1. Lecture 5 Artificial Selection
R = h2 S

2. Applications of Artificial Selection
Applications in agriculture and forestry
Creation of model systems of human diseases and disorders
Construction of genetically divergent lines for QTL mapping and gene expression (microarray) analysis
Inferences about numbers of loci, effects and frequencies
Evolutionary inferences: correlated characters, effects on fitness, long-term response, effect of mutations

3. Response to Selection
Selection can change the distribution of phenotypes, and we typically measure this by changes in mean
This is a within-generation change
Selection can also change the distribution of breeding values
This is the response to selection, the change in the trait in the next generation (the between-generation change)

4. The Selection Differential and the Response to Selection
The selection differential S measures the within-generation change in the mean
S = m* - m
The response R is the between-generation change in the mean
R(t) = m(t+1) - m(t)

5. Truncation selection
uppermost fraction
p chosen
Within-generation
change
Between-generation
change

6. The Breeders’ Equation: Translating S into R
Recall the regression of offspring value on midparent value y O = π P + h 2 f m ∂ ( )
Averaging over the selected midparents,
E[ (Pf + Pm)/2 ] = m*,
E[ yo - m ] = h2 ( m* - m ) = h2 S
Likewise, averaging over the regression gives
Since E[ yo - m ] is the change in the offspring mean, it
represents the response to selection, giving:
R = h2 S
The Breeders’ Equation

7. If males and females subjected to differing amounts of selection,
Note that no matter how strong S, if h2 is small, the response is small
S is a measure of selection, R the actual response. One can get lots of selection but no response
If offspring are asexual clones of their parents, the breeders’ equation becomes
R = H2 S
If males and females subjected to differing amounts of selection,
S = (Sf + Sm)/2
An Example: Selection on seed number in plants -- pollination (males) is random, so that S = Sf/2

8. Response over multiple generations
Strictly speaking, the breeders’ equation only holds for predicting a single generation of response from an unselected base population
Practically speaking, the breeders’ equation is usually pretty good for 5-10 generations
The validity for an initial h2 predicting response over several generations depends on:
The reliability of the initial h2 estimate
Absence of environmental change between generations
The absence of genetic change between the generation in which h2 was estimated and the generation in which selection is applied

9. The selection differential is a function of both
the phenotypic variance and the fraction selected
20% selected
Vp = 1, S = 1.4
50% selected
Vp = 4, S = 1.6
20% selected
Vp = 4, S = 2.8

10. The Selection Intensity, i
As the previous example shows, populations with the
same selection differential (S) may experience very
different amounts of selection
The selection intensity i provided a suitable measure
for comparisons between populations, i = S p V P æ
One important use of i is that for a normally-distributed
trait under truncation selection, the fraction saved p
determines i, i ' : 8 + 4 1 l n p ∂ ( )

11. Selection Intensity Versions of the Breeders’ Equation= h 2 S æ p i
Expressed another way, R æ p = i h 2
Alternatively, R = i æ 2 A p

12. The Realized Heritability
Since R = h2 S, this suggests h2 = R/S, so that
the ratio of the observed response over the
observed differential provides an estimate of
the heritability, the realized heritability
Obvious definition for a single generation of response.
What about for multiple generations of response?
Cumulative selection response = sum of all responses R C ( t = i 1 ) X

13. R ( t ) = h S + e b h = R ( T ) S P b = S ( ) R
Cumulative selection differential = sum of the S’s S C ( t ) = 1 i X
(1) The Ratio Estimator for realized heritability
= total response/total differential, b h 2 r = R C ( T ) S
(2) The Regression Estimator --- the slope of the
Regression of cumulative response on cumulative differential P b = t S C ( ) R 2
Regression passes through the
origin (R=0 when S=0). Slope = R C ( t ) = h 2 r S + e

14. Note x axis is differential, NOT generations
Ratio estimator
= 17.4/56.9 = 0.292 60 \
Cumulative Differential 5 10 15 20
Cumulative Response
Slope = 0.270
= Regression
estimator
Note x axis is differential,
NOT generations

15. Gene frequency changes under selection
Genotype
A1A1
A1A2
A2A2
Fitnesses 1
1+s
1+2s
Additive fitnesses
Let q = freq(A2). The change in q from one
generation of selection is: q = s ( 1 ) + 2 ' w h e n j
< D
In finite population, genetic drift can overpower
selection. In particular, when 4 N e j s
< 1
drift overpowers the effects of selection

16. Strength of selection on a QTL
Have to translate from the effects on a trait under
selection to fitnesses on an underlying locus (or QTL)
Suppose the contributions to the trait are additive:
Genotype
A1A1
A1A2
A2A2
Contribution to
Character a 2a
For a trait under selection (with intensity i) and
phenotypic variance sP2, the induced fitnesses
are additive with s = i (a /sP )
Thus, drift overpowers
selection on the QTL when 4 N e j s = a i æ P
< 1

17. D ¢ q ' 2 ( 1 ° ) [ + h ] More generally Change in allele frequency:
Genotype
A1A1
A1A2
A2A2
Contribution to trait
a(1+k) 2a
Fitness 1
1+s(1+h)
1+2s
Change in allele frequency: D q ' 2 ( 1 ) [ + h ]
s = i (a /sP )
Selection coefficients for a QTL
h = k

18. Changes in the Variance under Selection
The infinitesimal model --- each locus has a very small
effect on the trait.
Under the infinitesimal, require many generations
for significant change in allele frequencies
However, can have significant change in genetic
variances due to selection creating linkage disequilibrium
With positive linkage disequilibrium, f(AB) > f(A)f(B),
so that AB gametes are more frequent
With negativve linkage disequilibrium, f(AB) < f(A)f(B),
so that AB gametes are less frequent
Under linkage equilibrium,
freq(AB gamete) = freq(A)freq(B)

19. ± æ = ° V ( 1 ) = + d V ( 1 ) = + d d = æ ° h ±
Changes in VA with disequilibrium
Starting from an unselected base population, a single
generation of selection generates a disequilibrium
contribution d to the additive variance
Under the infinitesimal model, disequilibrium only
changes the additive variance.
Additive genetic variance after
one generation of selection
Additive genetic variance in the
unselected base population. Often
called the additive genic variance
disequilibrium V A ( 1 ) = a + d
Changes in VA changes the phenotypic variance V P ( 1 ) = A + D E d h 2 ( 1 ) = V A P a + d d = æ 2 O P h 4 z
The amount diseqilibrium generated by a single generation
of selection is
Changes in VA and VP change the heritability
Within-generation change
in the variance
A decrease in the variance
generates d < 0 and hence
negative disequilibrium
An increase in the variance
generates d > 0 and hence
positive disequilibrium æ 2 z = *

20. A “Breeders’ Equation” for Changes in Variance
d(0) = 0 (starting with an unselected base population)
Within-generation
change in the variance
-- akin to S
New disequilibrium generated by
selection that is passed onto the
sext generation h 2 ( t ) = V A P a + d
Decay in previous disequilibrium from recombination
d(t+1) - d(t) measures the response in selection
on the variance (akin to R measuring the mean) d ( t + 1 ) = 2 h 4 æ z æ 2 z ( t ) = 1 k
Many forms of selection (e.g., truncation) satisfy
k > 0. Within-generation
reduction in variance.
negative disequilibrium, d < 0
k < 0. Within-generation
increase in variance.
positive disequilibrium, d > 0 d ( t + 1 ) = 2 k h 4 æ z