, 2012)
and mimicked previously observed accuracies for various dairy cattle traits (Dassonneville
et al., 2011). Higher relatedness between the training animals and the validation animals
had a positive impact on the observed accuracy, as did higher average accuracy of EBV in
the validation animals. We implemented three separate imputation scenarios: 1. genotypes
were imputed in the validation animals using ∼ 1800 reference haplotypes, 2. genotypes
were imputed in the validation animals using 128 reference haplotypes, and 3. genotypes
were imputed in all animals using 128 reference haplotypes. Accuracy of imputation was
assessed as the squared correlation (R2 ) between observed and imputed genotypes. The
ﬁrst imputation scenario had the highest observed accuracy of imputation (0.95), which was
expected due to the larger number of reference haplotypes. Genomic evaluation based on
these genotypes did not show any signiﬁcant diﬀerence from the reference design without
imputation in any of the traits. The second and third scenario had slightly lower accuracy
of imputation (0.88) and as a result a decrease in accuracy of genomic evaluation compared
to the reference design was observed in all three traits. However, while the average accuracy
of genomic selection was decreased when genotypes were imputed in all animals, estimates
for individual GEBV accuracy were inﬂated in this scenario. As a result we would not recommend using genotypes imputed in all animals for genomic selection in pig breeding. In
conclusion, we were able to replicate previous results from pig (Cleveland and Hickey, 2013)
and dairy cattle breeding (Dassonneville et al., 2011; Weigel et al., 2010a; Wiggans et al.,
2012), reporting that genomic evaluation based on highly accurate imputed genotypes in
100

selection candidates is a cost eﬃcient and equally accurate alternative to genomic evaluation
based on observed high density genotypes.

5.2

Future Directions

In chapter 2 we exploited haplotypes to estimate LD and persistence of LD across four breeds
of US pigs. We focused on levels of LD to assess the future potential of low density genotypes in these populations for genotype imputation and genomic selection. Alternatively,
available haplotypes could be exploited for breed identiﬁcation and quantiﬁcation of breed
purity. Using high density genotypes to estimate breed composition could replace cost and
time consuming mating experiments to determine an animals purebred status. Recent results from our group (Huang et al., 2013) were successful in predicting an animals breed
composition using regression models, and identifying potentially non-purebred or crossbred
animals that should be further evaluated. The animals identiﬁed as non-purebred were
partially identical with a group of animals that had consistently low imputation accuracy
in chapter 3, implicating that this method was in fact able to identify individuals with a
distinct haplotype structure. However, for roughly half these animals diﬀerences in their
haplotype structure was not the result of cross-breeding, instead they were imported from
an unrelated population of the same breed. Further research is necessary to separate this
eﬀect of breed composition vs. population of origin, and further validate the ability of high
density genotypes to reliable predict recent cross-breeding events in an animals pedigree.
Especially, it would be interesting to assess the eﬀect of combining diﬀerent populations of
the same breed to be used as a reference for breed composition predictions (e. g. Finnish
populations used in Uimari and Tapio, 2011). Another issues with using high density geno-

101

types to predict breed purity is admixture between breeds. In chapter 2, using short-range
persistence of phase we approximated time since breed divergence between four US pig populations to be between 40 and 60 generations, with white breeds having diverged from each
other more recently (40). However, long-range persistence of phase between all four breeds
is larger than the expected value based on the approximated time of breed divergence, possibly due to more recent admixture between the populations. Using high density genotypes
to obtain regression estimates of breed composition will likely reﬂect these past cross-over
events between populations. This creates the need for thresholds of signiﬁcance to be established indicating whether an individual’s divergence from its assigned breed is large enough
to necessitate further testing to assess the animals pure-bred status. To assess the ability of haplotypes obtained from high density genotypes to predict breed purity within and
across populations of the same breed a panel of reference haplotypes could be assembled.
Many populations, especially in commercial settings, will have haplotypes available from
previous research. Our results for reference panel design in chapter 3 suggest that in these
pig populations haplotypes from randomly sampled animals will not be at a disadvantage
compared to more complex sampling designs involving sire/dam/oﬀspring trios or maximally
unrelated individuals provided a large (N ≥ 100) sample is assembled. As a result, using
available resources with minimal collection of additional genotypes from populations with
no previous genotyping should result in a usable reference panel for breed composition prediction. Validation animals to assess the accuracy of breed composition predictions with
known cross-bred ancestry will be necessary. Especially commercial settings, where crossbreeding is commonly implemented to obtain market pigs could provide validation animals
with genotypes already available.
In chapter 3 we estimated imputation accuracy from low (GGP Porcine) to high (Porci102

neSNP60) density SNP arrays. Advances in genotyping technology caused a signiﬁcant
decrease of the cost associated with sequencing, such that whole genome sequence is a likely
future source of data. Hayes et al. (2009a) noted that accuracy of genomic selection is a
function of the LD between the observed SNP and the QTL, such that accuracy can be
increased through an increase in marker density. If genomic selection is based on sequence,
prediction is no longer limited by the extent of LD between marker and causative polymorphism, as the later would be directly observed. As a result, accuracy of genomic selection
based on whole genome sequence is expected to be superior compared to results obtained
from high density SNP (Druet et al., 2013; Meuwissen and Goddard, 2010). In addition,
the currently observed decay in prediction accuracy observed over generations is expected to
signiﬁcantly decrease when causative polymorphism are directly observed (Meuwissen et al.,
2013). Results from simulation experiments indicate that a 5-10% increase in accuracy of
genomic evaluation can be expected through the use of sequence data (Druet et al., 2013;
Meuwissen and Goddard, 2010), which needs to be further validated in real data. This
advantage appeared especially pronounced for QTL with low allele frequency (Druet et al.,
2013). Inclusion of whole genome sequence will result in a data structure including animals
with low, high, and sequence density SNP, such that genotype imputation will continue to be
an important tool of genomic analysis. Current implementation of genotype imputation in
livestock populations is mainly based on reference panels of haplotypes sampled from within
the population (Badke et al., 2013; Hayes et al., 2012; Wiggans et al., 2011). Accuracy of imputation from population speciﬁc reference panels appears to be superior to mixed reference
panels at the current marker density and persistence of phase between populations (de Roos
et al., 2009). However, due to the cost of whole genome sequence, whole-sequence reference
haplotypes will likely be sampled across populations, such that the resulting panels will be
103

highly admixed (e .g http://www.1000bullgenomes.com/). Genotype imputation in human populations has shown that imputation in admixed populations from diverse reference
haplotypes can be highly accurate (Howie et al., 2009, 2011). In particular, a subroutine
implemented in Impute v2 sampling reference haplotypes based on a euclidean distance for
each imputation sample, thereby assembling a reference panel of ‘related’ haplotypes was
highly successful (Howie et al., 2011). Diﬀerently from human populations eﬀective population size in most livestock species is small and detailed pedigrees are available. As a result
across population reference panels can be assembled combining representative samples of
highly inﬂuential individuals (Druet et al., 2013) from each sub-population, and combining
pedigree information, such that whole sequence imputation can be based on both linkage
and LD information (e. g. AlphaImpute Hickey et al., 2011).
An initial study investigating the use of whole genome sequence for genomic research in
pigs should aim to address the following issues:
1. Optimal strategy for assembling a reference panel of haplotypes at sequence density.
Sequencing coverage is an important variable aﬀecting the certainty with which heterozygotes
can be called (Druet et al., 2013). However, higher coverage will also lead to a substantial
increase in cost, such that the relation between the number of animals and minimal coverage
should be optimized to allow for a maximal sample size of accurately called haplotypes. Chen
et al. (2013) introduce a design that allows for increased variant detection and genotype
calling even at low coverage through the use of trios instead of unrelated individuals. Using
simulated data, emulating human populations, they found that 30 trios would outperform
90 unrelated individuals in numbers of variants detected for low coverage (1x-2x), but the
eﬀect was reversed as fold coverage increased to 8x (Chen et al., 2013). They attributed this

104

diﬀerence to the additional familial information available to resolve variants and genotypes at
low coverage in trios (Chen et al., 2013). In chapter 3 we compared reference haplotype panels
consistent of haplotypes derived from a trio design to cost equivalent haplotypes obtained
from unrelated individuals (Ntrio = 64, Nunrelated = 96) and found an advantage in
imputation accuracy using trio based panels as reference only for extremely small reference
panels (N ≤ 32/48). Similarly, this advantage of the trio design when the number of reference
haplotypes was very small is likely a result of the increased phasing accuracy that can be
obtained from a trio design (Marchini et al., 2006). Implementing the concepts of Chen
et al. (2013) and expanding them include other close relatives to increase the number of
variants detected and genotypes called could aid the assembly of whole sequence reference
haplotypes. Exploiting the availability of detailed pedigrees and overall high relatedness
between animals in livestock populations has the potential to facilitate accurate reference
panels derived from cost eﬃcient low coverage whole genome sequence.
2. Implementation of genotype imputation and assessment of strategies to optimally exploit admixed reference haplotype panels.
Accuracy of imputation within a population can be maximized through the combined use of
pedigree (linkage) and LD information (Hickey et al., 2011). However, as we expect reference
panels for sequence imputation to be highly admixed, a shared pedigree may not be available
or very limited, such that direct exploitation of linkage may prove diﬃcult. Implementation
of algorithms such as Impute that internally assemble a reference panel of ‘related’ individuals
(Howie et al., 2011) may be better suited to exploit admixed reference panels of haplotypes.
One approach to optimize overall accuracy could be an initial imputation based on the
few within population reference haplotypes using a combined linkage and LD algorithm.
105

The results of that imputation are then followed by a secondary imputation focusing on
haplotypes that could not be resolved with appropriate certainty using the admixed reference
panel and an algorithm establishing indirect relationships between individuals. In addition,
variables aﬀecting accuracy of imputation such as sequence coverage, MAF, marker location,
and size of the reference panel of haplotypes for high density to sequence imputation should
be assessed.
3. Assess the gain in accuracy of genomic evaluation if prediction is based on whole
genome sequence (imputed) compared to high density SNP.
Simulation studies have projected between 5-10% gain in accuracy (Meuwissen and Goddard,
2010) of genomic evaluation. However, a study by VanRaden et al. (2011) using simulated
ultra high density SNP for genomic prediction in comparison to the widely implemented 50K
SNP panel found only a small gain in accuracy as a function of increased marker density.
They concluded that the size of the training population had a greater impact on improving
prediction accuracy than the tested increase in marker density (VanRaden et al., 2011). In
chapter 4 we evaluated the accuracy of genomic evaluation in a US Yorkshire population using
a training population of approximately 850 animals per fold. Observed signiﬁcant diﬀerences
in accuracy between folds of the cross-validation could indicate that this sample-size was not
large enough to obtain eﬀects invariant of the current sample. Therefore, a simulation study
using the available pedigree and high density genotypes as a basis to obtain realistic ultra
high density genotypes (Hickey and Gorjanc, 2012) could be used to compare the eﬀect of
increased training panel size vs. an increase in marker density in this population. The
possible beneﬁts of genomic evaluation based on whole genome sequence should be weighted
against the additional costs collection of sequence data would incur.

106

4. Assess the potential gain of using whole genome sequence for GWAS
GWAS based on sequence data has the potential to directly identify causative polymorphisms. This would enable research to focus on understanding the molecular processes involved, instead of focusing on potential candidate genes within a QTL region. However, the
number of parallel tests would further increase, such that an even larger reference population
is likely necessary to provide enough power to allow detection of causative polymorphisms.

Many of these issues could be initially addressed in a simulation study using the genotype data and pedigree available from this research to inform the simulation design, using
e. g. the program presented by Hickey and Gorjanc (2012). In addition, if whole genome
sequence is already available for some animals the approach presented in Macleod et al.
(2013) that was utilized by Druet et al. (2013) to implement a simulation with similar objectives in cattle could further reﬁne the design. Previous results in our own research (not
published) clearly indicate that simple simulation based on the estimated past and current
eﬀective population size using a gene-drop model (Sargolzaei and Schenkel, 2009) will likely
lead to a pattern of LD that poorly represents real data, such that results cannot be extrapolated to real data examples. High density genotypes are currently publicly available for
four US pig populations (Badke et al., 2012) and a US commercial population (Cleveland
et al., 2012), while many more research projects have also collected high density genotypes
on various pig-breeds worldwide (e. g. Uimari and Tapio, 2011). In addition, a thorough
pedigree is available for the Yorkshire population utilized in this research. Initial eﬀorts
are underway to collect whole genome sequence on a few select animals in Europe (Martien
Groenen, presentation). Collecting and combining this data should provide a solid base to

107

obtain a simulated dataset that is an adequate representation of whole genome sequence
data in swine breeds. The diversity and size of the available data would allow the formation
of a ’simulation training panel’, used to estimate within and across population structure of
LD, time since divergence, as well as size of the ancestral population, and the formation of a
’simulation validation panel’, to which the obtained simulated data could be compared. To
assess the practicality of this design a smaller initial simulation based on solely the Yorkshire
data could use the estimates of r2 from chapter 2 to determine an approximate size of the ancestral population and use the available pedigree to obtain simulated high density genotypes
(Hickey and Gorjanc, 2012). Subsequently, the LD structure within the simulated genotypes, as well as persistence of phase with the observed data of Hampshire, Landrace, and
Duroc can be estimated to assess similarity between the simulated and observed genotypes.
Phenotypes can be simulated based on a varying number of QTL that will be randomly
assigned to markers simulated above. The corresponding substitution eﬀects of QTL could
be sampled from a t-distribution and phenotypes obtained by summing the respective QTL
eﬀect and adding random residuals sampled from a normal distribution. The data released
as part of this study contains EBV, dEBV, and heritabilities for three economically important traits in swine. The heritabilities as well as distribution of EBV can be used to inform
the choice of parameters for the simulation of phenotypes with the goal of mimicking the
structure of actual traits. Furthermore, an initial GWAS performed on these traits could
provide an estimate of the number of QTL with large and medium eﬀects likely aﬀecting
each trait, providing a basis for these parameters as well. Obtaining a simulated data set
reﬂective of the diversity and real structure of future data is important to ensure that results
can be extrapolated to the real data case and used to inform investment decisions for future
research.
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In conclusion, the results presented in this dissertation can directly inform design decisions
for the implementation of genomic evaluation in the US Yorkshire pure-bred population utilized. Furthermore, due to the similarity of LD structure between the four breeds assessed in
chapter 2 we expect estimates of imputation accuracy of and accuracy of genomic evaluation
to be similar, once large enough samples of high density genotypes can be assembled, for
Landrace, Hampshire, and Duroc. Public availability of all data collected and computer
code written for this research facilitates the translation of the methods and design to other
populations. Combining the haplotypes of these four US pure-bred swine populations with
genotypes of other swine populations can facilitate a more detailed assessment of admixture
between populations and breed composition for individual animals. Also, the data can be
used as outlined above to inform simulation studies that will be able to allow a ﬁrst assessment of the usability of whole genome sequence data for genomic evaluation, especially with
genotype imputation, and genome wide association studies.

109

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