I. The Modern Synthetic Theory of Evolution
A. Initial Structure – 1940
Sources of Variation
Mutation
Recombination
- crossing over
- independent assortment
V
A
R
I
A
T
I
O
N
Agents of Change
Natural Selection
Drift
Mutation
Migration
Non-random Mating
B. Population Genetics
1. Hardy Weinberg
a. Definitions:
b. Basic computations:
1. Determining the Gene and Genotypic Array:
Individuals
AA
Aa
aa
60
80
60
(200)
B. Population Genetics
1. Hardy Weinberg
a. Definitions:
b. Basic computations:
1. Determining the Gene and Genotypic Array:
AA
Aa
aa
Individuals
60
80
60
(200)
Genotypic
Array
60/200 =
0.30
80/200 = .40
60/200 =
0.30
=1
''A' alleles
120
80
0
200/400 =
0.5
'a' alleles
0
80
120
200/400 =
0.5
B. Population Genetics
1. Hardy Weinberg
a. Definitions:
b. Basic computations:
1. Determining the Gene and Genotypic Array
2. Short Cut Method:
- Determining the Gene Array from the Genotypic Array
a. f(A) = f(AA) + f(Aa)/2 = .30 + .4/2 = .30 + .2 = .50
b. f(a) = f(aa) + f(Aa)/2 = .30 + .4/2 = .30 + .2 = .50
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.
B. Population Genetics
1. Hardy Weinberg
a. Definitions:
b. Basic computations:
c. Hardy-Weinberg Equilibrium:
1. If a population acts in a completely probabilistic manner, then:
- we envision an infinitely large population with no migration, mutation, or
selection, and random mating.
- we could calculate genotypic arrays from gene arrays
- the gene and genotypic arrays would equilibrate in one generation
B. Population Genetics
1. Hardy Weinberg
a. Definitions:
b. Basic computations:
c. Hardy-Weinberg Equilibrium:
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
f(A) = p = .36 + .48/2 = 0.6
.36
.48
1.0
f(a) = q = .2 + .4/2 = 0.4
q2 = .16
= 1.00
f(a) = q = .16 + .48/2 = 0.4
.16
1.00
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- mutation
1. Consider a population with:
f(A) = p = .6
f(a) = q = .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.
4. So, the new gene frequencies will be:
p1 = p + μq = .600004
q1 = q - μq = q(1-μ) = .399996…. VERY LITTLE EFFECT on GENE FREQ’s
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- migration
p1 = 0.2
q1 = 0.8
p2 = 0.7
q2 = 0.3
suppose migrants immigrate at a rate
such that the new immigrants represent
10% of the new population
B. Population Genetics
1. Hardy Weinberg
IMPORTANT EFFECT, BUT MAKES POPULATIONS
SIMILAR AND INHIBITS DIVERGENCE AND
ADAPTATION TO LOCAL CONDITIONS (EXCEPT IT
MAY INTRODUCE NEW ADAPTIVE ALLELES)
2. Effects of Different Agents
- migration
p1 = 0.2
q1 = 0.8
p(new) = p1(1-m) + p2(m)
= (0.2)(0.9) + (0.7)(0.1)
= 0.25
p2 = 0.7
q2 = 0.3
suppose migrants immigrate at a rate
such that the new immigrants represent
10% of the new population
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- non-random mating
1. Positive Assortative Mating
offspring
F1
AA
Aa
aa
.2
.6
.2
ALL AA
1/4AA:1/2Aa:1/4aa
ALL aa
.2
.15 + .3 + .15
.2
.35
.3
.35
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- non-random mating
1. Positive Assortative Mating
B. Inbreeding
- reduction of heterozygosity across the entire genome, at a rate that correlates with the
degree of relatedness.
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Genetic Drift
1. 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
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Genetic Drift
2. patterns
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Genetic Drift
2. patterns
- “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…
Fell to 100’s in the 1800s,
now in the 100,000’s
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Selection: Differential reproductive success
A. Measuring “fitness” – differential reproductive success
1. The mean number of reproducing offspring (or females)/female
2. Components of fitness:
- probability of female surviving to reproductive age
- number of offspring the female produces
- probability that offspring survive to reproductive age
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Selection: Differential reproductive success
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 0.73
Geno. Freq., breeders
0.22
0.66
0.12
= 1.00
Gene Freq's, gene pool
p = 0.55
Genotypes, F1
0.3025
= 1.00
q = 0.45
0.495
0.2025
= 100