Transcript ppt
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