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Lecture 7: Evolution I
I. Population Genetics
A. Overview
Agents of Change
Mutation
N.S.
Recombination
- crossing over
- independent assortment
VARIATION
Sources of Variation
mutation
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
G. Hardy and W. Weinberg
1. Definitions
- Evolution: a change in the genetic structure of a population
- Population: a group of interbreeding organisms that share a common gene
pool; spatiotemporally and genetically defined
- Gene Pool: sum total of alleles held by individuals in a population
- Genetic structure: Gene array and Genotypic array
- Gene/Allele Frequency: % of alleles at a locus of a particular type
- Gene Array: % of all alleles at a locus: must sum to 1.
- Genotypic Frequency: % of individuals with a particular genotype
- Genotypic Array: % of all genotypes for loci considered; must = 1.
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
1. Definitions
2. Basic Computations
Individuals
AA
Aa
aa
70
80
50
(200)
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
1. Definitions
2. Basic Computations
AA
Aa
aa
Individuals
70
80
50
(200)
Genotypic
Array
70/200 =
0.35
80/200 = .40
50/200 =
0.25
=1
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
1. Definitions
2. Basic Computations
AA
Aa
aa
Individuals
70
80
50
(200)
Genotypic
Array
70/200 =
0.35
80/200 = .40
50/200 =
0.25
=1
''A' alleles
140
80
0
220/400 =
0.55
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
1. Definitions
2. Basic Computations
AA
Aa
aa
Individuals
70
80
50
(200)
Genotypic
Array
70/200 =
0.35
80/200 = .40
50/200 =
0.25
=1
''A' alleles
140
80
0
220/400 =
0.55
'a' alleles
0
80
100
180/400 =
0.45
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
1. Definitions
2. Basic Computations
- Determining the Gene Array from the Genotypic Array
a. f(A) = f(AA) + f(Aa)/2 = .35 + .4/2 = .35 + .2 = .55
b. f(a) = f(aa) + f(Aa)/2 = .25 + .4/2 = .25 + .2 = .45
KEY: The Gene Array CAN ALWAYS be computed from the genotypic array; the
process just counts alleles instead of genotypes. No assumptions are made when you do
this.
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
1. Goal:
Describe what the genetic structure of the population would be if there were
NO evolutionary change – if the population was in equilibrium.
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
1. Goal:
Describe what the genetic structure of the population would be if there were
NO evolutionary change – if the population was in equilibrium.
For a population’s genetic structure to remain static, the following must be
true:
- random mating
- no selection
- no mutation
- no migration
- the population must be infinitely large
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
2.Example:
Initial
genotypic freq.
Gene freq.
Genotypes, F1
Gene Freq's
Genotypes, F2
AA
Aa
aa
0.4
0.4
0.2
1.0
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
2.Example:
Initial
genotypic freq.
Gene freq.
Genotypes, F1
Gene Freq's
Genotypes, F2
AA
Aa
aa
0.4
0.4
0.2
f(A) = p = .4 + .4/2 = 0.6
1.0
f(a) = q = .2 + .4/2 = 0.4
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
2.Example:
Initial
genotypic freq.
Gene freq.
Genotypes, F1
Gene Freq's
Genotypes, F2
AA
Aa
aa
0.4
0.4
0.2
f(A) = p = .4 + .4/2 = 0.6
p2 = .36
2pq = .48
1.0
f(a) = q = .2 + .4/2 = 0.4
q2 = .16
= 1.00
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
2.Example:
Initial
genotypic freq.
Gene freq.
Genotypes, F1
Gene Freq's
Genotypes, F2
AA
Aa
aa
0.4
0.4
0.2
f(A) = p = .4 + .4/2 = 0.6
p2 = .36
2pq = .48
1.0
f(a) = q = .2 + .4/2 = 0.4
q2 = .16
= 1.00
f(A) = p = .36 + .48/2 = 0.6
f(a) = q = .16 + .48/2 = 0.4
p2 = .36
q2 = .16
2pq = .48
= 1.00
After one generation with these conditions, the population equilibrates
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
2.Example
3. Utility:
If no populations meets these conditions explicitly, how can it be useful?
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
2.Example
3. Utility:
If no populations meets these conditions explicitly, how can it be useful?
For comparison, like a “perfectly balanced coin”
Initial
genotypic freq.
Gene freq.
HWE
expections
AA
Aa
aa
0.5
0.2
0.3
f(A) = p = .5 + .2/2 = 0.6
p2 = .36
2pq = .48
1.0
f(a) = q = .3 + .2/2 = 0.4
q2 = .16
CONCLUSION:The real population is NOT in HWE.
= 1.00
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
3. Utility:
- if a population is NOT in HWE, then one of the assumptions must be violated.
Sources of Variation
Recombination
- crossing over
VARIATION
Mutation
Agents of Change
- independent assortment
So, if NO AGENTS are acting on a population, then it
will be in equilibrium and WON'T change.
N.S.
Drift
Migration
Mutation
Non-random Mating
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
3. Utility:
- if a population is NOT in HWE, then one of the assumptions must be violated.
-Also, If HWCE is assumed and the frequency of homozygous recessives can be
measured, then the number of heterozygous carriers can be estimated.
For example:
If f(aa) = .01, then estimate f(a) = .1 and f(A) must be .9. f(Aa) = 2(.1)(.9) = 0.18.
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
3. Utility:
- if a population is NOT in HWE, then one of the assumptions must be violated.
Sources of Variation
Recombination
- crossing over
VARIATION
Mutation
Agents of Change
- independent assortment
So, if NO AGENTS are acting on a population, then it
will be in equilibrium and WON'T change.
N.S.
Drift
Migration
Mutation
Non-random Mating
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
D. Deviations from HWE
1. mutation
1. Consider a population with:
f(A) = p = 0.6
f(a) = q = 0.4
2. Suppose 'a' mutates to 'A' at a realistic rate of:
μ = 1 x 10-5
3. Well, what fraction of alleles will change?
'a' will decline by: qm = .4 x 0.00001 = 0.000004
'A' will increase by the same amount.
f(A) = p1 = 0.600004
f(a1) = q = 0.399996
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
D. Deviations from HWE
1. mutation
2. migration
p2 = 0.7
p1 = 0.2
q2 = 0.3
q1 = 0.8
suppose migrants immigrate at a rate
such that the new immigrants represent
10% of the new population
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
D. Deviations from HWE
1. mutation
2. migration
p2 = 0.7
p1 = 0.2
q2 = 0.3
q1 = 0.8
M = 10%
p(new) = p1(1-m) + p2(m)
= 0.2(0.9) + 0.7(0.1)
= 0.18 + 0.07 = 0.25
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
a. Positive Assortative Mating – “Like mates with Like”
offspring
F1
AA
Aa
aa
0.2
0.6
0.2
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
a. Positive Assortative Mating – “Like mates with Like”
offspring
F1
AA
Aa
aa
0.2
0.6
0.2
ALL AA
1/4AA:1/2Aa:1/4aa
ALL aa
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
a. Positive Assortative Mating – “Like mates with Like”
offspring
F1
AA
Aa
aa
0.2
0.6
0.2
ALL AA
1/4AA:1/2Aa:1/4aa
ALL aa
0.2
0.15 + 0.3 + 0.15
0.2
0.35
0.3
0.35
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
a. Positive Assortative Mating – “Like mates with Like”
b. Inbreeding: Mating with Relatives
Decreases heterozygosity across the genome, at a rate dependent on the degree
of relatedness among mates.
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
4. Finite Population Sizes: Genetic Drift
The organisms that actually reproduce in a population may not be representative
of the genetics structure of the population; they may vary just due to
sampling error
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
4. Finite Population Sizes: Genetic Drift
1 - small pops will differ more, just by chance, from the original
population
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
4. Finite Population Sizes: Genetic Drift
1 - small pops will differ more, just by chance, from the original
population
2 - small pops will vary more from one another than large
D. Deviations from HWE
1. mutation
2. migration
3. Non-random Mating
4. Finite Population Sizes: Genetic Drift
- “Founder Effect”
The Amish, a very small, close-knit
group decended from an initial
population of founders, has a high
incidence of genetic abnormalities
such as polydactyly
- “Founder Effect” and Huntington’s Chorea
HC is a neurodegenerative disorder caused by an
autosomal lethal dominant allele.
The fishing villages around Lake Maracaibo in
Venezuela have the highest incidence of
Huntington’s Chorea in the world, approaching
50% in some communities.
- “Founder Effect” and Huntington’s Chorea
HC is a neurodegenerative disorder caused by an
autosomal lethal dominant allele.
The fishing villages around Lake Maracaibo in
Venezuela have the highest incidence of
Huntington’s Chorea in the world, approaching
50% in some communities.
The gene was mapped to chromosome 4, and the HC
allele was caused by a repeated sequence of over
35 “CAG’s”. Dr. Nancy Wexler found homozygotes in
Maracaibo and described it as the first truly
dominant human disease (most are incompletely
dominant and cause death in the homozygous
condition).
- “Founder Effect” and Huntington’s Chorea
HC is a neurodegenerative disorder caused by an
autosomal lethal dominant allele.
The fishing villages around Lake Maracaibo in
Venezuela have the highest incidence of
Huntington’s Chorea in the world, approaching
50% in some communities.
By comparing pedigrees, she traced the incidence to
a single woman who lived 200 years ago. When the
population was small, she had 10 children who
survived and reproduced. Folks with HC now trace
their ancestry to this lineage.
- “Genetic Bottleneck”
If a population crashes (perhaps as the result of a plague) there will be both selection and
drift. There will be selection for those resistant to the disease (and correlated selection
for genes close to the genes conferring resistance), but there will also be drift at other loci
simply by reducing the size of the breeding population.
European Bison, hunted to
12 individuals, now number
over 1000.
Cheetah have very low
genetic diversity,
suggesting a severe
bottleneck in the past.
They can even
exchange skin grafts
without rejection…
Elephant seals fell to 100’s in
the 1800s, now in the
100,000’s
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
D. Deviations From HWE:
1. Mutation
2. Migration
3. Non-Random Mating:
4. Populations of Finite Size and Sampling Error - "Genetic Drift"
5. Natural Selection
1. Fitness Components:
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
Fitness = The mean number of reproducing offspring / genotype
- probability of surviving to reproductive age
- number of offspring
- probability that offspring survive to reproductive age
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
Fitness = The mean number of reproducing offspring / genotype
- probability of surviving to reproductive age
- number of offspring
- probability that offspring survive to reproductive age
2. Constraints:
i. finite energy budgets and necessary trade-offs:
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
Fitness = The mean number of reproducing offspring / genotype
- probability of surviving to reproductive age
- number of offspring
- probability that offspring survive to reproductive age
2. Constraints:
i. finite energy budgets and necessary trade-offs:
GROWTH
METABOLISM
REPRODUCTION
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
i.
finite energy budgets and necessary trade-offs:
TRADE OFF #1: Survival vs. Reproduction
Maximize probability of survival
Maximize reproduction
GROWTH
GROWTH
METABOLISM
REPRODUCTION
METABOLISM
REPRODUCTION
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
i.
finite energy budgets and necessary trade-offs:
TRADE OFF #1: Survival vs. Reproduction
TRADE OFF #2: Lots of small offspring vs. few large offspring
REPRODUCTION
METABOLISM
REPRODUCTION
METABOLISM
Lots of small, low
prob of survival
A few large, high
prob of survival
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
i.
ii.
finite energy budgets and necessary trade-offs:
Contradictory selective pressures:
Photosynthetic potential
Water Retention
Leaf Size
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
i.
ii.
finite energy budgets and necessary trade-offs:
Contradictory selective pressures:
Rainforest understory – dark, wet
Photosynthetic potential
Water Retention
Big leaves adaptive
Leaf Size
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
i.
ii.
finite energy budgets and necessary trade-offs:
Contradictory selective pressures:
Desert – sunny, dry
Photosynthetic potential
Small leaves adaptive
Leaf Size
Water Retention
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
3. Modeling Selection:
a. Calculating relative fitness
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.4
0.2
Relative Fitness
0.8/0.8=1
0.4/0.8 = 0.5 0.2/0.8=0.25
= 1.00
D. Deviations From HWE:
5. Natural Selection
1. Fitness Components:
2. Constraints:
3. Modeling Selection:
a. Calculating relative fitness
b. Modeling Selection
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.4
0.2
Relative Fitness
1
0.5
0.25
Survival to Reproduction
0.16
0.24
0.09
= 0.49
Freq’s in Breeding Adults
0.16/0.49
= 0.33
0.24/0.49
= 0.49
0.09/0.49
= 0.18
= 1.00
Gene Frequencies
F(A) = 0.575
Freq’s in F1 (p2, 2pq, q2)
0.33
0.49
= 1.00
F(a) = 0.425
0.18
= 1.00
D. Deviations From HWE:
5. Natural Selection
1.
2.
3.
4.
Fitness Components:
Constraints:
Modeling Selection:
Types of Selection
D. Deviations From HWE:
5. Natural Selection
1.
2.
3.
4.
Fitness Components:
Constraints:
Modeling Selection:
Types of Selection
Sexual Selection
Some traits that decrease survival may be
selected for because they have a direct
and disproportional benefit on probability of
mating.
Intrasexual – competition within a sex for
access to mates.
Intersexual – mates are chosen by the
opposite sex.
Modern Evolutionary Biology
I. Population Genetics
A. Overview
B. The Genetic Structure of a Population
C. The Hardy-Weinberg Equilibrium Model
D. Deviations From HWE
E. Summary; The Modern Synthetic Theory of Evolution
Agents of Change
Mutation
Natural Selection
Recombination
- crossing over
- independent assortment
VARIATION
Sources of Variation
Genetic Drift
Migration
Mutation
Non-random Mating