Lecture 7: Introduction
to Selection
January 31, 2014
Last Time
Effects of inbreeding on heterozygosity
and genetic diversity
Estimating inbreeding coefficients from
pedigrees
Mixed mating systems
Inbreeding equilibrium
Introduction to selection
Today
Inbreeding and selection:
inbreeding depression
The basic selection model
Dominance and selection
Relatedness in Natural Populations
Number of matings
 White-toothed shrew
inbreeding (Crocidura
russula) (Duarte et al.
2003, Evol. 57:638-645)
 Breeding pairs defend
territory
 Some female offspring
disperse away from
parents
 12 microsatellite loci used
to calculate relatedness in
population and determine
parentage
 17% of matings from
inbreeding
Offspring Heterozygosity
 How much inbreeding
occurs?
Relatedness
Parental Relatedness
What will be the long-term effects of inbreeding
on this shrew population?
Inbreeding and allele frequency
Inbreeding alone does not alter
allele frequencies
Yet in real populations, frequencies
DO change when inbreeding occurs
What causes allele frequency
change?
Natural Selection
Non-random and differential
reproduction of genotypes
Preserve favorable variants
Exclude nonfavorable variants
Primary driving force behind adaptive
evolution of quantitative traits
Fitness
 Very specific meaning in evolutionary biology:
 Relative competitive ability of a given genotype
 Usually quantified as the average number of
surviving progeny of one genotype compared to a
competing genotype, or the relative contribution
of one genotype to the next generation
 Heritable variation is the primary focus
 Extremely difficult to measure in practice. Often
look at fitness components
 Consider only survival, assume fecundity is equal
Inbreeding, Heterozygosity, and Fitness
 Inbreeding reduces heterozygosity on genome-wide
scale
 Heterozygosity of individual can be index of extent of
inbreeding
 Multilocus Heterozygosity:
 Proportion of loci for which individual is heterozygous
 Often shows relationship with fitness
Simulated
Number of heterozygous loci
Deng and Fu 1998 Genetics 148:1333
Observed
Correlation Between Heterozygosity and Fitness
Reed and Frankham 2003 Cons Biol 17:230
Inbreeding Depression
 Reduced fitness of inbred
individuals compared to
outcrossed individuals
terrierman.com/inbredthinking.htm
notexactlyrocketscience.wordpress.com
 Negative correlation
between fitness and
inbreeding coefficient
observed in wide variety of
organisms
 Inbreeding depression often
more prevalent under
stressful conditions
Lynch and Walsh 1998
www.myrmecos.net/
wikipedia
Mechanisms of Inbreeding Depression
 Two major hypotheses: Partial Dominance and
Overdominance
 Partial Dominance (really a misnomer)
 Inbreeding depression is due to exposure of
recessive deleterious alleles
 Overdominance
 Inherent advantage of heterozygosity
 Enhanced fitness of heterozygote due to pleiotropy
(one gene affects multiple traits): differentiation
of allele functions
 Bypass homeostasis/regulation
What about long-term effects on the shrew?
 Fecundity (measured by number
of offspring weaned) was not
affected by relatedness
between mating pairs or
heterozygosity of individuals
 No evidence of inbreeding
depression in this species
 Why not?
How do we quantify the effects of natural
selection on allele frequencies over time?
Can we predict and model evolution?
Relative Fitness of Diploids
 Consider a population of newborns with variable
survival among three genotypes:
N
A1A1
A1A2
A2A2
100
100
100
Survival
80
56
40
 New parameter: ω, relative fitness (assuming
equal fecundity of genotypes in this case)
 Define ω=1 for best performer; others are
ratios relative to best performer:
N11s
N 22 s
80
40
Where N
is number of A A
offspring surviving after selection in
N11 100
N 22 100
11 

 1 22 

 0.5
current generation
N Ms
80
N Ms
80
And N is the best-performing genotype
100
100
NM
NM
11s
M
1
1
Average Fitness
 Use genotype frequencies to calculate weighted
fitness for entire population
ω
A1A1
A1A2
A2A2
1
0.7
0.5
ω = D(ω11) + H(ω12) + R(ω22)
ω = (100/300)(1) + (100/300)(0.7) + (100/300)(0.5)
= 0.733
 When fitness varies among genotypes, average
fitness of the population is less than 1
Frequency After Selection
D’ = D(ω11)/ω = (0.33)(1)/0.733 = 0.45
H’ = H(ω12)/ω = (0.33)(0.7)/0.733 = 0.32
R’ = R(ω22)/ω = (0.33)(0.5)/0.733 = 0.23
 Selection causes increase in more fit genotype and
reduction in less fit genotypes
 Allele Frequency Change:
q = (N22 + N12/2)/N = (100 + 100/2)/300 = 0.5
q’ = (40+56/2)/176 = 0.39
Δq = q’ – q = 0.39 – 0.5 = -0.11
Over time, what will
happen to p and q in this
population?
What is Δp in the
previous example?
Starting from Allele Frequencies
A1A1
A1A2
A2A2
freq0
p2
2pq
q2
ω
ω11
ω12
ω22
freq1
p2 ω11/ω
2pq ω12/ω
q2 ω22/ω
ω = p2(ω11) + 2pq(ω12) + q2(ω22)
q’ = q2ω22+pqω12
ω
Change in Allele Frequencies due to
Selection (i.e., evolution)
q2ω22+pqω12 - qω
q2ω22+pqω12
- q =
q’ - q =
ω
ω
Simplifies to:
Δq =pq[q(ω22- ω12) - p(ω11 – ω12)]
ω
See p. 118 in your text for derivation
“The single most important equation in all of
population genetics and evolution!”
Gillespie 2004, p. 62
Fitness effects of individual alleles
Δq =pq[q(ω22 – ω12) - p(ω11- ω12)]
ω
 Effects of substituting one allele for another
 Conceptually, compare fitness of homozygote to
heterozygote
 Rate of change inversely proportional to mean
fitness of population: allele frequencies don’t
change much in a fit population!
 Marginal fitness: the effects of an individual
allele on fitness (the average fitness genotypes
containing that allele)
Incorporating Selection and Dominance
Selection Coefficient (s)
 Measure of the relative fitness of one homozygote compared
to another.
 ω11 = 1 and ω22 = 1-s
 s ranges 0 to 1 in most cases (more fit allele always A1 by
convention)
Heterozygous Effect (level of
dominance) (h)
 Measure of the fitness of the heterozygote relative to the
selective difference between homozygotes
 ω12 = 1 - hs
Heterozygous Effect
A1A1
Relative Fitness (ω)
Relative Fitness (hs)
ω11
1
h = 0, A1 dominant, A2 recessive
h = 1, A2 dominant, A1 recessive
0 < h < 1, incomplete dominance
h = 0.5, additivity
h < 0, overdominance
h > 1, underdominance
A1A2
A2A2
ω12
ω22
1-hs
1-s
Putting it all together
A1A1
Relative Fitness (ω)
ω11
Relative Fitness (hs)
1
A1A2
ω12
ω22
1-hs
1-s
Δq =pq[q(ω22 – ω12) - p(ω11- ω12)]
Reduces to:
ω
Δq =-pqs[ph + q(1-h)]
1-2pqhs-q2s
A2A2
Modes of Selection on Single Loci
 Directional – One homozygous genotype
has the highest fitness
 Purifying selection AND
Darwinian/positive/adaptive selection
1
0.8
ω
0.6
0.4
0.2
0
 Depends on your perspective!
AAA
1A1
aa
AAa
1A2 A2A2
AAA
1A1
aa
AAa
1A2 A2A2
AAA
1A1
AAa1A2 A2aaA2
 0 ≤ h ≤ 1
1
 Overdominance – Heterozygous
genotype has the highest fitness
(balancing selection)
0.8
ω
 Underdominance – The heterozygous
h>1, (1-hs) < (1 – s) < 1 for s > 0
0.4
0.2
0
h<0, 1-hs > 1
genotypes has the lowest fitness
(diversifying selection)
0.6
1
0.8
ω
0.6
0.4
0.2
0
Directional Selection
Δq =-pqs[ph + q(1-h)]
1-2pqhs-q2s
0 ≤ h ≤ 1
q
Δq
0
0.5
q
1
h=0.5, s=0.1
Time
Lethal Recessives
A1A1
Relative Fitness (ω)
ω11
Relative Fitness (hs)
1
A1A2
A2A2
ω12
ω22
1-hs
1-s
For completely recessive case, h=0
What is s for lethal alleles?
1
0.8
0.6
ω
0.4
0.2
0
A1 1
1A
AAA11A
1
A22
A
AAA111A
2
AA22
AAA222A
2