I. The Modern Synthetic Theory of EvolutionA. Initial Structure – 1940
Sources of Variation Agents of Change
Mutation Natural Selection
Recombination Drift
- crossing over Mutation
- independent assortment Migration
Non-random Mating
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)
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:
AA Aa aa
Initial genotypic freq.
0.4 0.4 0.2 1.0
Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4
Genotypes, F1 p2 = .36 2pq = .48 q2 = .16 = 1.00
Gene Freq's f(A) = p = .36 + .48/2 = 0.6 f(a) = q = .16 + .48/2 = 0.4
Genotypes, F2 .36 .48 .16 1.00
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- mutation1. 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
p2 = 0.7
q2 = 0.3
suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population
p1 = 0.2
q1 = 0.8
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- migration
p2 = 0.7
q2 = 0.3
suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population
p1 = 0.2
q1 = 0.8
p(new) = p1(1-m) + p2(m)
= (0.2)(0.9) + (0.7)(0.1)
= 0.25
IMPORTANT EFFECT, BUT MAKES POPULATIONS SIMILAR AND INHIBITS DIVERGENCE AND ADAPTATION TO LOCAL CONDITIONS (EXCEPT IT MAY INTRODUCE NEW ADAPTIVE ALLELES)
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- non-random mating1. Positive Assortative Mating
AA Aa aa
.2 .6 .2
offspring ALL AA 1/4AA:1/2Aa:1/4aa ALL aa
.2 .15 + .3 + .15 .2
F1 .35 .3 .35
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- non-random mating1. Positive Assortative MatingB. 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 Drift1. 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 Drift2. patterns
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Genetic Drift2. 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
A. Measuring “fitness” – differential reproductive success
1. The mean number of reproducing offspring (or females)/female2. 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 = 1.00
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 q = 0.45
Genotypes, F1 0.3025 0.495 0.2025 = 100
B. Population Genetics
1. Hardy Weinberg
2. Effects of Different Agents
- Selection: Differential reproductive success
