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Department of Animal Sciences
Quantitative Genetics and
Animal Breeding
Lecture notes for ANSC 241
Prof
...
A
...
Kahi
May 2013
Egerton University
TABLE OF CONTENTS
TABLE OF CONTENTS
2
TOPICS WITHIN LECTURES
3
GLOSSARY OF TERMS
6
1
...
QUANTITATIVE GENETICS - INTRODUCTION
12
3
...
PREDICTING BREEDING VALUE: HERITABILITY
24
5
...
REPEATABILITY, GENOTYPE X ENVIRONMENTAL INTERACTION, DATA CORRECTION
38
7
GENETIC CORRELATION AND INDIRECT SELECTION
44
8
GENETIC RELATIONSHIPS AND RESEMBLANCE AMONG RELATIVES
47
9
PARAMETER ESTIMATION
53
10
USE OF INFORMATION FROM RELATIVES
61
11
GENETIC CHANGE OF MULTIPLE TRAITS
70
12
BEST LINEAR UNBIASED PREDICTION – BLUP
77
13
INBREEDING
87
14
RESULTS FROM SELECTION PROGRAMS
95
15
CROSSBREEDING – PART 1
98
16
CROSSBREEDING- PART 2
...
D
...
Falconer and T
...
C
...
1996
...
Fourth
Edition
...
2
...
C
...
Weller, J
...
Economic aspects of animal breeding
...
4
...
1997
...
Sinauer
...
This is a guide to
course objectives and not what is likely to appear in an exam! With few exceptions an
understanding of these things can be demonstrated using words and no algebra
...
1) Introduction
n
Objectives of animal breeding
n
Some basic concepts/definitions in animal breeding
2) Introduction to the role of quantitative genetics in animal breeding
...
n
Objectives in animal breeding, how does it fit in production systems
...
n
Selection and crossbreeding are the two main quantitative genetics "tools"
...
The concept of breeding value
...
n
Assumptions in Hardy Weinberg equilibrium
...
n
The additivity of Breeding value
...
4) Variation in components of merit; predicting breeding value; heritability
...
n
P=G+E=A+D+E
n
The covariance between Breeding value and Phenotype is the variance of Breeding value
...
n
Considering effects as deviations from means
...
n
The regression of offspring on mean of parents is heritability
...
n
The factors which affect response (R) to selection, and the significance of each of these
...
n
The definition of generation interval
...
n
The effect of generation interval on annual response (Ryr) to selection
...
n
The relationship between intensity of selection and generation interval
...
n
Repeatability defines an upper limit to heritability
...
n
The effect of repeated measurement on response to selection
...
The effect of this on response to
selection
...
n
Correlations: rA, rE and rP
...
n
The factors that affect correlated responses to selection
...
8) Genetic relationships and Resemblance
...
n
A method of calculating rA and rD between relatives
...
n
The significance of each factor that contributes to variance of observed half sib and full
sib family means
...
n
The analysis of variance approach to estimating repeatability and heritability
...
n
Use of regression to estimate heritability
...
(A comprehensive understanding of this is not necessary)
...
10) Use of information from relatives
...
n
The conditions which favour each of the first three of thesen
The superiority of family index selection over each of the first three
...
n
Factors that affect the heritability of the progeny test
...
n
Factors which affect the efficiency of (response under) progeny testing
...
n
Response and correlated response
n
The use of information from a correlated trait
n
The concept of a selection index as an overall se1ection criterion
...
n
Selection for multiple traits: multiple trait objective
n
Objectives and criteria can involve different traits
...
12) Introduction to BLUP
...
n
It can handle unbalanced structure, environmental effects, non-random mating and
selection bias
...
n
It can separate environmental and genetic trends over time
...
13) Inbreeding
...
n
The definition of inbreeding and inbreeding coefficient
...
n
Consequences of inbreeding
n
F can be calculated from knowledge of breeding population size
...
14) Results from selection programs, reliability of predictions, causes of deviations
...
n
Systematic factors that cause deviations from predicted responses
...
15) Selection between populations, crossing populations, genetic basis of heterosis
...
n
Heterosis is an observable phenomenon, not a mechanism
...
You should
understand the biological significance of these in simple terms
...
n
Calculating expected expression of heterosis from breed-of- origin heterozygosity
...
n
Predicting the genetic merit of different crossing systems given suitable parameters
...
n
The main factors which affect choice of crossing system
...
n
The structures and properties of open and closed nucleus sytems
...
n
The role of A
...
18) Breeding objectives and the state of the art in each animal industry
...
n
Breeding programs should be subject to cost-benefit scrutiny
...
n
A basic 'knowledge of the breeding structures, objectives and criteria and use of
quantitative genetics in the wool, meat sheep, beef, dairy, pig and poultry industries
...
n
Molecular genetic markers (eg
...
n
These have led to the recent development of linkage maps for most domestic species
...
n
The use of QTLs in Marker Assisted Selection
5
GLOSSARY OF TERMS
This glossary summarizes the symbols most frequently used in quantitative genetics
...
Vx
σx
P
A
E
D
G
S
i
h2
r
R
CR
L
bxy
rA
rP
HS
FS
aij
rIA
(T)BV
EBV
BLUP
Fx
Ne
F1 (F2)
QTL
Variance of x (also σ2 or var(x))
Standard deviation of x (note: var(x)=σ2x)
Phenotypic Value
Vp=Phenotypic var
...
VA=Add
...
Var
Additive genetic value
Environmental value
VE=Environm
...
(often used for 'residual effect': sum of
every thing which is not breeding value)
Dominance deviation
VD=Dominance Var
...
Var
...
Environm
...
(True) Breeding Value
Estimated Breeding Value
Best Linear Unbiased Prediction
Inbreeding coefficient of individual x
Effective population size
First (second) cross
Quantitative Trait Locus
6
1
...
As populations increase, and economic status of people improves, they
tend to shift towards a diet based on more animal products
...
- Faster growth rates of broiler chickens
- Improved egg quality in layers
- Good quality beef / meats from younger animals with improved carcass characteristics
- Increased milk production (better quality of milk etc)
- Great improvement in the pig industry
This pattern is expected to continue
...
With finite resources and an increasingly vulnerable environment, it is critically important
that growth in efficiency, rather than in numbers should be the dominant factor in the
doubling of output of livestock products expected
...
Increasing efficiency of production is essential for:
- Economic and physical sustainability of different farming systems
- The long term reduction in the cost of food
Biotechnology
Definition: The application of biological knowledge to practical needs
...
It is an age of great
promise
...
n
Much current research in reproduction has been focused on cattle because of greater
commercial opportunities
...
n
Potential benefits from biotechnology are however global!
Biotechnology offers the prospect of new increments in efficiency of livestock production
...
Technologies for altering reproduction—eg Artificial insemination, embryo transfer
7
and sex control
2
...
DNA fingerprinting, marker assisted selection, gene transfer
...
One needs to take account of the costs of each new technology—both current
and future cost considerations are important
...
A population can be
defined as a group of intermating individuals
...
To be able to improve a
population, two basic tools are usually applied by animal breeders: Selection and Mating
...
Selection can be defined as the process that determines which individuals become parents,
how many offspring they may produce, and how long they remain in the breeding population
...
In mating, one decides which of the selected males will be bred to which females that have
been selected
...
For example in commercial poultry
and pig production there is a clear division between seedstock and commercial sectors, hence
it is common to find breeders of pure-bred seedstock
...
Selection and mating are interdependent--animals are selected first, then mated to produce
offspring that comprise the next generation
...
Some basic concepts/definition in animal breeding and genetics
Simply inherited and polygenic traits
A simply inherited trait is a trait that is affected by only a few genes e
...
Coat colour and
presence of horn
...
Second, the traits are affected
very little by the environment
...
8
A polygenic trait is a trait affected by many genes, no single gene having an overriding
influence
...
Such traits are generally numerically measured-eg
...
Note:
The distinction between genes concerned with Simply inherited traits and metric traits lies in
the magnitude of their effects relative to other sources of variation
...
A gene whose effect is not large enough to cause discontinuity cannot be studied
individually
...
There are however no fundamental differences between genes
...
However, very different breeding approaches are taken to improve simply inherited and
polygenic traits
...
The more the genes affecting a trait, the more difficult it is to observe the effects of individual
genes, and thus the less specific information we have about those genes
...
Population genetics
The study of the factors that affect gene and genotypic frequencies in a population
comprises the branch of genetics known as population genetics
Causes of genetic change in a population
1
...
The gene frequencies are subject to "sampling variation"
between successive generations
...
2
...
Different genotypes among newly formed zygotes
may have different survival rates, hence gene frequencies in the new generation may
change
...
Mutation
...
4
...
The movement of individuals between populations
...
5
...
Continuous variation
Generally, we are dealing with variation in a population—not variation in an individual
...
For example,
why does milk yield vary?
9
Single gene characters constitute a small part of the naturally occurring variation in living
organisms
...
Differences in height or weight are a matter of degree and are rarely clear cut as if
attributable to a single gene
...
Genetic principles underlying the inheritance of metric characters are basically those of
population genetics, but since we cannot follow the effect of a single gene, new methods and
concepts are needed
...
The challenge for the animal breeder is to improve the mean performance for a trait or a
number of traits, and also try and reduce the variation about the mean
...
Selection results in an increase in the gene frequency of favourable alleles and a
decrease in the frequency of the less favourable alleles
...
Differences in fitness may be associated with the presence or absence of a particular gene in
the individual’s genotype—hence selection will operate
...
Different types of gene action—eg dominance/ recessive genes will also affect the rate at
which selection can cause a change in a population
...
The proportion of the population that suffers genetic death is called the Load
borne by the population
...
Load is
particularly felt in populations of species with a low reproductive rate---eg Human population,
or cattle populations, relative to Drosophila population
...
The aim is to try
and select replacements that have the best sets of genes that suit the particular environment
...
However,
when dealing with metric characters, the effects of changes in individual gene frequencies are
hidden
...
The response to selection (R) is the difference in mean phenotypic value between the selected
parents and that of the complete parental generation before selection
...
10
Response can seldom be measured with accuracy until several generations of selection have
been carried out
...
Note:
The “trend” lines are usually variable and can have a positive or negative slope depending on
the trait in question
...
Genetic drift (due to small populations)
2
...
Differences in the selection differential
4
...
Maternal effects
...
QUANTITATIVE GENETICS - INTRODUCTION
Genetic resources constitute the engines of food production systems:
IN
OUT
Grass
Meat
Fences
Fibre
Labour
Milk
Climate
Bread
Quantitative Genetics-is the science of exploiting natural genetic variation to give
genetic improvement of quantitative or metric traits
...
In addition, this course encompasses introduction to:
Animal breeding theory
With special consideration to animal and
plant biology and population structures
...
Molecular genetics
OVERVIEW OF LECTURES 1-45
These lectures cover Quantitative Genetics and Animal Breeding theory
...
Understanding is more important than
knowledge
...
The aim is to
improve traits of commercial importance
...
The objective is to find animals with
the best breeding values for this overall score
...
25 x Body Weight
KSh/kg
...
+
KSh/kg
...
The economic value of improving fleece weight on sheep by 1kg is at KSh 10 (per animal )
and economic value of one unit fibre diameter has a cost of KSh 2
...
For example
...
13
The following diagram shows the likely effect of animal size on gross food conversion
efficiency: The line for the small genotype shows that when we give more food to an animal,
it gains weight
...
With selective breeding, we change the genetic makeup of animals, and the line for
the large genotype has the same shape but is moved upwards
...
In addition, they have higher
birth weight
...
There are similar pitfalls for other traits,
especially reproductive traits, and these must be carefully considered
...
"
-Charles Darwin c 1859
...
It
is not the fleece on the back of rams which interest us so much as the genes they have to
make their progeny grow good fleeces
...
14
Phenotype
SYMBOL
P
MEANING
Observed merit
Genetic value
G
Value of genes to SELF
Breeding value
A
Value of genes to PROGENY
Dominance value
D
Difference between G and A
Environmental value
E
'LUCK'
TERM
The main aim of selection is to predict the breeding values
...
For example, notice the simple averaging for Kg milk
yield:
ANIMAL
'Bert' 'Daisy' Offspring prediction
...
We can do this by regressing P values towards
the mean:
n
An exceptionally good animal can be good for two reasons: Good environment (E) or
good genes (A+D)
15
n
Part of this elephant's high P is due to good E and D, so we estimate his A to be
somewhere between his P and the population mean
...
Again, we want to predict A (Genotype), but we see only P (Phenotype)
...
In other words: for an observed difference in P (difference between two animals) the
regression (slope of the line) tells us what the expected genetic difference will be
...
Note that the concept of breeding value estimation, i
...
regression of breeding value on
observed performance, can be extended to many traits
...
The
optimum weights depend on the objective, and on what has been measured
...
Any set of measurement can be
used to aim at any declared objective
...
EXAMPLE OBJECTIVES(A's in KSh) Breeding
Objective
10FW(Fleece weight)
10FW - 2FD(Fibre diam
...
Rate)
Ditto
2(carcass wt) +
...
6FW -
...
2FW -
...
0FW -
...
3(body weight) + 3(back fat)
16
Overview of Crossbreeding
Example, Yearling weight in cattle:
Mean yearling weight of progeny
Breed of cow
1
1
294
2
309
2
304
279
Breed of bull
Hterosis
= (Mean of crosses) - (Mean of pures)
=
306
...
5 = 20Kg
...
This helps gives the basis for choosing which crossing system
to adopt in a given situation
...
Reduce maternal costs-
Large bulls over small cow give reduced maternal costs in
relation to cost of growing stock
...
They are cheap to buy in and this might help
drive Kenya's meat sheep crossing structure
...
GENETIC COMPONENTS OF MERIT
This chapter considers:
How genes are transmitted to the next generation
How useful an individual's genes are to its progeny
...
Consider a single locus with two alleles segregating
...
Genotype
A 1A 1
A 1A 2
A 2A 2
Frequency
P
H
Q
∑=1
Freq(A1)
P
½H
-
=p
Freq(A2)
-
½H
Q
=q
∑= 1
Diploid
To
Haploid
and assuming Hardy-Weinberg Equilibrium we can predict genotype frequencies from allele
frequencies
...
1
...
Equal fertility of genotype
3
...
Random mating of animals
5
...
and 2
...
MESSAGE
Genotype:
A 1A 1
A 1A 2
A 2A 2
Frequency:
p²
2pq
q²
is assumed hereafter
Whereas Population Genetics is concerned with the fitness of different genes (i
...
their
likelihood of surviving and increasing in frequency over generations), quantitative genetics is
concerned with the merit of different genotypes (i
...
their value to as in agricultural terms)
...
7):
Single Locus Model Of Genotypic Merit
The object of this section is to illustrate:
-
The concept of Genetic value - the value of an animal's genes to itself
...
-
The concept of Breeding value - the value of an animal's genes to its progeny
...
For illustration assume
genotype A1A1 to have the greatest merit, and genotype A1A2 to be better than the average of
the two homozygotes-i
...
showing some dominance
...
8]
Genetic value G:
[=gx,y – 315
...
64
G1,1
+4
...
32
G1,2
-5
...
04
G2,2
-35
...
g1,1 +2pq
...
g2,2 =315
...
G1,1 +2pq
...
G2,2 = 0kg
Genetic Value And Breeding Value - The Difference
...
Thus the value of its progeny is different from the value of
its genes to itself
Its BREEDING VALUE - the value of its genes to its progeny, depends on the single genes it
can transmit,A1 and A2
...
Its BREEDING VALUE - is thus the sum of average effects of the genes it carries
...
Consider the average effect of gene A1 (or: the effect of a gamete containing A1)
Sperm
A1
Egg
A1
Freq
...
8 x 4
...
2 x -5
...
8
α2 = pG1,2 +qG2,2 = (
...
2) + (
...
2) =-11
...
2 + -11
...
4
BV(A1A2) = α1 + α2 = 2
...
2 = -8
...
8 =+5
...
The breeding value of the heterozygote is always
halfway the two homozygotes, irrespective of dominance or not
...
:
0
...
32
0
...
8
-5
...
2
0
+10
A
+5
...
4
-22
...
8
+3
...
8
0
+10
2
G = Genotype effect
A = Additive effect(= breeding value)
D = Dominance effect
ABSOLUTE VALUES versus DEVIATIONS : G = A = 0
Note that in the above example the mean Genetic value and the mean breeding value both
equal zero
...
Thus all individuals’ value reflect their superiority or inferiority compared to their
contemporaries
...
So from now on:
P=A=D=G=E=0
Note that Dominance deviation (D) is simply difference between G and A
...
e
...
Note
also that breeding value is additive - A12 the average of A11 and A22
...
For example if a ram with a high breeding value is over
randomly selected ewes, his progeny show only half of his breeding value superiority in their
genetic values
...
6 + 0
eg
...
8
G0 =
2
2
where G 0 is the predicted genetic value of offspring (o)
...
In our example, the predicted value of progeny of A1A1 is 5
...
8+315
...
To check this
is easy, by looking at the frequencies and values of the progeny of an A1A1 individual
21
The following illustrates the calculation
...
x
VALUE
A 1A 1
p2
A 1A 1
p2 =
...
8
320
51
...
16
A 1A 2
A 1A 2
pq =
...
6
A 2A 2
q2
A 1A 2
q2 =
...
4
Sum the products of progeny frequencies and values (last column) to give the predicted 318
kg
...
Additive genetic variance (= variance of breeding values): VA = 2pq(α1-α2)2
Dominance Variance
VD = (2pqd)2
Total Genetic Variance
VG = VA+VD
This shows that VA, VD and VG have some basis at the gene level
...
We will consider traits with
continuous variation, and assume that each trait is determined by very many alleles at very
many loci
...
Falconer’s
notation is better for more detailed considerations, but the present notation is sufficient for the
level required here
...
Falconer uses the values
a= half the difference between the homozygotes
d= difference between the heterozygote and the homozygotes means
From this we can derive:
Population mean = a(p-q)+2pqd
Average effect of gene substitution = α = a+d(d-p)
The connection is with Falconer (Table 7
...
PREDICTING BREEDING VALUE: HERITABILITY
Introduction
We may now understand a one locus model, and how differences in merit between genotypes
can occur
...
Traits like hair or eye colour are examples of this
...
In particular for quantitative traits, we usually
observe a continuous variation and the observed values follow a normal distribution
...
The distribution of genetic effects
become normal if traits are influenced by genes at many loci, possibly with more than
two alleles at each locus
...
From genes to distributions
Assume gene frequencies p = q = ½ at all loci, and contributions to genetic value as shown:
A1 A1
1
A1 A2
0
A2 A2
-1
B1B1
1
B1B2
0
B2B2
-1
Example: Single locus model (Locus A)
A1 A2 x A1 A2
Offspring
A1A1 +1
A1A2 0
A1A2 0
A2A2 -1
¼
-1
½
0
¼
1
Example: Two loci model (Loci A and B)
A1A2 B1B2 x A1A2 B1B2
Offspring
A1A1 B1B1
A1A1 B1B2
A1A1 B2B1
A1A1 B2B2
+2
+1
+1
0
A1A2 B1B1
A1A2 B1B2
A1A2 B2B1
A1A2 B2B2
+1
0
0
-1
A2A1 B1B1
A2A1 B1B2
A2A1 B2B1
A2A1 B2B2
24
+1
0
0
-1
A2A2 B1B1
A2A2 B1B2
A2A2 B2B1
A2A2 B2B2
0
-1
-1
-2
As more loci are added, the distribution of genetic values becomes normal
...
It is the square root of variance
...
The variance
describes the spread
...
in words: a phenotype of +100 (say a body weight of 400kg whereas the population mean is
300kg) can be caused by additive genetic effects (+ 90 kg), dominance effects (+40kg) and a
negative environmental effects can of -30kg
...
It is often assumed that the
size of genetic effects is independent of the size of environmental effects
...
It is also likely to be superior in A, D and E
...
26
For example, for a superior phenotype of +100, we expect the additive genetic value to be +25
if 25% of the total variance is due to additive genetic effects
...
At an
individual's level, this may seem a rather crude way to estimate the contributions of the
different effects
...
However, the method works well if we apply it to groups
of animals
...
g
...
The slope of the regression line (the regression coefficient) gives the amount of units the yaxis variable would change per unit of change along the variable along the x axis
...
In statistics, regression coefficient =
Cov(X,Y)
VarX
In our case we are interested in how much difference there would be in breeding value (yaxis) for a given observed phenotypic difference (x-axis)
...
 and P are expressed as deviations from their group means
...
h2 =
Why the square in h2??-Because the correlation between A and P is h(you can prove this for
yourself), and this used to be a more 'popular' parameter
Using Estimated Breeding Values
A + Af
Following the last lecture: G o = m
o for offspring, m for males, f for females
...
EXAMPLE- Yearling weight in beef cattle
Average yearling weight = µ = 300kg
h2=0
...
4 x +40 = +16kg
A + A f +16 + 0
Go = m
=
= +8kg
2
2
Note ‘0’ for random cows
...
28
If he were mated to a top cow, YW = 330Kg……
ˆ
ˆ
A + A f +16+ (
...
NOTE: The predicted value of 314 is an expected value for the offspring
...
There are two causes for this:
1
...
)
E
...
: Mating [A1A1 x A1A2] gives A1A1 or A1A2 progeny - and so chance can play a role here
...
There is environmental variation of 2 types
-The whole progeny mean deviates systematically (droughts, good seasons, e
...
c
...
In estimating breeding values, we have to know the values of heritabilities
...
Heritabilities of quantitative traits are rarely
larger than 50% (see the table on the next page)
...
Some populations are in a more heterogeneous environment, reducing heritability
...
The same trait in different environments may actually act as two traits-e-g
...
3
...
For
example, growth on ad-lib feeding is not regulated by exactly the same genes (i
...
it is not the
same trait) as growth under restricted feeding
...
29
Some Heritability Estimates for Commercial Traits
Species and traits
Beef cattle
Calving interval
Age at puberty
Scrotal circumference
Birth weight
Weaning weight
Post weaning gain
Yearling weight
Yearling hip frame size
Mature weight
Carcass quality grade
Yield grade
Eye cancer
Percent
heritability
Species and trait
Thoroughbred racing
Log of earnings
Time
Pacer: bets time
Trotter
Log earnings
Time
10
40
50
40
30
45
40
40
50
40
30
30
Percentage
heritability
50
15
15
40
30
Milking speed
Mature weight
Excitability
Goats
Milk production
Mohair production
30
20
Horses
Withers height
Pulling power
Riding performance
15
30
30
40
40
40
Face covering
Loin eye area
Carcass fat thickness
Weight of retail
Fibre diameter
55
55
50
50
50
Swine
Litter size
Birth weight
Litter weaning weight
Post weaning Post weaning gain
Back fat probe
20
20
5
10
5
15
30
40
Carcass fat thickness
Loin eye area
Percent lean cuts
45
25
Jumping(earnings)
Dressage (earnings)
Cutting ability
10
10
Sheep
Number born
Birth weight
Weaning weight
Post weaning gain
Mature weight
Fleece weight
30
35
25
45
Egg hatchability
Livability
5
50
25
25
25
25
30
20
10
35
25
40
40
Shank length
Dairy cattle
Services per conception
Birth weight
Milk production
Fat production
Protein
Solids-not-fat
Type score
Teat placement
Mastitis susceptibility
Poultry
Age at sexual mature
Total egg production
Egg weight
Body weight
50
45
45
Adapted from: Scientific farm Animal Production, 1988, Taylor and Bogart, MacMillan
...
RESPONSE TO SELECTION IN A POPULATION
Last lecture: From individual parents predict progeny merit
- estimate breeding values of each parent
- average these to predict progeny superiority
This chapter: From selection policy predict progeny merit
- predict phenotypic superiority of selected parents
- predicts superiority of progeny generation
...
To predict the genetic change, or the response to selection, it is
critical to know how much of the selection differential (i
...
the superiority of the selected
parents) is transmitted to the next generation
...
We can draw again a regression line, and the slope this line
indicates how much of a given difference in parents is found back in the progeny of those
parents
...
All parents pair higher
than a pre-defined truncation point T are selected, and the mean of the selected group of
parent pairs equal to S (S for selection superiority, S is a deviation from the population mean)
...
S
...
1
...
or
Heritability is the efficiency of transmission of parental superiority to the next generation
...
and the mean of the progeny will be:
R = Response to selection = Offspring mean superiority over no-selection policy
...
The overall selection differential is
Regressed by heritability to predict
Response
...
We tackle this by predicting S
itself from acknowledge of the proportion of
animals retained for breeding (p) and
assuming normality:
Selection Intensity i is the number of
standard deviation units (σp's) that the
selected parents are superior to the mean
...
05
0
...
50
0
...
95
Selection intensity
i
2
...
3
0
...
4
0
...
The ^ is conventionally dropped from S and R
...
25
σp = 30kg
What is expected average weight of the top 10 bulls?
Sm =iσp
pm = 10/100
giving im = 1
...
755 x 30 = +52
...
σp = 30kg
Answer = 352
...
755 + 0) x 0
...
58kg response
...
58kg for male progeny and 275 + 6
...
What is response to selecting these bulls over the best half of the heifers?
pf = 0
...
798
R = ih2σp = ½ (1
...
798)x 0
...
57kg response
...
57kg for male progeny and 275 +9
...
34
Note that we can use the prediction formulae flexibly
...
65kg bull over the best 50% of heifers:
Individual male: Pm =+52
...
12
Top 50% group of heifers: P = 0
...
798→ Sf = ifh2σp = 5
...
58 + 2
...
57Kg
Generation Interval
GENERATION INTERVAL: L, the average age of parents when their progeny are born
...
If all parents are bred only once, and they drop their progeny at 2 years (2 years after they
themselves were dropped) then it takes 2 years to cycle through one generation and Ryr:
However parents are usually bred more than once, and breeding females are often kept longer
than breeding males-so we need a more comprehensive way of calculating generation interval
and response per year Ryr:
First calculate the average age of the parents when their progeny are born separately for each
sex, Lm and Lf, then average the two results to get overall generation interval, L
...
Consider a 1000 ewe flock with an age structure typified by the numbers in the table below
...
Mating ratio is 1 ram to 50 ewes, and there is some mortality
...
Age at drop
of progeny
No
...
of ewes:
Heritability 0
...
4kg
Weaning rate 0
...
4 years = average age of rams ‘dropping’ progeny
12 + 8
Lf =
250x2 + 200x3 + 180x4 + 150x5 + 120x6 + 100x7
= 3
...
8 x 1000 = progeny, 400 male and 400 female
pm = 12 young rams selected out of 400 available = 12/400 = 0
...
03 gives im = 2
...
625 giving if = 0
...
268 + 0
...
3 x 0
...
054 kg
Lm + Lf
2
...
99
Ryear = 0
...
However, if we would cull ewes older than 4 years of age, we would need to keep nearly all
newly born female lambs as breeding females (no selection intensity left) and this breeding
program would be less optimal
...
For
example, if females would leave more lambs each, we need to keep less breeding females,
resulting in higher female selection intensities
...
37
6
...
g
...
But
by how much? This depends on the repeatability
...
Assuming that difference between subsequent measures are due to transient environmental
effect, we have:
VE =VE g + VEs
g for general (permanent), s for special (temporary)
EXAMPLES:
Permanent effects (Eg)
Temporary effects (Es)
Lost a leg
Born as a twin
Pregnancy status
Gut fill state
just had a pee
Pregnancy status
Note that most environmental effects, of both types, are not identifiable
...
g
...
Measured on subsequent days)
...
These effects would tend to be more important
when measurements are far apart (in time), e
...
-for traits such as fleece eight in different
years
...
38
USES OF REPEATABILITY
1 As h2 = VA/Vp and r is as above, an estimate of repeatability can act as an upper estimate of
repeatability
...
Knowledge of repeatability tells the value of taking repeated measures, as shown next
...
Vp(n) = VG + VEg + VEs/n
Variance of mean of n measurements of
a trait on each animal
⎛ 1− r ⎞
VP(n) = ⎜ r +
⎟ VP
⎝
n ⎠
Showing the proportional reduction in VP
⎛ 1− r ⎞
σ P(n) = ⎜ r +
⎟σ p
⎝
n ⎠
Showing the proportional reduction in σ P
SELECTION STRATEGY
...
Select animals on the mean of n measures
...
39
REPEATABILITY EXAMPLES
Fertility in cattle r =0
...
8
Vp(2) =Vp = [0
...
8/2] 0
...
096
σ p=0
...
16
⎛ 1− r ⎞
VP(2) = ⎜ r +
⎟ VP = (0
...
8 / 2) = 0
...
16/0
...
29R
29% more response
n
Body weight in cattle:
r = 0
...
95 + 0
...
5
⎝
2 ⎠
Rn = R
σP
=R
σP
( 900/877
...
01R
1% more response
...
However, lowly repeatable traits yield useful new information with each new
measurement
...
40
This is an effect of environment
This is an effect of genotype
...
As an hypothetical
example consider the
yearling weight of
beef cattle in
different
environments:
Bos taurus
Bos indicus
...
5
Tropical
230
250
240
-37
...
5
Effects
+7
...
5
The interaction can be seen by predicting performances given the mean and effects
...
5 + (+37
...
5) =
322
...
Predicted weights given mean and main effects
alone
kg
Temperate
Tropical
B
...
5
247
...
indicus
307
...
5
The ranking of the breeds changes between the environments
...
For example, in the case that Bos taurus would always be better than Bos indicus, but
the difference is much larger for temperate environments, we would also speak of a G by E
interaction
...
Hence, each individual within the breed is expected to perform according to the
pattern
...
The same phenomenon of G by E interaction relates to individual animals, for example, with
ANIMAL x REGION interaction for breeding value, the breeding value of an animal depends
on the geographic region in which its progeny will have to perform
...
DATA CORRECTION
We try to make inferences about individual's genetic merit by using phenotypic observations
...
The environmental effects are not all due to random
chance
...
We can split the environmental effects into identifiable components and non-identifiable or
random component
...
In fact, the heritability increases, and therefore response to selection increases
...
VA + VE
How do we account for identifiable environmental effects?
Fixed effects e
...
: Birth type, herd, management group
...
A 25kg
...
but a 25kg Triple is given a value of 25-20 = +5kKg
Continuous effects e
...
: age of individual, lactation length
...
age at weight:
Strategy: express all phenotypes as deviations from the "age-corrected mean":
Example:
The 'yearling' of Alice (Animal A) is
The 'yearling weight' of Bessy (Animal B) is
280kg at 11 months of age,
295kg at 13 months of age
...
4kg/day, we expect Bessy to be 0
...
When both animals are corrected to 12 month of age, the age-corrected yearling weights are
280-0
...
4(395-365) =283kg
for Bessy
...
Correction
for synthetic environmental effects is also important for comparisons between individuals
...
Unbiased breeding values are
important at an individual level
...
In a later lecture we will see that the proposed correction method here is not always sufficient,
and we need to use a more sophisticated method to estimate breeding values unbiasedly
...
However, that we need to
correct for systematic environmental effects remains always important
...
∑ ( X − X ) ( Y − Y)
Cov(X,Y) =
Covariance
n −1
Cov X,Y
Regression
b Y,X =
VX
Cov X,Y
Correlation
rX,Y =
σ Xσ Y
When we apply it to the correlation between animals' observed values (phenotypes, P) for
traits, x and y we get the phenotypic correlation:
rP =
Cov ( PX , PY )
σ Pxσ Py
However, it is the correlation of animals' breeding values (commonly known as the genetic
correlation, rA, A for breeding value ) which is of greater interest
...
rA =
We know σA = VA but what is CovA? Well just as VP = VA + VE (if VD =0) then Covp =
CovA + CovE (Assuming no Dominance for simplicity)
...
g
...
e
...
As CovA = 0 then rA = 0
...
44
Correlated response
When selection is for a given trait x, we can also expect an effect on trait y if y is correlated to
x
...
Correlated Response (CRy) - Response in trait y due to selection on trait x
If we knew animals' breeding values, we could draw the relationship between breeding values
for two traits, say trait x = growth and y = fat depth
...
h2x
...
As the breeding value of y can be predicted from the BV of x, so can the Response for y
(average of BV in selected group) be predicted from the response for x
...
Now we can express this in terms we have already handled:
Correlated Response =
CR y = b A R x = rA
CR y = rA
σA
y
σA
σ Ay
R
σ Ax x
ix h 2σ Px
x
⎡
Cov(A x ,A y )
Cov(A x ,A y ) ⎤
and rA =
⎢ as b A =
⎥
2
σ Ax
σ Ax σ Ay ⎦
⎢
⎥
⎣
as CR y = bA R
x
CR y = rA
h yσ Py
h xσ Px
i x h 2σ Px
x
as σ A = hσ P
45
CR y = i x rA h x h yσ Py
Direct versus indirect selection
...
The response for indirect selection relative to the response for direct selecting for that trait is:
indirect CR y i x rA h x h yσ Py L x i x h x L y
=
=
=
rA
direct
Ry
i y h 2σ Py L y
i y h y Lx
y
Not here that generation intervals must be considered separately for two selection policies
...
INDIRECT SELECTION EXAMPLE-Objective is to increase weight in Tilapia
Parameters
...
09
h2 length = 0
...
95
Call weight y and length x
...
16
rA =
= 1
...
09
Selection on length gives 27% more response in weight than does direct selection on weight
itself, in this case
...
This INDIRECT
SELECTION can be of use where the two traits are highly genetically correlated, and the
secondary trait is more heritable
...
However, also other considerations play a role, e
...
the correlated
trait can be measured earlier (so animals can be earlier selected giving shorter generation
interval), or the correlated trait is easier or cheaper to measure than the direct trait
...
Basically,
we have estimated an individual's breeding value based on phenotype only
...
Because we know that animals can be
genetically related
...
We can do this if we know how much
different animals have in common, genetically
...
Knowledge about genetic relationships is genetically useful if we want to know the
probability of two individuals sharing the same genes
...
We also
use knowledge about resemblance between relatives in estimation of heritability and in
prediction of breeding value of offspring
...
EXAMPLES- if X and Y are full sibs, consider one locus:
Dad
Mum
D1 D2
M1M2
X
Y
D1M1
Possible genotype… D1M2
D2M1
D2M2
Pick a GENE,
D1M1
D1M2
D2M1
D2M2
chances of 2nd choice of animal having same gene is r = ½
Pick a GENOTYPE, chances of 2nd choice of animal having same genotype as u =¼
47
We now have a basis to describe what proportion of GENES and GENOTYPES relatives
share in common- to what extent they are genetically similar
...
Pick a GENE
...
Pick a GENE in Y, chances of 2nd choice of animal (X) having same gene is 0 (if a
maternal gene had been picked) or 1 (if paternal gene had been picked)
averaging r =½
...
48
SUMMARISING:
Relationship
Full sib
Half sib
Parent-offspring
Grandparent-offspring
Degree
1st
2nd
1st
2nd
r
½
¼
½
¼
u
¼
0
0
0
Consider a pair of half sibs
...
This means that they tend to resemble
each other, because, on average, each has ¼ of its breeding value determined by the average
effects of the same genes
...
For example, if we observe a lot of variance in length of
humans, but at the same time we observe that members of the same family are quite similar,
then there is a strong family effect on length
...
We might suspect that length in humans may be caused by genetics, and that the genetic
effects are relatively important
...
The environmental effect common for members of a family is in
that case ''the same food''
...
We would also observe that the
larger the difference between families, (relative to the differences within families) the more
we find family members alike
...
Covariance within groups is equivalent to variance between groups
...
Similarity
within =
groups
e
...
=
Covariance within full
sib families
CovFS =
Distinction between groups
Variance between full sib
families
σB2
49
To illustrate this for another example, consider 9 animal to be allocated to three groups
...
The table shows
three ways of allocating animals to groups:
Type of allocation to groups
...
0
2
...
7
2
3
We can use knowledge of similarity (covariance) between group members to
§ predict performance of relatives: we expect an animal to be good because its full sib was
good
§ determine the importance of the effects that cause similarity: common genetic effects to
family members is the most important one for us, we want to know what extent difference
that we observe are heritable
...
For a quantitative trait, this is measured by covariance
...
Suppose individual y has an extreme value, a covariance would tell us what extend another
individual should also have a similar extreme value
Note that covariance is used to indicate similarity between individuals (for the trait)
...
There is a
parallel here: genetic correlations indicate to what extend the genes for two different trait are
common
...
The genetic covariance between two individuals is equal to their genetic relationship times the
genetic variance
additive genetic covariance between individuals x and y:
Cov(Ax,Ay)=axy VA
dominance covariance between individuals x and y:
Cov(Dx,Dy)=dxy VD
genetic covariance between individuals x and y:
Cov(Ax,Ay)+Cov(Dx,Dy)
50
Covariance among half sibs
The genetic relationship is aHS = ¼
...
e
...
Each sire progeny's performance can be written as
Pind
...
The 'other effects' are different for
each progeny of a particular sire, but their sire effects is common to all
...
If we can measure the covariance of
half sibs, we can estimate VA (multiply the half-sib covariance by 4!)
...
If we analyse the data on a number of half-sib families (e
...
in an ANOVA table), then we can
estimate the variance between half-sib groups
...
The variance among half sib families is equal to:
V(true HS family means) = σB2 = ¼ VA
The variance among observed HS family group is equal to:
V(observed HS family means) = σB2 + σW2/n
V(observed HS family means) = ¼ VA +
(n animals per family)
VP − 14 VA
n
Systematic bit + Random bit
51
Covariance among full sibs
The only thing makes half sibs is that they share a quarter of their genes in common, giving
CovHS = ¼ VA
...
Full sibs share ¼ of their genotypes in common
...
This adds ¼ VD to CovFS
...
Here we have yet another way of
splitting environmental effects: e = Ec + Ew
...
g
...
Ew is the residual environmental effect due to all
other effects within families
...
So CovFS = ½ VA + ¼VD + VEc where VEc is variance due to common maternal effects
V(observed FS family means) =
σB 2
σW2/n
+
1
V(observed FS family means) = ½ VA+¼+VD+VEc +
2
VA +
...
As we will see in
the next chapter, this makes using sib family information to estimate h2 a bit difficult
...
We also said that determining the covariance between observations
within a group allows us to estimate the importance of the effects that are common to
members within a group
...
In this chapter we show how similarity between families can be used to estimate heritability
...
Similarity within a group can also be applied to repeated measures on animals
...
If repeated measurements are similar, we have a
high repeatability, and the importance of the repeatability has been outlined in chapter 6
...
What is important in this chapter is to understand the concepts
...
Consider three repeated measures on each of five animals
...
Example data set 1:
Sheep No
...
:
Day 1
Day 2
Day 3
Means
1
17
20
23
20
2
21
29
28
26
3
25
28
34
29
4
22
16
16
18
5
24
22
32
26
By simply looking at the data we can already observe that
n
the variation of observed values on the same animal is larger in data set 2
...
53
This 'gut-feel' the data can be formally quantified with an analysis of variance
...
We expect to find
n
more random error in data set 2
n
a lower repeatability in data set 2
...
In reality we do not have this knowledge, but the example shows that larger
effects mean more variance
...
Observed phenotypes P for each measure are the sums of permanent (Pp)
and temporary (Pt) effects: P = Pp + Pt
We can call the temporary effects 'measurement error'
...
The actual measurements (P) are shown in bold, the other numbers are the
underlying effects and the means
...
The variance of observed group means
(i
...
means per animal) (21, 25, 29 and 26 in example data 1) is made up of the variance of mean
permanent effects (σ2B: 22, 24, 27, 19, 25) plus one nth of the variance of mean temporary effects
(σ2W/n, -1, 1, 2, 0, 1)
...
We divide these SS groups by the degrees of freedom for groups (equal to the
number of comparisons we can make between groups)
...
e
...
These deviations are called residual effects and if we square all these within group
deviations, we obtain the residual sums of squares
...
of Free
Mean
Group effect
(Between groups )
Residual
(Within groups)
Total
Sums of squares
1
4
8640
192
10
18
15
Mean Squares
Expected mean
squares
8850
48
σ2w + 3σ2B
1
...
1)
2)
3)
4)
sums of squares due to means:
15 x 242 = 8640
sums of squares due to differences:
3 x (212 + 252 + 292 + 192 + 262) = 8832
corrected for mean:
3 x ((21-24)2 + (25-24)2 + (29-24)2+(19+24)2(26-24)2) = 192
or directly: 8832 - 8640 = 192
total sums of squares
212 + 222 +…
residual sums of squares
total SS-SS groups = 8850-8832 = 18
notice that also: (-1)2 + 0 + (-2)2 +…
...
4
Within groups
σ2w = 1
...
2
Repeatability = intra-class correlation = 15
...
2 = 0
...
4 + 18 / 3 = 16
...
Degr
...
4
63
...
8
σ 2w
15
8929
The estimated variance components for example data set 2:
Between groups
σ2B = 15
...
8
Total variance is
σB2 + σw2 = 33
...
3/33
...
46
Variance of the group means
σ2 +
B
σ2
W
n
= 15
...
8 / 3 = 212
...
The group means are nearly the same (essentially, we have the same animals), they are only changed
due to more variation in measurement error
...
Summary of the example
It is not critical to be able to do all these sums, they serve more as an illustration
...
We call these variance components
...
If differences between groups are large in relation to the differences we
observe within group, then observations within the same groups are very much 'alike'
...
n
Since the covariance among related animals is due to genetic components, the between group
(full-sibs or half sibs) variance component can be used determine genetic variance
...
We can do again an analysis of variance, and
estimate the components of variance
...
Thes depends on how defined the groups, and what we think
are the causes of common effects for the observed values within a group
...
In
addition, there are often other (than additive genetic) sources of variation that cause full sib
groups to differ from each other
...
Interpreting variance components, depending on the grouping made
V(observed group
means variance)
Applications:
V(observed
HS
family means)
V(observed
FS
family means)
σ2B between
groups
2
σ2w/n
within groups
¼ VA
1
+
+
...
75V + V
2 A
D
Ew
n
VA + 1 4 VD + Vec +
Analysis of half-sib families
Generally we have paternal half-sibs groups, i
...
animals are only related through their sires
...
One Progeny/dam:
From the previous chapter:
The variance between half-sib groups is equal to the covariance between half-sib individuals
σ2B = CovHS = V(due to sires) = ¼VA
From analysis of variance we obtain estimates for between and within half-sib family
B
W
variance: σ 2 and σ 2
The correlation between 2 half sibs is r =
1 V
B
σ2
= 4 A = 14 h2
W
σ 2 +σ 2
VP
B
This is an intraclass correlation between half sibs
...
h2= 4 x intraclass correlation between half sibs…
Analysis of full-sib families
A common structure of the data is that we have observation on full sib families, where each
sire is mated to more dams, and each dam has more than one offspring
...
(This is called a Nested or Hierarchical design: dams are
nested within sires)
...
This example gives the following table:
SOURCE
Sires
Dams
Progeny
EXPCTED MEAN SQUARE
σw2 +8σd2 + 32σs2
σw2 + 8σd2
σw 2
Note: 8 progeny per dam
32 progeny per sire
And the expected value of the variance components is:
Variance due to
Sires
Dams within sire
Progeny within dam
Total
Sires + dams
Component
σS 2
σd 2
σW 2
σp2
σ S 2 + σd 2
Expectation/ interpretation
¼VA
¼VA + ¼VD + VEc
½VA +
...
VEc = Common environmental variance for full sibs
VEw = Environmental variance specific for each individual
The intraclass correlation between full sibs is the between group (full sib family)
58
t FS =
(σˆ
ˆ2
+σd )
=
ˆ2
σp
2
s
1
2
ˆ
ˆ
ˆ
VA + 1 4 VD + VEc 1 2
≥ 2h
ˆ
VP
So h 2 ≤ 2t FS
Since full sibs have more in common that just genetic effects, their intra-class correlation will
overestimate heritability
...
Assumptions in such ANOVA estimates of heritability:
1
...
The variance among a
selected group of sires will be smaller
...
2
...
Equal environment for each progeny group
Estimation of Heritability - by Regression
1
...
Of all the variation we observe between performances of sire (i
...
the phenotypic
variance) we expect the sire only to transfer its genetic effects to its offspring
...
Since the sire has
only half of its genes in common with its offspring
...
The regression of the performances of offspring on
performances of their parents is therefore
...
We can use this knowledge
to estimate heritability based on data
...
If the parents differ an amount of 40 (say in mature weight) we
expect their offspring to differ an amount to ½h2* 40
...
Deviation offspri Deviation Dad
Calculation
-5
-10
Covariance =(50+0+50)/2
0
0
VDad=(100+0+100)/2
5
10
b=½ =½h2 so here h2=1
2
...
b OP =
Cov(O, 12 Pm + 12 Pf )
=
V( 12 Pm + 12 Pf )
1
2
( 12 VA + 12 VA ) VA
=
= h2
1 V
VP
2 P
Recall Definition: Heritability is the regression of Offspring on the mean of parents!!
Accuracy Of Methods
See pages 179, Falconer
...
METHOD
h2 = 2bOP
h = b OP
h2 = 4tHS
h2 = 2tFS
2
ACCURACY
LOW h2
HIGH h2
**
**
**
**
***
***
*
**
BIAS
Maternal effects
Maternal effects
None
(½VD + 2VEc)/VP
Note that the accuracies (and therefore the standard errors) of the AoV estimates depends on
the value of h2 itself
...
Note: this is given as a guide for reference only, to give an idea, don’t memorize such figures
h 2 = 2b OP
with 400 pairs of observations gives h2 ± 0
...
1
h 2 = 4t HS
If the estimate of h2 is 0
...
3 ± 0
...
h 2 = 2t FS
If the estimate of h2 is 0
...
3 ± 0
...
60
10
USE OF INFORMATION FROM RELATIVES
Introduction
If we want to select the best from individuals of a population in order to achieve genetic
improvement, it is important that we are able to rank these individuals based on expected
genetic merit
...
However, generally we have more information available
...
In addition, if a bull has good performing sibs, or very good offspring, we tend to
give more credit to its breeding value
...
It is not instead of own phenotype, but additional
information
...
If a trait can be measured on one sex only, we can not use own
information at all
...
In this chapter we will analyse when relatives' information can be important, and how it can
be used in estimating breeding value
...
Principle of estimation of breeding values
We would like to rank and select animals on their true breeding values (TBV' or A) but we
don’t have this perfect knowledge- we can not see genes and breeding values
...
ESTIMATED BREEDING VALUES-EBV's are estimating TRUE BREEDING
VALUES using phenotypic information
The most obvious piece of phenotypic information we can use to estimate an animal's
breeding value is the animal's own phenotype
...
The principle of breeding value estimation is based on regression
...
If we
regress the breeding values on phenotypic observation, the slope of the regression line tells us
how much difference we have in breeding values per unit of difference in phenotype
...
Using quantitative genetic theory:
b xy =
Cov(x, y)
Cov(P,A) Var(A)
which is now equal to
=
= h2
var(y)
Var(P)
Var(P)
recalling that cov(P,A) = cov(A + E,A) = cov(A,A) = var(A)
...
If
the information of family members is to be added we have to know how important it is
compared to in individual performance of the animals itself
...
The data consist of litter size of mice
...
Now suppose we are intending to select the 4 best animals out of
these 16
...
This is called individual selection or mass selection
...
For the same
reason, we might even prefer A3 to B2
...
This strategy is called family selection
...
This strategy
makes sense if we believe that differences between families are more due to environment
than due to genetics
...
Table 1:
Select 4 animals with highest breeding value from:
Individual within family
A
1
2
3
4
Family Mean
Overall Mean
Phenotype P =
SELECTION
P
Pf
Pw
13
10
8
5
9
Family
B
11
9
6
6
8
C
D
7
7
6
4
9
5
3
3
6
5
7
Family mean Pf
+
NAME OF STRATEGY
Individual(mass) selection
Family selection
Within Family selection
Within family deviation Pw
ANIMALS SELECTED
A1 B1 A2 {D1 or B2}
A1 A2 A3 A4
A1 B1 C1 D1
Three factors are important in determining the relative importance of each strategy
...
In other words, a positive deviation in phenotype
can very well be the result of a good environment or 'random luck' rather than of good genes
...
The size of the family
The family mean reflects the true genetic value of the family's genes if it is an average of
many family members, because the environmental effects of the different phenotypes are
averaged out
...
62
The type of family
Half sibs are genetically more distant than full sibs, and the information from a half sibs
family will have less weight than the information on a full sib family
...
g
...
WHICH STRATEGY SHOULD BE USED WHEN ??
INDIVIDUAL(I)
Generally effective, especially if heritability is high, as
individual phenotype is then a good indicator of breeding value
...
WITHIN FAMILY(w)
High VEc swamps genetic differences between family means
...
g
...
Within family selection eliminates VEc from the variance which
selection works on
...
In the practise it is not so much a matter of choosing one strategy above the other, but more of
valuing one source of information more than another
...
Combined or index selection
We can write the EBV as an index, weighing these different types of information as
EBV = index = b1P + b2Pf
Where P and Pf are own performance and family information, respectively, and b1 and b2 are
index weights
...
It turns out that these weights are again regression coefficients: they
indicate what proportion of variation in information sources predicts breeding value
...
Working out the weights in a selection index requires some quantitative genetic theory and
some algebra, which can in fact become quite tedious
...
we have to account for the relationship between different
63
phenotypic sources, otherwise we tend to 'double count' the same information
...
We need matrices to work this out
...
Variance and covariance of information sources:
⎛ var(P)
⎛ P ⎞
cov(P,Pf )
var ⎜
=P=⎜
⎟
⎜ cov(Pf ,P) var(Pf )
⎝ Pf ⎠
⎝
⎞
⎟
⎟
⎠
2
...
g
...
Cov(P,Pf)
= Cov(Pw+Pf,+Pf) = Cov(Pw, Pf) + Cov(Pf, Pf) = 0+Var(Pf) = Var(Pf)
We can look at the index weights for the example, depending on heritability and number of
animals in a full sib family (no common environment):
b1 = weight for own phenotype
b2 = mean of n full sibs
h2
0
...
30
0
...
70
n=3
b1
0
...
26
0
...
62
n=10
b1
0
...
22
0
...
57
b2
0
...
26
0
...
24
64
b2
0
...
49
0
...
36
We see that:
n
Own performance more important with high heritability and small family size
n
Otherwise, family size more important
Selection of animals based on a selection index (using relatives' information) tends therefore
to look more like mass selection for high heritable traits, and more like family selection for
low heritable trait
...
The selection index theory is general and can be used to drive the weight of different
information sources in predicting an animal's breeding value
...
g
...
A selection index based on n source of information is
 = b1P1 + b2P2 + b3P3 +……+ bnPn
and the weights are derived by multiple regression
...
In practise, this would be quite cumbersome to compute selection index weights
...
Response to selection based on an index
The more information, the more accurate the selection index(EBV)
R is directly dependant on the accuracy of selection
We had for Response to individual selection base on phenotype
R=i h2 σp
This is the same as:
(per generation)
R=i h σA
When more information is used, the formula to predict selection response has to be
generalized
...
Some examples of accuracy
h2= 0
...
30
Information used
1) Own information only
2) Mean of 5 full sibs
3) Mean of 10 half sibs
4) 1 + 2 + 3
5) Mean of 1000 half sibs
6) Mean of 1000 full sibs
7) Mean of 20 progeny
8) Mean of 100 progeny
0
...
32
0
...
43
0
...
70
0
...
85
0
...
48
0
...
65
0
...
71
0
...
94
Progeny testing
The use of information on a group of test progeny is in some way a special form of using
relative' information
...
From the previous Table you may have observed that the maximum
accuracy attained by very many full sibs is 0
...
5 (which is √¼)
...
The index weight for a progeny test is again found by regression:
 = EBV = Index = b1P1
 = sires' breeding value
P1 is the mean of n progeny
b1 is the index weight
b1 depends on the number of progeny and the heritability:
b1 =
note that 0
Each progeny's performance can be written as
Pind
...
The 'other effects' are different for each progeny of a sire,
but their sire effect is common to all
...
This makes sense,
because we know that if a sire has an EBV of +20, we expect his progeny to receive half of
that (with average dams)
...
We could the term ½b1 =
67
CONCEPT:
The heritability of a progeny test (h2PT):
This is the proportion of variance in
progeny group means, which is due to
sires’ breeding values
...
OPMs
are penalised for luck by h2PT to predict
TPMs
Like b1,h2PT depends on the number of current progeny, and the individual heritability h2
...
h2 = 0
...
A bull has 20 daughters with a mean first lactation yield of 5500kg
...
What is the expected yield of subsequent daughters (True Progeny Mean)?
h2pt = n/(n+a) = 20/(20+15) = 0
...
57 x 500 = +286kg
Expected yield = 5000 + 268 =kg
2
...
OPM x OPM = 2n/(n+a) x +500 = +572kg(which is twice 286 kg)
The accuracy of the progeny test
For progeny testing, the rÂA in R =i rÂA σA is also the square root of a ''heritability'', the
heritability of the progeny test [h2pt = n/(n+a)]
...
e
...
n+a
This simple formula allows you to quickly determine the accuracy, for a given progeny test
based on n progeny, for a trait with heritability h2 (where a = (4-h2)/h2)
...
Of progeny
h2
5
50
100
0
...
5
0
...
91
0
...
99
0
...
995
Selection based on a progeny test
Comparison of: individual (Mass) selection and progeny testing:
For individual selection, selection accuracy
=h
For progeny selection, selection accuracy
=
n
n+a
Thus the two strategies give equal accuracy if:
n
n+a
h=
i
...
if n =
4 − h2
4 − h2
and if n >
then selection accuracy is higher for progeny testing
1 − h2
1 − h2
If h2 is low
then progeny testing is better if n>4 or 5 progeny
...
but an individual performance will never reach near perfect accuracy, whereas the progeny
test does (with enough progeny)
...
A reliable EBV is also good for marketing bull!
OTHER FACTORS OF IMPORTANCE
Against progeny testing:
n
Generation interval increases a lot with progeny testing
n
Selection intensity is usually lower with progeny testing as fewer animals can be tested
...
For progeny testing:
n
Progeny testing gives the ability to market 'proven' sires
n
Sex limitedness may make progeny testing necessary, as in Dairy cattle
...
The correlated
response for traits when selection is on other traits is calculated
...
Specific examples like indirect selection and
selection in more environments (genotype-environment interaction) are discussed
Animal breeding is aiming for the improvement of animal production and the quality of the
animal products by utilizing the differences in genetic ability between animals
...
Improving
efficiency and quality of animal production can be achieved by improving several
characteristics on the animals
...
In addition, such high producing animals should preferably have no
fertility problems, not suffer from diseases and have a high roughage intake capacity
...
Is it possible to change animals in each direction we want, and, more
interesting, can different valuable characteristics be improved simultaneously?
When genetic change is (to be) achieved for a certain trait it is important to consider possible
genetic change for other traits since traits can be phenotypically or genetically correlated
...
The methodology to
select animals and to predict the response to selection has been presented in the previous
chapters
...
Some of this changes may be desired,
and even more or less intention
...
Pigs that grow faster have also a better feed
conversion
...
g
...
From an economic view point it is important to predict how correlated characters change
when animals are selected for a certain characteristics
...
Did they 'overall' become
efficient? How did the higher production change the animals' physiology
...
Are there any side effects from
selection for a certain trait?
In this chapter we will reconsider the change of correlated traits when selection is for one trait
only
...
Subsequently we will consider selection for several traits simultaneously
...
This method will be used here to select for a multiple to select for a
multiple trait goal
...
Assuming the genetic correlation between these traits is 0
...
3
...
50 and for
feed intake it is 0
...
We assume selection of parents is on individual phenotype and the selection fraction is 25%
for both males and females (selection intensity i=1
...
Correlated response to selection
In chapter 7, we have discussed selection on a given trait, and calculated the expected
response for a correlated trait
...
h2
...
=
1
...
5 x 17 = 10
...
The response for trait B when selection is practised on trait A is calculated by regression
...
hA hB rg σpB
=1
...
5) x 0
...
3) x 25 = 5
...
Hence, with selection on weight, we increase weight but we also feed intake
...
2 x
...
0Kg
and the correlated response for weaning weight would be
CR=-1
...
5 x√(0
...
5) x 17=-3,96Kg
...
20)
Response
Selection on
Weight
Feed Intake
Weight
10
...
0
Feed intake
5
...
0
Use of information from correlated trait
To improve a certain trait (say A), we can select on phenotype of A (to give direct response),
phenotype of B (to give a correlated response), but we can also select based on information
from both traits
...
We can apply this to our
example where we combine the phenotypic information of weaning weight and feed intake to
estimate a breeding value for weaning weight (see the box for illustration)
...
We
71
can compare the resulting response by combining information on the two traits with the
results of the previous paragraph
...
20)
Trait in Index
objective
Response
Weight
Weight
Feed intake
Weight + Feed
Weight + Feed
Weight
-Feed intake
Weight
-Feed intake
10
...
0
10
...
9
Feed intake
5
...
0
6
...
6
Example selection index: information from two traits (W + F ), one trait (W) in the objective
(reference only !, this is an illustration and not examination)
1
...
5 ⎞
⎟ =⎜
⎟ ⎝ 127
...
Covariance between information sources and breeding value that we want to predict:
⎛ PW
⎞
⎛ cov(PW ,A W )
cov ⎜
,A W ⎟ = G = ⎜
⎜ PF
⎟
⎜ cov(PF ,A W )
⎝
⎠
⎝
such that in index weights become:
⎞ ⎛ 144
...
3 ⎟
⎠
⎠
⎛ b1 ⎞
⎛ 0
...
11 ⎟
⎠
⎝
⎠
= regression
index = EBVWW =0
...
11PF
When combing the information from weight and feed intake, we notice that the resulting
response is slightly improved for the objective trait (i
...
the trait we want to improve)
...
If this the reality, we need to redefine our selection criterion by defining the breeding
objective appropriately
...
Multiple trait selection
Most selection programs in livestock production aim for the simultaneous improvement of
several traits
...
We can again use the principle of selection index, but the optimal
weights are now derived, taking into account that we have two traits in the objective
...
We use economic values for this purpose
...
For example, the index is the best
ranking of genetic merit of a weighted aggregate of genotypes that form the different traits in
the breeding objective
...
Index criteria
Objective traits
Phenotypic
Information sources
Breeding values for all
traits in the objective,
each weighted by its
economic value
Phenotype of individual,
relative, correlated traits,
‘other traits
This value has to be assessed, assuming other traits remain equal
...
The selection is now generalized, we have to find optimal weight for all possible information
sources (index criteria), and optimal defined such that the joint genetic improvement of the
objective traits is maximized
...
If we consider only selection for
one trait, a selection index is nothing else than the best prediction of a breeding value
...
We still use all possible information
but now to optimally change genetic gain for an aggregate of traits
...
If we rank the animals on the index, we have the best chance of ranking the
animals according to their true genetic merit
...
Optimal weights are determined by regression of objective traits on information sources
73
Example selection index
Information from two traits (W + F), two traits (W+F) in the objective
(you don’t have to remember this exactly!
...
5 ⎫
⎪
⎬= ⎨
⎬
⎪ ⎩ 127
...
⎛⎧ P
⎪ W
cov ⎜ ⎨
⎜ ⎪ PF
⎝⎩
⎞
⎫
⎧ cov(PW ,A W ) cov(PW ,A F )
⎪
⎪
(a W A W + a F A F ⎟ = G
...
5 82
...
3 67
...
45 0
...
11 0
...
If the economic values are aW = 1 and aF = -1, then
Index = EBVYW = 0
...
07PF
The example in the box shows that if the economic values are aW = 1 and aF = -1 for Weight
and Feed, respectively, then the index weight for weight will be a low compared with the
previous box where the objective was to improve weight only
...
More practically, if the objective was only weight, we would also select the
big eater, because Feed intake is positively correlated to Weight
...
The following Table shows that we can manipulate genetic change for the two
traits, depending on the objective, i
...
economic weight for the traits)
...
20)
Response
Traits in index
Weight + Feed
Weight + Feed
Weight + Feed
Weight + Feed
Weight + Feed
Weight + Feed
Weight + Feed
objective
W
W – 0
...
4 F
W – 0
...
4
10
...
6
7
...
8
-1
...
9
74
Feed intake
6
...
3
3
...
3
-3
...
1
-9
...
This reflects a method to determine economic weight based on desired gains
...
The danger is that one puts potentially very much emphasis on traits that are difficult to
improve (e
...
due to a low heritability)
...
Therefore, if economic weights could be derived without too much uncertainty,
using these in selection index is the most efficient approach
...
In the case, the ‘desired gains’ approach
may be appropriate
...
g
...
Accuracy of index selection
rI,A is the accuracy of index = the correlation between index and A!
The variance of the index increases when it is more accurate
Var (Index) = accuracy2 x True genetic variance
σ I2 = r 2 σ A2
I,A
Remember: index = estimated BV
Units of index are KSh (mostly)
Breeding objective = True BV
Response to selection
Selection criterion is an index
Selection differential =
i
...
σ I
= irI,A σ A
selection intensity x selection accuracy x genetic SD
75
Concluding remarks
Objectives and Criteria can involve different traits and different numbers of traits
...
(Objectives are to identify individuals of
high breeding value, so no relatives involved here)
...
1
...
g
...
g
...
If we have BLUP – BV, we do not need to derive selection index weights, but we can
simply multiply the EBV’s for each trait with their economic value
...
BLUP is used to give EBVs for commercially important traits
...
Whereas the selection index uses
information from defined sources (e
...
FW on self, FD on self, FW on sibs), BLUP uses
all available information
...
BLUP makes full use of information from all relatives
...
R
...
25
...
25
1
...
125
Willy
...
05
1
0
Daisy
0
0125
0
1
…
…
…
…
…
BLUP does not give separate attention to sib testing, progeny testing, own
performance e
...
c
...
This gives more accurate EBVs and more selection response
...
BLUP accounts for fixed environmental effects (management group, herd, season, year
etc)
...
For example, comparing across age means that older animals have to prove
their competitiveness at every round of selection
...
5 and 5
...
Is the second flock of 0
...
Using a reference sire with random mate allocation helps:
Progeny of reference sires
Flock 1
5
...
0 kg
Flock 2
5
...
5 kg
Progeny of flock 1 sires
The reference sire is inferior in the 4
...
0 kg – so the 4
...
77
But by how much?
In Flock 1, the reference sire’s progeny are worse than Flock 2 sire’s progeny by
0
...
Assuming many progeny, the reference sire’s breeding value inferiority
must be twice this, because of the diluting effect of ewe mates of equal merit
...
Thus, if the flock
sires are representative of their flocks ( or if they are equally selected) then Flock
1 is 2kg genetically superior to Flock 2
...
5kg below that of Flock 2
...
e
...
3
...
The approach used in the last example could be used to test the
genetic differences between animals born in different years, instead of different flocks
...
Here is an
example from Ojango and Pollot (2001) for the Kenyan Holsteins
...
BLUP can handle unbalanced designs easily
...
from lecture on using sib information
The weight for the family information (bf) depends, besides on heritability and the type
of family, also on the number of individuals in the family
...
BLUP only
needs to report the EBV’s (Â’s) and not the index weights (b’s)
...
BLUP can cater for non random mating – such that males can be compared via their
progeny even if some had been allocated better mates
...
6
...
E
...
consider ranking bulls on the first two
lactations of their daughters
...
BLUP relies on good genetic parameters:
As with the selection index, BLUP assumes that the estimates of genetic parameters it uses
are valid (i
...
reasonably close to the truth) and that the genetic model we use is valid (e
...
that the variance due to sires is ¼ VA
...
The breeder
only needs to weight these by economic weights to provide an index which she/he can select
on:
Index = a1Â1 + a2Â2 + a3Â3 +
...
This is a
prediction of the value of daughters’ calves…
Maternal Value = 1/ 2 EBVmilk + 1/ 4 EBVgrowth
AN ILLUSTRATION OF HOW BLUP WORKS (for your information only!)
In using BLUP the aim is to obtain estimates of the breeding values of various animals, taking account
of so-called fixed effects such as herd-year-season or age
...
In this paragraph the basic method of obtaining BLUP estimates of
breeding values is described and an example is presented
...
These environmental factors have to be represented in the statistical model
...
For
example we could have herd and year as environmental factors
...
When there are 5 herds, the factor herd would
have 5 classes
...
Initially we will only
look at models with a single additive genetic factor
...
In case
79
of a single additive genetic effect, two different models can be distinguished: sire model and animal
model
...
With such a model breeding values for only sires can be estimated
...
The model to describe the observations contains fixed effects for the environmental factors and
random effects for the genetic effects
...
In matrix notation, a mixed model can be expressed as
follows:
y=Xb+Zg+e
where, y
b
vector with n observations (n*1),
vector with f fixed effects (f*1),
g
vector with s random effects (s*1),
e
vector with error terms (n*1),
X
incidence-matrix indicating for each observation the fixed effects by which it
is influenced (n*f),
Z
incidence-matrix indicating for each observation the random effects by which it is
influenced (n*s)
...
Write down the set of so-called least squares equations corresponding to the model
In setting up the least squares equations, all effects in the model (b and g) are treated as fixed effects
...
Let us look at this expression in more detail
...
In case we have only one fixed effect with several classes, the matrix X'X contains the number
of observations in each class at the diagonal and zero elsewhere
...
They represent how observations for one class of a fixed effect are distributed over
the classes for the other fixed effects
...
Z'Z is a diagonal matrix which contains information on the
number of observations for each class of g
...
The size of the matrices can be derived from the size of X and Z which are (n*f) and (n*s), where the
first number represents the number of rows and the second the number of columns
...
The result is a (f*n)x(n*s)=(f*s) matrix
...
The vector X'y
contains the sum of the observations in each class in b and Z'y contains the sum of observations for
each class in g
...
To include this information, the part of the left-hand sides of the
equations that relates to the genetic effects has to be modified
...
For now we look at a sire model without relationships between sires
...
The mixed model equations for a sire model without relationships between sires is:
⎡ X ′X
⎢
⎣ Z ′X
⎡ X ′y ⎤
X ′Z ⎤ ⎡ b ⎤
⎥ ⎢ ⎥ = ⎢ ⎥
Z ′Z + αI ⎦ ⎣ g ⎦
⎢ Z ′y ⎥
⎣
⎦
2
where I is the identity matrix and α is σ e /σs2=(1-¼h²)/(¼h²)
...
The term α represents the variance ratio of the error in the model and the genetic effect in the model
...
The half results from the fact that the sire only contributes 50%
of the genes of the animals on which we have the observations
...
By adding αI to the Z'Z and solving the equation
p
p
p
we get BLUP estimates for sires
...
In other words, adding α to the appropriate diagonal coefficients
has an effect analogous to multiplying the mean of daughter performances (adjusted for fixed effects)
by the appropriate selection index weighting factor
...
The estimated transmitting
ability is half the breeding value of the sire
...
Note: When there is more than one fixed effect in the model, restrictions have to be used to avoid that
the matrix is singular, in which case the generalized inverse rather than inverse of the left hand sides
should be used
...
All productions
were observed in the same year and all cows had the same age
...
The objective is to estimate the breeding value of these sires using a sire model
...
The fixed effects are represented in b and the random effects in g:
⎡ sire1⎤
⎡ herd 1⎤
⎢
⎥
b= ⎢
⎥ , g = ⎢ sire2 ⎥
⎢herd 2 ⎥
⎢
⎥
⎣
⎦
⎢ sire3⎥
⎣
⎦
The matrix X is used to specify the fixed effects for each observation
...
In this example X has 7 rows and 2
columns
...
e
...
The design matrices are:
⎡1
⎢
⎢1
⎢1
⎢
X = ⎢ 1
⎢
⎢0
⎢0
⎢
⎢0
⎣
0⎤
⎡1
⎥
⎢
0⎥
⎢0
⎢0
0⎥
⎥
⎢
0 ⎥ , Z = ⎢0
⎥
⎢
1⎥
⎢0
⎥
⎢0
1⎥
⎢
⎢0
1⎥
⎦
⎣
0 0⎤
⎥
1 0⎥
0 1⎥
⎥
0 1⎥
⎥
1 0⎥
1 0⎥
⎥
⎥
0 1⎦
Step 2) Write down the set of so-called least squares equations corresponding to the model
The left hand sides are:
⎡ X ′X
⎢
⎣ Z ′X
⎡4
⎢
0
′Z ⎤ ⎢
X
⎥ = ⎢ 1
Z ′Z ⎦ ⎢
⎢ 1
⎢
⎣2
0
3
0
2
1
1 1 2⎤
⎥
0 2 1⎥
1 0 0 ⎥
⎥
0 3 0⎥
⎥
0 0 3⎦
while the right hand sides are:
⎡27600 ⎤
⎢
⎥
25200 ⎥
⎡ X ′y ⎤ ⎢
⎢ ⎥ = ⎢ 7000 ⎥
⎥
⎢ Z ′y ⎥ ⎢
⎣ ⎦
⎢22900 ⎥
⎢
⎥
⎣22900 ⎦
Step 3 and 4) Transform the least squares equations into mixed model equation and obtain
estimates
82
2
The heritability of the trait is 0
...
Consequently: α= σ e /σs2=(1-¼h²)/(¼h²)=15
...
9 ⎥
⎢
⎥ ⎢
⎥
⎢ 22900 ⎥ ⎢ -‐ 45
...
0 ⎦
The estimated transmitting ability of sire 1 is equal to 6
...
The estimated breeding value for that sire is
2*6
...
8
...
8 and 78, respectively
...
The estimated
breeding values are very different
...
Genetic evaluation methods
have moved to the use of animal models to be able to account for genetic effects of sires and dams
...
In addition it is
assumed that all dams are unrelated
...
Dams
may have more progeny and, consequently, animals may have more genetic covariances than only
through their sires
...
Expectations of
different dams are often not equal, particularly when we have practised selection, or when we have
dams from different breeds or crosses between breeds
...
A more general
analysis will be obtained when we write each observation as a function of the breeding value of the
animal that made that record (rather then a function of the breeding value of the sire)
...
In an animal model it is
important to include the genetic relationships between all animals
...
Mixed model equations for an animal model have an equation for every animal
...
Since 1980, it has become feasible to construct and
solve an animal model with the computer
...
On the one hand, genetic and statistical advantages became apparent
...
On the other
hand, computational procedures were proposed that made it feasible to solve the equations for many
animals
...
Animal models are implemented for dairy populations with several million
animals
...
We will follow the 4
steps as outlined in the previous chapter
...
Dam no
...
1
1
3
Observation
11
7
10
8
9
The parents of cows 2 and 4 are unknown
...
Cow 2 was chosen over cow 4 for ET because she had a better record
...
Step 1) Define the model to describe the data
For simplicity, it is assumed that the only fixed effect is the mean
...
We consider the model
yi = µ + ai + ei
where, µ
ai
ei
= overall mean,
= the breeding value of the animal i,
= random environmental effect for animal i
Step 2) Write down the set of so-called least squares equations corresponding to the model
The LS equations for this problem are:
⎡5
⎢
⎢1
⎢1
⎢
⎢1
⎢
⎢1
⎢1
⎣
µ
1 1 1 1 1⎤ ⎡ ⎤
⎡45 ⎤
⎢ ⎥
⎥ ⎢ a2 ⎥
⎢ ⎥
1 0 0 0 0⎥
⎢ 11⎥
⎢ ⎥
⎥ ⎢a4 ⎥
⎢ 7⎥
0 1 0 0 0
⎥ ⎢ ⎥ = ⎢ ⎥
⎢10 ⎥
0 0 1 0 0 ⎥ ⎢ a5 ⎥
⎥ ⎢ ⎥
⎢ ⎥
0 0 0 1 0 ⎥ a6
⎢ 8⎥
⎢ ⎥
⎥ ⎢ ⎥
⎢ 9⎥
0 0 0 0 1⎦ a
⎣ ⎦
⎣ 7⎦
Step 3) Transform the least squares equations into mixed model equations
The heritability of the trait (h2) is 0
...
The variance of a is the genetic variance which is
2
2
2
2
2
σ g = h 2σ p where σ P is the phenotypic variance
...
Note
that the variance ratio differs between the animal model and the sire model
...
When we ignore the relationships between the animals, the mixed model
p
p
equations can be constructed for this example:
1
1
1
1
1⎤ ⎡ µ ⎤
⎡5
⎡45 ⎤
⎢
⎥ ⎢ a2 ⎥
⎢ ⎥
⎢ ⎥
0
0
0
0⎥
⎢ 1 1+ 1
⎢ 11⎥
⎢1
⎥ ⎢a4 ⎥
⎢ 7⎥
0 1+ 1
0
0
0 ⎢ ⎥
⎢
⎥ ⎢ ⎥ = ⎢ ⎥
⎢1
⎢10 ⎥
0
0 1+ 1
0
0 ⎥ ⎢ a5 ⎥
⎢
⎥ ⎢ ⎥
⎢ ⎥
0
0
0 1+ 1
0 ⎥ a6
⎢1
⎢ 8⎥
⎢
⎥ ⎢ ⎥
⎢ 9⎥
⎣ ⎦
0
0
0
0 1+ 1⎦ ⎢a ⎥
⎣1
⎣ 7⎦
Step 4) Obtain estimates
Below we solved the mixed model equations for the cows:
84
ˆ
⎡ µ⎤
9⎤
⎡
⎢ ⎥
⎢
⎥
ˆ
a2 ⎥
⎢
1⎥
⎢
⎢ ⎥
⎢ -‐ 1 ⎥
ˆ
⎢ a4 ⎥
⎥
⎢ ⎥ = ⎢
⎢ 0
...
5 ⎥
⎢ a6 ⎥
⎢
⎢ˆ ⎥
0⎥
⎣
⎦
⎣ a7 ⎦
Remarks on the results:
The average breeding value of all individuals is equal to zero
...
Principles: relationships
Sofar, we have treated cows as unrelated which means that we have ignored information about
relationships among the cows (as illustrated by point 2 above)
...
To solve this we have to look at the meaning of αI what we added to the least
squares equations to get mixed model equations in the case where animals were unrelated
...
When there are no relations between animals A-1 = I
...
These
effects were not included in the least squares equations in the previous paragraph
...
Remember, Z has a row for every observations (5 in the example) and a column for
every genetic effect (7 in the example, 5 cows with observations and 2 sires)
...
926
-‐ 0
...
938
...
889
...
062
-‐
...
e
...
86
13
INBREEDING
Introduction
Control of inbreeding is an important aspect of breeding programs
...
In
addition, reproductive technologies such as Artificial Insemination (AI) and Multiple
Ovulation Embryo Transfer (MOET) have enhanced the intensive use of the best genetic
material
...
However, the other side of the coin is that populations become effectively smaller, since all the
new-born animals descend from only a few highly selected parents
...
If all animals in a population relate to
one or only a few ‘golden’ rams or bulls
...
Inbreeding and erosion of genetic variation are two phenomena that are closely related
...
We will calculate the coefficient
of inbreeding of individuals from known pedigree relationships
...
Alternatively, we will also predict the rate of inbreeding from
population characteristics (mostly related to the population size)
...
Definition of inbreeding
INBREEDING – the mating of individuals which are related
...
F = Probability of the 2 alleles at a randomly chosen locus being identical by descent
Calculation of inbreeding coefficients from pedigree
- Gives exact answers for individuals
...
The probability that ban individual has two alleles
identical by descent is one half the probability that its parents have alleles in common by
descent
...
If individual k has parents i and j, then Fk = ½ aij
Therefore, both F and aij are calculated in a similar way
...
If we draw a pedigree tree, then the relationship between individuals P and Q can be found by
counting the number of steps up (n1) from P to a common ancestor, and the number of steps
down (n2) from the common ancestor to Q
...
If P and Q have more ancestors, the relationship is found by summing the
probabilities of each of p paths
p
a ij = ∑ (1/ 2)
n1 + n 2
k =1
and if animal X is the offspring of I and J, its inbreeding coefficient will be equal to
Fx = 1 / 2 a IJ
Example 1
What is the inbreeding coefficient on the offspring of a mating of half sibs?
We can first look at the relationship between D and E
...
The
inbreeding coefficient of X is then ½ aDE = 1/8
...
These are labelled as being
different, i
...
not identical by descent, such
that A is either known or considered to be B
not inbred
...
This means X is inbred
...
The chance of X getting A1 through D is ½
(A to D) times ½ (D to X), and the chance
of X getting A1 through E is ½ (A to E)
times ½ (E to X)
...
Shortcut: n = 3 descendants (D, A, E) in the closed loop – Fx = (1/2)3 = 1/8
88
Example 2:
Inbreeding coefficient on the offspring of a full-sib mating
...
Recipe so far is Fx = ∑ (1 / 2) n where
∑
is the sum over loops, and n is the number of
animals in each loop, excluding X itself
...
From this consideration we get
the final formula:
Fx = ∑ (1 / 2) n (1 + FA )
- where FA is the inbreeding coefficient of common ancestor A for each loop
...
- The summation is over all possible loops
...
28125
Example 4:
Note that some loops cross over, e
...
QXDYP
...
There may be many loops possible
...
For complicated pedigrees it might be safer to use a computer program
...
PATH
PXCADYQ
QXCADYP
PXCBDYP
QXCBDYP
PXCBYQ
QXCBYP
PXDBYQ
QXDBYP
PXDYQ
QXDYP
PXQ
PYQ
TOTAL…
n
7
7
7
7
6
6
6
6
5
5
3
3
COMMON ANCESTOR
A
A
B
B
B
B
B
B
D
D
X
Y
CONTRIBUTION
(½)7
(½)7
(½)7
(½)7
(½)6
(½)6
(½)6
(½)6
(½)5
(½)5
(½)3(1+1/4)
(½)3(1+1/4)
FR =15/32 =0
...
One might even argue that every locus that is homozygous carries two alleles that are
somehow identical by descend, because they have to relate to the original mutation
...
Therefore, the inbreeding coefficient tells us how much more probability there is that genes
are in common, relative to a certain base population (practically, the first ancestors in the
pedigree)
...
However, the probability that an
inbred descendant carries the same alleles would be increased
...
We usually talk about F (rate
of inbreeding (increase) rather than an (absolute) value ate a current time
...
Although
homozygotes are increased with inbreeding, there is also homozygosity by randomness
...
In the following paragraph we see that this has negative consequences, for example in case of
genetic defects
...
It is a configuration of genotype frequencies that typically has
more homozygotes (of either kind)
...
§ Of course, if we had no 'other' lines, an inbred populations might fix its genes due to drift
(or due to selection if selected), thereby loosing its genetic variation
...
Consequences of Inbreeding
Why is inbreeding bad?
1) Increased frequency of affected individuals due to genetic defects'
Inbreeding increases the frequency of homozygotes
...
The effect of deleterious recessive alleles comes only to
expression in homozygotes (carrying two copies of the recessive allele)
...
If the frequency of the recessive allele is q, than in a non-inbred population, the
probability of being an affected individual is q2
...
Let q be equal to 1 %
...
125)
13
...
Increased homozygosity means most traits are depressed by between 2% and 7%
per 10% increase in F
...
Those are typically traits that
relate to fitness and reproduction
...
Heterosis if more distant line or
91
breeds are crossed (see next chapter) We will find a lot of heterosis for the same traits that
show a lot of inbreeding depression
...
The variance in an inbred population will decrease, because the animals become increasingly
related and therefore more and more 'alike', hence less variation within the population
...
For a long term genetic response, it is therefore important to keep inbreeding below a certain
level ((see the end of this chapter)
...
This is calculation of inbreeding 'after the fact'
...
We want then to obtain an approximate answer averaged over the population
...
The reason is that in
a small population there is a large chance for an individual to mate with a related individual
...
If males have a lot more offspring than
females, we only need a few males to breed a next generation
...
Inbreeding does depend on effective population
size
...
This formula gives much more weighting to the lesser represented sex
...
example
nr males/generation
Nr females/generation
Ne effective population size
2
2
4
2
20
7
...
9
5
200
19
...
7
Prediction of rate of inbreeding
We need the probability that alleles in individuals are identical by descent'
...
In a population with Ne individuals, there are 2Ne alleles
...
In reality, there is selection going on in breeding programs and the
inbreeding rate can be a multiple of the one predicted with the no-selection
assumption
...
5
Lf =4
3
1
20
4
5
6
20
20
20
L =3
...
25 = 3
...
Nf =20 x 3
...
4N m N f
845
Ne =
=
= 12
...
25
F20years = F20\3
...
38)] 20\3
...
224
which is probably unacceptable – but you need to look at response to
selection together with this when looking for the best overall strategy
...
Alternative strategy: Use only 4 new rams each year:
AGE:
2
3
4
5
6
RAMS
4
EWES
20
20
20
20
20
Lm =2
Lf =4
L =3 years
Calculation
Lm =2, Lf =4, L = 3
Nm
...
0804 which is probably acceptable
...
For the previous example, F = 0
...
93
Balancing Response and Inbreeding
In commercial breeding population the aim is to achieve a high rate of genetic improvement
...
The fewer animals
selected, the higher the selection intensity, the higher the predicted response
...
To
design a breeding program, we need therefore to balance Rate of Response and Rate of
Inbreeding and find an optimum between the two
...
This is called 'mate allocation'
...
This graph shows the effect of
inbreeding on fleece weight response to 10
years selection in a simulated 1000 ewe
sheep population
...
At very low numbers
...
In small population that are not actively selecting, but rather need to be maintained (zoo
animals, endangered species)
...
The inbreeding rate
ultimately depends on effective population size
...
12
WE CAN PREDICT RESPONSE TO SELECTION:
im + i f 2
i +i
R yr =
h σ p or R yr = m f rAAσ A
Lm + Lf
Lm + Lf
Typically we predict rates of genetic improvement of 1 to 2% per year
How reliable are these predictions? What are the causes of deviations from predictions?
There are two types of error - random drift and
Random Drift Giving Prediction Errors
If we run several breeding programs in parallel, each derived from the same base population
of animals, with the same environment and breeding policy, we get equal predictions – but
different results
...
1:
This is mostly because with a finite number of parents, the average breeding value of selected
parents can vary considerably between replicates and between generations
...
Sampling error in estimating h2
...
2
...
This is possible when using Analysis of Variance on full sib
families or Dam-Offspring regression to estimate h2
...
Selection Differentials lower than anticipated – due to excessive mortality among
candidate, heavy culling on other traits and / or 'non-working' breeders
...
Inbreeding – causing depression in the traits of interest, lowered selection intensities
due to poorer fertility, and lowered genetic variance (Ch 15, Falconer)
...
Assortative mating - mating the best-selected females to the best selected males
increases genetic variation in the progeny, resulting in increased selection response in
later generation
...
In practical
breeding programs using BLUP selection, the increase due to assortative mating can be
as high as 15%
...
6
...
g
...
7
...
Selecting for high litter size can give negative responses in short
term
...
,
making them phenotypically predisposed to have small litters
...
Variance loss due to selection
...
This means genetic
variance in the progeny generation is reduced, as are h2 and selection response (see
p203, Falconer)
...
Changes in the environment
...
What Responses Can We Achieve In Practice?
This table is condensed from Tables 1 to 4 of Charles Smith's 1948 paper "Rates of genetic
change in farm livestock", Research and Development in Agriculture, 1: 79-85
...
% of Mean per year
SHEEP
BEEF
PIGS
POULTRY
DAIRY
Growth
Lean %
Litter size
Growth
Lean %
Growth
Lean %
Litter size
Growth
Lean %
Egg Prodn
Milk yield
Predicted
responses
1
...
9
2
...
4
0
...
7
1
...
0
3
...
2
2
...
5
96
Experimental
programs
1
...
2
0
...
1(fat)
0
...
1
1
...
1
Commercial
programs
1
...
9
0
...
8 (index Gr+L%)
1
...
1
1
...
9
Realised responses have matched their predictions quite well
...
Commercial response in growth in beef and yield in dairy probably suffer from
excessive attention to conformation and type traits (which may be of some value in
themselves)
...
Crossing lines at limits may
permit further responses to selection
...
a) Due to fixation – all the best genes are fixed in homozygous form, with no variation left
...
The following example gives a case where the average effects of A1 and A2 are
equal despite A1 being the 'better' allele
...
Note the frequency of A1 is p =1/3
Average effect of A1:
A1 A1
p = 1/3
100
A1 A2
q = 2/3
120
Average effect of A2:
A2 A1
p = 1/3
120
A2 A2
q = 2/3
110
A2 A2
110
Redsults
113
...
333
2
...
For example, the extreme phenotypes foe
then selected trait may suffer high mortality and low fertility
...
Physiological or environmental limits are reached
...
K
...
Thorpe, G
...
L
...
2000
...
I
...
Livestock Production Science 63: 3954
...
K
...
Nitter, W
...
F
...
2000
...
II
...
Livestock Production Science 63: 55-63
...
By selecting only the best, we
obtain an increase of the genetic mean
...
However, there is generally more variation between breeds
...
The value of crossbreeding
1
...
g
...
2
...
Crossbred individual often exhibit heterosis
...
The
percentage increase in performance ranges about 0- 10% for growth traits and 5- 25% for
fertility traits
...
3
...
Crossbred dams can exhibit considerable heterosis in their ability to
raise many, fast growing, and viable offspring
...
Sire-Dam complementation
...
When a
large breed of sire is used the proportion of feed directed to growing animals is increase
and the production system benefits accordingly
...
Possibly cheap source of breeding animals
...
In Kenya, cast/cull for age Red Maasai ewes
are still good for crossing to Dorper rams to give first cross ewes which can act as prime
lamb dams
...
6
...
The genetic basis of heterosis
We need to know this to predict the value of untested genotypes
...
98
Genotype
Merit
=
Breed A
Breed B
Breed C
AxB
Ax (BxC)
Ax (AxB)
10
12
16
16
17
?
=
=
=
=
=
=
Average of
parental breeds
10
12
16
11
12
10
...
For this we need to know the genetic basis
of heterosis
...
Where the individual’s parents come from two different breeds, the individual
will carry a wider range of genes sampled from two breeds rather than just one
...
We would thus expect dominance to be a positive effect and there is much
evidence to support this
...
When we cross breeds, genes find themselves having to interact or ‘cooperate’ with
other genes which they are not used to
...
The dominance model of heterosis
If heterosis were due to ‘breed dominance ‘alone:
Breed dominance is greatest when all loci consist of two genes derived from different breeds
as in a first cross or F1 cross
...
The idealized example here is milk yield per lactation, viewed as
the product of yield per day and days lactation
...
However, due to the multiplicative derivation of the total milk
yield, there is notable heterosis in both crosses, with the F2 expressing as much as the F1 due
to additive inheritance of the two sub-traits
...
We generally have little
information on this phenomenon, and it is common practice to assume breed dominance in
the mechanism underlying heterosis
...
101
16
CROSSBREEDING- PART 2
...
The
proportion of F1 heterosis (i
...
the coefficient of dominance) expressed in a synthetic at
equilibrium (i
...
once well mixed) is found by subtracting the square of each breed’s
contribution from one
...
332 – 0
...
332 = 0
...
In optimum
synthetics, the proportion of genes from each breed is determined in a way that maximizes
performance – more use of better breeds improves additive value, but at some compromise in
heterosis expression
...
Milking Zebu
Sahiwal, Red Sindhi
Brangus
Brahman, Angus
Murray Grey
Roan Shorthorn, Angus
Santa Getrudis
Brahman, Shorthorn, others
Polwarth
Warridale
Corriedale
Kenya Dual Purpose
Goat
Dorper
Merino, Lincoln
Border Leicester, Merino
Merino, Lincoln
Toggenburg, Anglo-Nubian,
Gall and Small East African
Dorset, Persian fat- tail
Rotations
Here a different pure breed sire is used each generation, rotating between n breeds
...
The following describes a 2- breed rotation:
PERIOIC ROTATIONS: Here the pattern of rotation gives different emphasis to different
breeds
...
gives more emphasis to
breed A
...
ROTA – TERMINALS: Here a terminal sire is put over a dam which is produced in a
rotational crossing programme
...
Hypothetical values
of the following parameters:
Direct additive effects Ad1, Ad2 and Ad3
...
Maternal additive effects Am1, Am2 and Am3
...
Note that these effects add to zero- they
describe the relative maternal performance of each pure breed
...
this is the effect of heterosis in crossbred individuals, when fully
expressed as in an F1 cross
...
this is the effect of heterosis due to crossbreeding in the dam,
when fully expressed as in an F1 dam
...
Adding the products gives the prediction of yearling weight, MERIT in
the last column
...
EFFECTS
Ad1
Ad2
Ad3
Am1 Am2 Am3 Dd
Dm MERIT
VALUES (KG)
300 280 260 -6
-1
+7
20
10
Breed 1
1
0
0
1
0
0
0
0
294
...
0
Breed3
0
0
1
0
0
1
0
0
267
...
0
Best 3Brd-X (1x23) ½
¼
¼
0
½
½
1
1
318
...
75 ¼
0
½
½
0
½
1
311
...
5
Synthetics (1, 2, 3)
0
...
33 0
...
33 0
...
33 0
...
67 300
...
63 0
...
63 0
...
47 0
...
4
Synthetics (1, 2, 3)
0
...
31 0
...
57 0
...
12 0
...
56 303
...
67 0
...
5
(1, 2, 3)
0
...
33 0
...
33 0
...
33 0
...
86 305
...
To estimate the values (b) from merit (Y) use the least squares approach
∧
β = ( X X)
'
−1
X ' Y Where X is the matrix formed by the body of this table
...
5
286
...
5 Kg and Am2 = 2
...
This alters the values of Ad and Am
effects compares to the previous example which used a third breed
...
Additive direct effects:
Breed 1 MERIT = Ad1 + Am1 = 294 à Ad1 = 294- (-2
...
5
Breed 2 MERIT = Ad2 + Am2 =279 à Ad2 = 279 – (+2
...
5
104
Predicted merit of backcross 1x (12)
(coefficients from previous page):
0
...
375 + 69
...
25) + 1
...
5 Kg
Note this is the same as in the table on the previous page
Which Crossing System to Adopt (If Any)?
PUREBREED
F1 CROSS
3 BREED CROSS
4 BREED CROSS
BACKCROSS
ROTATIONAL CROSSES
OPEN OR CLOSED
SYNTHETICS
When no cross is better
...
When both direct and maternal heterosis are important
...
When only 2 good parental breeds are available and/or
when direct heterosis is not important
...
When both males and females are too expensive
...
The best possible system for maximum genetic merit is always a fully structured system,
with a short pedigree back to purebreds on both sire and dam sides
...
g
...
However, we usually find that such systems are the most
expensive to run
...
High fecundity reduces the relative cost of breeding units dedicated to generating
crossbred parents, making highly structured systems more viable:
Industry
Fecundity
Typical crossbreeding systems
Poultry
Highest
4- breed crosses
Pigs
Higher
3-breed crosses; backcrosses
Meat sheep
High
3- breed crosses
Wool sheep
Medium
Purebred*
Dairy
Low
Purebred*
Temperate beef
Lower
Rotations; composites
Tropical beef
Lowest
Composites
*
Wool sheep and dairy industries are exceptions due to availability of an outstanding pure
breed in each
...
) and breeds, as well as within flocks
...
It is not worth including them all in a breeding
program due to measurement costs, recording costs, and lack of proper control
...
Illustrations of closed and open nucleus breeding schemes
...
In
reality, there is usually a fair bit of migration between different flocks and herds in the top one
or two tiers
...
Here are some key properties of closed schemes:
1
...
2
...
106
3
...
Figure 2
...
The base lags about 2 generations behind the
nucleus
...
Opening the nucleus will give more sustained returns from selection in the base
...
This is most true for animals of low fecundity, such as ewes
...
This pushes the nucleus to progress more quickly and this benefits the whole
scheme as the base will move as fast as the nucleus after things have settled down
...
Different measurement strategies in nucleus and base
A major use of nucleus schemes is to avoid or reduce measurement costs in lower tiers
...
As rAA increases, σ A
increases ( σ A = rAA σ A ), and the distribution of EBV widen as shown in figure in the next
page
...
If the only information available is animal’s
tag numbers, then there is no power to
identify superior (or inferior) animals and
there is no variation in EBV’s
...
Animals of exceptional breeding
value are difficult to identify as the most
important trait is not measured
...
Information from relatives also helps here, as
the distribution at the bottom which uses
BLUP genetic evaluation
...
This in turn affects the average superiority of parents, migration rates and
overall response selection
...
There can be some increased lag between the tiers, but this is compensated
for quite quickly
...
Assortative mating (mating best to best)
gives extra response due to increased genetic variation in the next generation
...
However, the open nucleus
design has an added advantage- knowing the source of an animal (the tier of its birth) tells us
something about its likely genetic merit even if we do not know its pedigree or its
measurements:
Because each tier contains many animals, tier means for given traits constitute high
quality information – they are highly heritable
...
If we add this to the flock- of-birth genetic means we get simple estimates of
across-the flock EBV’s
...
Thus, in the
108
absence of normal pedigree information, we get an added boost in overall selection
accuracy through use of this crude but effective “family” information
...
This means that we could capture all the benefits of an open nucleus
scheme by using the pedigree information to select on BLUP EBVs, and mating assortatively
...
Geographically diffused nucleus schemes
As suggested in the last section, we can enjoy the full benefits of an open nucleus scheme
without nominating one flock or herd to be the nucleus
...
This
relies on good pedigree information without which lack the useful information about the tier
of birth that a simple open nucleus scheme manages to exploit
...
The classical fourpathway dairy breeding design, is in fact a geographically diffused nucleus design
...
Also the dairy industry is relatively advanced in taking up
new technologies, such as use of EBVs, A
...
It is
therefore an interesting case to study when it comes to the effect of new technologies on
breeding program design
...
n
-Widespread use of A
...
I
...
I, i
...
using sires across many herds,
provides a good structure for genetic evaluation
...
Of all livestock industries, the use of information provided
by EBVs is mostly accepted in dairy
...
The two main reasons for a special design is that:n
n
-many more females are needed for breeding than males
...
Progeny testing is expensive and obviously not all males born in the dairy population are
tested
...
On the other hand, most of the newborn females are needed
as replacement and their parents can not be so highly selected
...
1971
...
Animal Production 13: 401-411
...
W
...
Open nucleus breeding schems
...
24: 287-305
...
K
...
Nitter
...
Developing breeding schemes for pasture based dairy
production systems in Kenya
...
Derivation of economic values using profit functions
...
Kahi, A
...
, G
...
F
...
2004
...
II
...
Livestock Production Science 88:179-192
...
S
...
A
...
and Baker, R
...
Economic values for traits of meat
sheep in areas of the tropics with medium to high production potential
...
ANIMAL BREEDING = WHERE TO GO? + HOW TO GET THERE?
Breeding objectives
Breeding objectives are all about where to go
...
Maximise KSh/hectare or minimise cost per unit product – these are more appropriate as they
consider changes in resource utilisation which accommodate genetic change
...
Unfortunately these approaches are much more difficult to handle
...
They should be constructed in a manner which allows them to
play an appropriate role, together with parameters such as heritability and correlations, as part
of a genetic evaluation system, in order to facilitate ranking of animals on genetic merit and
implementation of effective breeding program design
...
These
economic weightings can be used directly to help evaluate different breeds and crosses, or,
more commonly, they can be used in conjunction with generic parameters and knowledge of
population structure to rank animals on an index of genetic merit in monetary units
...
For example, lean percentage may be a
breeding objective, and ultrasonically measured back fat thickness a selection criterion
...
The economically rational approach
111
The classic approach to calculating economic weightings is economically rationale – it takes
no account of genetic parameters
...
These
difficulties can be handled appropriately at the genetic evaluation phase
...
A simple example
A very simple breeding objective is presented here
...
The key tactical objective of a selection programme is
to choose animals of high breeding value to be used as parents
...
The breeding objective is simply a multi-trait
breeding value, with each trait weighted by a relative economic weight, for example:
Breeding objective:
Units = KSh
6 x fleece weight
KSh /Kg
...
µ
In order to combine different traits into such a single soccer they have to be converted to a
common scale
...
The economic weights
in this simple example are taken to have been calculated from market prices of KSh 6 per
kilogram of wool and - KSh1 per micron for an average fleece
...
Note that these weights involved no
consideration of genetic parameters
...
Choice of this basis can have an
important influence on the consequences of using the breeding objective
...
A less simple basis is ‘dollars per breeding ewe per year’, which accommodates both
production and reproduction traits
...
20 per kg per breeding ewe per year x clean fleece weight
+ KSh -120 per micron per breeding ewe per year x Fibre diameter
+ KSh 7
...
20 x 150 = KSh1,080 per year
...
The economic weight for an increase of one lamb weaned is more difficult to
calculate, due to expression via progeny, but in this case it is the same as for clean fleece
weight
...
112
Economic weights calculate on a ‘KSh per head shorn’ or ‘KSh per breeding ewe per year’
basis suffer a potentially important drawback
...
As an example consider two
breeds of meat sheep:
Breed
Small
Large
Value of weight at
slaughter
KSh200
KSh350
Value of food
consumed
KSh100
KSh200
Profit per
head
KSh100
KSh150
KSh
efficiency
2:1
1
...
However, a breeding objective based on ‘dollars per hectare’ would target the small breed
...
Economic values can be calculated from several different perspectives e
...
with the aim of
maximising the profitability of an enterprise for an individual producer, or with the aim of
improving the efficiency of a national livestock industry
...
As an extreme example, consider the two breeds in the
figure below
...
Also, if body weight
achieved for a given level of accumulated food intake is taken as a key objective trait, then the
small breed cannot compete
...
However, if we consider two small animals as a single large individual, then they will
compete equally well on both these objective traits
...
But
even this is an illusion-larger animal consume less per kilogram of body weight (Taylor,
113
1980), such that fixed food resources can carry more kilograms of large animals, and the net
result is that the two breed sizes are of equal value (Kinghorn, 1985)
...
Some traits of economic importance in the livestock industry:
Meat production
1
...
2
...
Aim at desired fat cover
n
Downward anywhere : pigs, cattle, sheep and poultry
n
market demand
n
FCE due to high energy cost of fat)
n
Major problems with buying fat animals on the hoof
...
Aim at increased lean per cent
n
Difficult to do directly – scanner in some developed countries
n
Sib testing in pigs
n
Progeny testing in sheep (e
...
in Norway)
n
Generally via dressing percent and fat cover score
5
...
Other traits
n
Weaning rate (major importance)
n
Many components traits – fertility, fecundity, mothering ability, survival
n
Adaptation to production system (especially in tropics) disease resistance – ticks, worms,
fleece rot
n
Suitable conformation for extensive management (ranginess etc
...
Milk yield – Increase
2
...
FCE to milk – not in evidence due to costs of recording food intake
4
...
Fertility traits – not as important as for meat due to ongoing harvesting
...
Disease resistance – e
...
mastitis needs good recording as in Norway, tropical diseases
Lymphocytes cell counts in Sweden
7
...
Wool production
1
...
C
...
2
...
Modern processing techniques
require many small fibres in yarns to minimise co-incidence of weak spots and therefore
breaks on automated machinery
...
Pigmentation – avoid black fibre, ginger spots
...
Length and strength – coming into objective marketing?
5
...
6
...
Adaptation to production system
n
Resistance to fleece rot
...
n
Low water requirement
Egg production
1
...
High egg weight (but genetic correlation with egg number = -0
...
Age at first egg – younger gives less resource input
...
Food conversion efficiency: food → eggs
5
...
Disease resistance - (expose and select)
7
...
Molecular genetics techniques aim to locate and exploit gene loci which have a major effect
on quantitative traits (hence QTL - Quantitative Trait Loci)
...
EBVs are best calculated using BLUP, meaning that they are based on
performance information of several traits from the individual animal and its relatives
...
Although the idea of genetic selection is to improve the genes in our breeding animals, we
actually never really observe those genes
...
The strategy makes sense, since we select based on what we actually want to
improve
...
For this, reason selection for the best genes based on animal
performance alone can never reach perfect 100% accuracy
...
But this is expensive for some traits (e
...
for traits related to
carcass quality), and we have to wait several years before progeny test can be used
...
The top drawing gives the true allelic values at the different
genes affecting body weight, the bottom situation illustrates what would be observed if QTL could be identified
in addition to phenotype, adding significant information about true genotype
117
Successful breeding programs are characterised by selecting animal at a young age, leading to
short generation intervals and faster genetic improvement per year
...
Genetic Markers
Genetic markers are loci, which are easily genotyped (i
...
alleles each individual carries can
be determined easily)
...
Genetic markers that have been used a lot in the past include blood groups and
polymorphic enzymes
...
Two of these are described briefly here
...
1
...
Eco R1 cuts at the 'recognition sequence' GAATTC)
...
Also mutation to give a
new recognition sequence gives a pair of shorter fragments
...
Using a battery of restriction endonucleases, thousand
of RFLP markers can be generated
...
Each microsatelite locus is recognised or targeted
by its primers - the two unique sequences adjacent to the repeating region
...
there can be
many different lengths of the repeat region
...
118
Molecular markers that are closely linked to desirable traits would be very useful to animal
breeders, especially markers for traits which are only expressed at maturity or at slaughter
(e
...
meat tenderness) or traits that are expressed in only one sex (milk yield)
...
Gel Electrophoresis
The DNA which has been cleaved with restriction enzymes is separated by electrophoresis
...
This diagram represents the electrophoretic
gel in which microsatellites DNA fragments
of different size (different alleles) have been
run
...
In this example there are four alleles
and of course each individual can carry only
two! The genotypes of the four animals are
deduced to be bc, ad, ac and bd, respectively
...
This model of a
genetic map shows the location of 8 markers (called here A-H) along the chromosome
...
Distances in genetic maps are measured in centimorgans (cM,
about 1 million base pairs) (in other words, a genetic map is a set of genetic markers that
have been assigned to particular chromosomal locations based on linkage analysis
...
The genetic map describes the behaviour of genetic markers as they are transmitted
from one generation to another ie whether markers tend to segregate together during meiosis
because the markers are located close together on the same chromosome)
...
DNA
is snipped into fragments by the action of restriction enzymes, then cloned and stored in a
variety of forms such as plasmids in bacteria
...
(in other words, the physical map of an organism describes the actual structure of the genetic
material, not its behaviour
...
The physical map is measured in nucleotides or base pairs,
because DNA is a chain of base pairs
...
A physical map is measured in base pairs
If a physical map, linked to the genetic map is available, then the gene that is responsible for
the trait under consideration can be isolated
...
However, isolation of a gene by this
method is extremely laborious and time consuming and the production of transgenic animals
is not considered acceptable by many individuals
...
Molecular genetics techniques aim to locate and exploit genes, which have a major effect on
quantitative traits (hence QTL - Quantitative trait loci)
...
It could improve the efficacy of selective breeding, especially for traits with low
heritability or that can only be measured in one sex
...
Transgenic technology might be applied to quantitative traits
...
In medicine, the identification of alleles causing predisposition to common
multifactorial disease, such as heart disease or diabetes, could lead to improved
methods of prevention
...
Quantitative genetic theory will be made more realistic when the numbers and
properties of the genes are known and the more realistic theories will improve our
understanding of evolution
...
There are two types of 'gene
searching'
...
Here are some examples
- The Boorola and Inverdale gene in sheep (giving high fecundity)
- The N gene in sheep (giving carpet wool in Drysdales)
- The Halothane gene in pigs (giving increased lean percent but also stress
susceptibility)
...
- The double muscling gene in cattle (givng increased muscle mass)
...
Searching for unknown QTL
Locating these major genes is much more difficult because we only have animals' phenotype
to detect presence or absence of a QTL
...
These include by:
1
...
Backcrossing with selection
3
...
Heterogeneity of variance
5
...
Complex segregation analysis
...
For more on QTL please refer to the last chapter of, D
...
Falconer and T
...
C
...
1996
...
Fourth Edition
...
A copy of this last
chapter can be provided
...
Some traits are controlled by single genes (e
...
hair colour) but most traits of economic importance are quantitative traits that most likely are
controlled by a fairly large number of genes
...
Such genes can be called major genes located at QTLs
...
Following the inheritance at such QTL might
assist in selection
...
The figure below shows the
principle of inheritance of a marker and a linked QTL
...
The last is really what we want to know because of its effect on
economically important traits
...
In the example, the
M marker allele is linked to the G in the sire
...
As shown in the figure above, there are 4 types of progeny
...
The sire will provide them with either an M- or an m- allele
and either G or g
...
However, in 10% of the cases while the sire produces gametes, there will be a recombination
between the two loci, and animals that inherited an M-allele from the father have received a gallele rather than a Q-allele
...
Animals may be selected based on the marker information only
...
Usually we imagine that
there may be a major gene/QTL, but there are many other important genes, not covered by the
marker
...
The first aims to get the good QTL, the second aims at getting also good 'other
genes'
...
Direct markers
The easy scenario is when the marker allele M and the QTL-allele G are always together
...
Such a direct marker is very convenient, because the marker genotype
will directly inform us about the QTL genotype
...
Linked markers
Linked markers require some ongoing activity in trait measurement and pedigree recording
which makes them less appealing than direct markers
...
For a randomly chosen animal in the population, we have no
clue whether one or another maker allele is associated with a preferable QTL allele
...
But this information is only useful for this particular sire, and its family!
With linked markers, the information on which marker genotype is linked to the positive QTL
allele is family specific
...
In
addition, it will in most cases be useful to also genotype dams, since otherwise it will be
unclear which marker allele an animal received from its sire
...
It may be obvious that there is a considerable need to gather trait and pedigree information for
use of linked genetic markers because for each family the linkage phase between marker and
QTL needs to be established
...
Furthermore, the need for large half-sib
families is also reduced over time, as marker and trait information is gathered on a deeper
pedigree
...
Once a linkage phase has been established for a family, as is the case for a tested sire, trait
measurement is not required for additional progeny of that sire
...
In spite of this, the genotype of animals for specific genes cannot be given with
certainty in the case of indirect markers
...
Selecting for QTL genotypes
Where a direct marker (DNA-test) exists for a QTL, we can use Genotype Assisted Selection
(GAS)
...
In either case, the aim is to determine QTL genotypes to assist selection decisions,
either to increasing the frequency of favourable QTL alleles, or targeting their introgression
into other lines
...
- Where the trait(s) of interest cannot be measured on one sex, marker information gives
a basis to rank animals of that sex
...
- If a trait is difficult to measure or requires sacrifice (as with many carcass traits)
marker information can be used instead
...
P
...
The application of biotechnologies to enhance animal
production in different farming systems
...
123
20
APPENDIX
124
21
SOME USEFUL FORMULAE
SIMPLE STATISTICS
Note the convention: x = X − X and y = Y − Y
Variance: Vx =
∑x
2
n −1
=
∑ (x − x)
=
n −1
Standard deviation: σx =
Variance of mean: σx =
2
Note that: τ X,Y = b
cov x
...
Y - nXY
n -1
SINGLE GENES
Population mean:p
...
g + q
...
Plus any covariances if
they exist, and they generally don’t
...
e
...
Also, h 2 = A
Vp
BREEDING VALUE, A
A simple estimate of breeding value: E
...
V
...
Vp
VA
...
ioverall = (im + if)/2
Generation interval: Lm (and Lf) is the average age from birth of male (and female) parents
when their progeny are born
...
rA (noting i x = i y )
hp
Variance of phenotypes correlated by regression: VPcorr = (1 − r 2 )Vp (where r is the correlation
between phenotype and the correction variable)
...
Dev
...
VA = 4σ 2 s S for sires
σ 2s =
mean square between - mean square within
number per family
127
1 / 4V A
= 1 / 4h 2
VP
Intra class correlation for half sibs:
4σ 2 s
= 4t HS
σ 2s + σ 2w
1 / 2V A + 1 / 4VD + VEg
h 2 HS =
t FS =
h 2 FS =
VP
≈ 1 / 2h 2
2σ 2 P
= 2t FS
σ 2B + σ 2w
VP / 2 + 2VEg
h 2 from FS is biased upwards by
VP
rA =
cov A
σ A2
...
T
...
T
...
128
( 1 )n (1+ FA )
2
t
⎡
1 ⎤
Inbreeding coefficient from population size: F = 1− ⎢1−
⎥
...
129