PBG 650 Advanced Plant Breeding
Module 3:
Changes in gene frequency due to selection
Systematic changes in gene frequency
•
Predictable in both magnitude and direction
– Migration
– Mutation
– Selection
•
Quantities of interest
– Δq = q1 – q0
– qt
– q at equilibrium (when Δq = 0)
• Multiple forces at work (e.g., mutation and selection)
• Important in nature (maybe less so in breeding populations)
Falconer & Mackay, Chapter 2
Selection
Individuals differ in their contribution of genes to the
next generation
 fitness = adaptive value = selective value
Types of selection
•
Viability - the probability of survival through each
reproductive stage
– Darwin’s natural selection
•
Fertility – number of offspring produced
– may work in opposition to survival
– Darwin’s sexual selection
Components of fitness
Zygote
viability
(survival)
Adult
Artificial selection
mating success
fertility (capability to have offspring)
fecundity (#gametes)
Gamete
viability
Zygote
•
fitness is defined in the context of the environment in
which individuals live, mate, and reproduce
Relative fitness
•
•
Absolute fitness refers to the number of gametes
transmitted by a zygote, but this is seldom observed
directly
We generally make observations on zygotes, so we
measure relative fitness in comparison to either the
average for the population or the best genotype
Genotype
Fitness
A1A1
A1A2
A2A2
W11
1
W11
W12
 1  hs
W11
W22
 1 s
W11
s = coefficient of selection
Selection
• To quantify fitness, we have to consider the
degree of dominance with respect to fitness
– may not be the same as the dominance with
respect to the expression of the primary trait
controlled by the gene
W12
 1  hs
Relative fitness of A1A2
W11
s is the selection coefficient
h is the degree of dominance
When h = 0
When h = 1
W12 = W11 (A1 is completely dominant)
W12 = W22 (A2 is completely dominant)
Degree of Dominance for Fitness
A2A2
A1A2
A1A1
1-s
1-(1/2)s
1
no dominance
A2A2
A1A2
A1A1
1-s
1-hs
1
partial dominance
complete dominance
A2A2
A1A2
A1A1
1-s
1
A2A2
A1A1
1-s2
1-s1
A1A2
overdominance
fitness
1
Selection against a recessive gene
Genotype
Initial frequencies
Fitness
From gametes
A 1A 1
p2
1
p2
A 1A 2
2pq
1
2pq
A 2A 2
q2
1-s
q2(1-s)
Total
1
1-sq2
q 2 1  s   pq q 2 1  s   1  q q q  sq 2
q1 


2
2
1  sq
1  sq
1  sq 2
q  sq 2
sq 2 (1  q )
q  q1  q 
q  
2
1  sq
1  sq 2
Genetic load = proportion of the population that does not reproduce
due to presence of a gene i.e., the reduction in fitness
Selection against a recessive lethal - example
•
What will the frequency of the recessive allele be
after t generations?
s=1
q0
q  sq 2 q  q 2
q(1  q )
q1 



2
2
1  sq
1 q
(1  q )(1  q ) 1  q0
q0
qt 
1  tq0
1 1
t 
qt q0
1
1
to go from q=0.20  0.01 t 

 105 generations
0.01 0.20
What could a breeder do to speed up the process?
Change in gene frequency with selection
no dominance
partial dominance
complete dominance of A1
selection against A2
complete dominance of A1
selection against A1
overdominance
Falconer & Mackay, pg 28
Change of gene frequency due to selection
Complete Dominance
s=0.20
(-)=selection against A2
(+)=selection for A2
Falconer & Mackay, pg 30
q
Selection for a favorable allele
For the case of s = 0.5, p0 = 0.05
Haldane’s Sieve: In nature, favorable alleles tend to be dominant
Direction of selection
Other possibilities:
• Frequency dependent selection
• Multiple peak epistasis
Which types of selection are common in plant breeding?
http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/E/Evolution.html#Fitness