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Quantitative Genetics and
Animal Breeding in the Age of
Bruce Walsh
Classical Quantitative Genetics
• Quantitative genetics deals with the observed variation in a
trait both within and between populations
• Basic model (Fisher 1918): The phenotype (z) is the sum
of (unseen) genetic (g) and environmental values (e)
• z=g+e
• The genetic value needs to be further decomposed into an
additive part A passed for parent to offspring, separate
from dominance (D) and epistatic effects (I) that are only
fully passed along in clones
• g =A+ D + I
• Var(g)/Var(z) is quantitative measure of nature vs. nurture
– fraction of all trait variation due to genetic differences
Fisher’s great insight: Phenotypic covariances between
relatives can estimate the variances of g, e, etc.
• For example, in the simplest settings,
– Cov(parent,offspring) = Var(A)/2
– Cov(Full sibs) = Var(A)/2 + Var(D)/4
– Cov(clones) = Var(g) = Var(A)+Var(D)+Var(I)
• Random-effects model
• Thus, in classical quantitative genetics, a few statistical
descriptors describe the underlying complex genetics
– This leaves an uneasy feeling among most of my molecular
– Does the age of genomics usher in the death knell of Quantitative
“Classical” Animal Breeding
• Using the records (phenotypes) of individuals from a
known (often very complex) pedigree, estimates for the
breeding values (A) for individuals are obtained
– This is usually done using the machinery of BLUP -- best linear
unbiased predictor.
– To do this, we also have to estimate Var(A), typically this is done
using REML -- restricted (or residual) maximum likelihood
• Predicted value of offspring from two parents is the
average of the parental breeding values
• How will genomics alter this classical approach?
Approximate costs of genome projects
• Arabidopsis Genome Project
... $500 million
• Drosophila Genome Project
... $1 billion
• Human Genome Project
... $10 billion
• Working knowledge of multivariate statistics
... Priceless
Neoclassical Quantitative Genetics
• Use information from both an individual’s phenotype (z)
and marker genotype (m)
• z = u + Gm + g + e
– Gm is genotypic value associated with the scored genotype (m )
– Obvious extensions: include Gm x e and Gm x g
• Mixed model: can treat as the Gm as fixed effects; g and
e as random
• My molecular colleagues hope that Gm accounts for most
of the variance in the trait
– If true, then Var(g)/Var(z) trivial
Neoclassical Animal Breeding
• Selection decisions are based on some weighted index of
phenotype and genetic marker information
• Base selection on an index, I = a E(BV) + b Gm
– MAS = marker assisted selection
• The larger the amount of phenotypic variance accounted
for by the genetic marker information (Gm), the more
selection is directly on the genotypes (i.e., much more
weight on G than on the expected breeding value).
Limitations on Gm
• The importance of particular genotypes may be quite fleeting
– can easily change as populations evolve and as the biotic and abiotic
environments change
– If epistasis and/or genotype-environment interactions are significant,
any particular genotype may be a good, but not exceptional, predictor
of phenotype
• Quantitative genetics provides the machinery necessary for
managing all this uncertainty in the face of some knowledge of
important genotypes
– e.g., proper accounting of correlations between relatives in the
unmeasured genetic values (g)
Limitations with MAS
• Tradeoff between increased short-term response under
MAS vs. decreased short-term response compared with
phenotypic selection.
– Reduced selection on phenotype
– Reduction in effective population size
• MAS may not be cost-effective compared to phenotypic
• Optimal setting for MAS
– Genes of major effect (e.g., scrapie (prion) resistance)
– Sex-limited expression
– Traits difficult/expensive to score directly (i.e., carcass traits)
How do we obtain Gm?
• Ideally, we screen a number of candidate loci
• QTL (Quantitative trait locus) mapping
• Uses molecular markers to follow which chromosome
segments are common between individuals
This allows construction of a likelihood function, e.g.,
` ( z j š ; æ2A ; æ2A § ; æ2e ) = p
exp ° (z ° š ) T V ° 1 (z ° š )
(2º ) n jV j
Estimated QTL ef f ect
Background genetic eff ects
Estimated from marker inf ormation
R ij =
V = R æ2A + A æ2A § + I æ2e
Know n f rom pedigree relationships
for i = j
for i =
6 j
A ij =
2£ i j
for i = j
for i =
6 j
A typical QTL map from a likelihood analysis
Estimated QTL location
Support interval
Genomics and candidate loci
• Typical QTL confidence interval 20-50 cM
• The big question: how do we find suitable
• The hope is that a genomic sequence will suggest
Genomics tools to probe for candidates
• Dense marker maps
• Complete genome sequence
– Expression data (microarrays)
– Proteomics
– Metablomics
The accelerating pace of genomics
• Faster and cheaper sequencing
• Rapid screening of thousands of loci via DNA
• Phylogenetic bootstrapping from model systems to
distant relatives
Prediction of Candidate Genes
• Try homologous candidates from other species
• Examine all Open Reading Frames (ORFs) within a QTL
confidence interval
– Expression array analysis of these ORFs
– Lack of tissue-specific expression does not exclude a gene
• Proteomics
– Specific protein motifs may provide functional clues
• Cracking the regulatory code (in silico genetics)
Searching for Natural Variation
• This may be the area where genomics has the largest
• Source (natural and/or weakly domesticated) populations
contain more variation than the current highly
domesticated lines
• Key is to first detect and localize importance variants, then
introgress them into elite lines
The impact of other biotechnologies
• Cloning, other reproductive technologies
Maintain elite lines as cell cultures?
Trans-species maintenance of tissue cultures
Embryo transplantation into elite maternal lines?
Creation of permanently heterotic lines
• Transgenics
– Important tool in both breeding and evolutionary biology
• Complications:
– Silencing of multiple copies in some species
– Strong position effects
– Currently restricted to major genes
• Major genes can have deleterious effects on other characters
• Importance of quantitative genetics for selecting for background
polygenic modifiers
Useful Tools for Quantitative Genetic analysis
• Four subfields of Quantitative Genetics
Plant breeding
Animal breeding (forest genetics)
Evolutionary Genetics
Human Genetics
• Restricted communications between fields
• Important tools often unknown outside a field
Tools from Plant Breeding
• Special features dealt with by plant breeders
– Diversity of mating systems (esp. selfing)
– Sessile individuals
• Issues
Creation and selection of inbred lines
Hybridization between lines
Genotype x Environment interactions
• Plant breeding tools useful in Animal Breeding
– Field-plot designs
– G x E analysis models: AMMI and biplots
• These designs are also excellent candidates for the analysis of
microarray expression data
– Covariance between inbred relatives
– Line cross analysis
Animal Breeding
• Special features
Complex pedigrees
Large half-sib (more rarely full-sib) families
Long life spans
Overlapping generations
• Tree breeders face many of these same issues
• Animal breeding tools useful in other fields
– BLUP (best linear unbiased predictors) for genotypic values
– REML (restricted maximum likelihood) for variance components
• BLUP/REML allow for arbitrary pedigrees, very complex models
– Maternal effects designs
• Endosperm work of Shaw and Waser
– Selection response in structured populations
Evolutionary Genetics
• Issues
– Estimating the nature and amount of selection
– Population-genetic models of evolution
• Tools
– Estimation of the nature of natural selection on any specified
• Lande-Arnold fitness estimation; cubic splines
– Using DNA sequences to detect selection on a locus
• Example: teosinte-branched 1
– Coalescent theory
• The genealogy of DNA sequences within a random sample
– Analysis of finite-locus and non-Gaussian models of selection
• Barton and Turelli; Burger
Human Genetics
• Issues
– Very small family sizes
– Lack of controlled mating designs
• Tools of potential use
– Sib-pair approaches for QTL mapping
• QTL mapping in populations
– Transmission-disequilibrium test (TDT)
• Account for population structure
– Linkage-disequilibrium mapping
• Use historical recombinations to fine-map genes
– Random-effects models for QTL mapping
• BLUP/REML-type analysis over arbitrary pedigrees
• Genomics will increase, not decrease, the importance of
quantitative genetics
• The machinery of classical quantitative genetics is easily
modified to account for massive advances in genomics and
other fields of biotechonology
• Useful and powerful tools have been developed to address
specific issues in the various subfields of quantitative
• The future of animal breeding is a natural fusion of
genomic information into an expanded quantitativegenetics framework, exploiting advances in reproductive