BSC 297 Biological Evolution October 12

1
BSC 297Biological EvolutionOctober 12

• Quiz 4 Today
• Reading
• Chapter 6.2
• Exam 2 moved to Wed 11/4

2
The Hardy Weinberg Model
1N
2N
A1 A2 Alleles
Genotypes A1A1 A1A2 A2A2
Genotypes A1A1 A1A2 A2A2
Genotypes A1A1 A1A2 A2A2
Fig 6.1
3
Assumptions of Hardy-Weinberg Equilibrium Model

• random mating
• violations
• assortative mating (like prefers like)
• disassortative mating (opposites attract)
• no immigration or emigration
• no mutation
• large population size (no genetic drift)
• no selection
• Under these assumptions - NO EVOLUTION
• If all these assumptions are met, then the
  distribution of genotypes in the NEXT generation
  will be described by the formula
• p2 2pq q2 1

4
The HD Model Founder Effects

• Example coastal butterfly species
• wing color determined by a single gene
  (co-dominance)
• A1A1 orange
• A1A2 yellow
• A2A2 white
• random colonization event (100 colonizers)
• 60 orange, 20 yellow, 20 white
• What kind of frequencies are these?

5
Frequencies of Genotypes in Populations

• Convert phenotype frequencies to genotype
  frequencies
• Founding Population genotype frequencies
• 60 A1A1 (orange) 60/100 0.6
• 20 A1A2 (yellow) 20/100 0.2
• 20 A2A2 (white) 20/100 0.2
• 100 Total 1.00
• Allele Frequencies
• frequency of A1 (p) 60x2 20x1 140
  140/2000.7
• frequency of A2 (q) 20x1 20x2 60
  60/2000.3
• total gene pool ( of gametes) 200

6
The Hardy Weinberg Model
1N
2N
Alleles A1 A2 0.7 0.3
Genotypes A1A1 A1A2 A2A2 Gen 2 will be a
function of Gen 1 Allele frequencies
Genotypes A1A1 A1A2 A2A2 0.6 0.2 0.2
Fig 6.1
7
Frequencies of Genotypes in Populations

• Next generation
• Allele frequencies in generation 1
• p 0.7 and q 0.3
• For both male and female gametes
• Then using Hardy Weinberg
• allele frequencies (gen 1) to genotypes
  frequencies (gen 2)
• p and q to p2 2pq q2
• 0.49 0.42 0.09 1
• If the population size is 100 individuals
• 0.49 x 100 49 of A1A1 Orange
• 0.42 x 100 42 of A1A2 Yellow
• 0.09 x 100 9 of A2A2 White

8
The Hardy Weinberg Model
1N
2N
Alleles (Gen1) A1 A2 0.7 0.3
Genotypes (Gen2) A1A1 A1A2 A2A2 0.49 0.42
0.09
Phenotypes (Gen2) Org Yel Wht 49 42
9
Fig 6.1
9
HW Model Predictions
10
Frequencies of Genotypes in Populations

• Another generation
• Allele frequencies (gametes) from this population
• 49x2 42x1 140 140/200 0.7
• 9x2 42x1 60 48/200 0.3
• Genotypes frequencies using the allele freq.
• p2 2pq q2 1
• 0.49 0.42 0.09 1 genotype freq.
• 49 42 9 of individuals if 100 in population
• And so on..
• Initial population was a random subset of a
  population and was not in the expected genotype
  frequencies due to founder effect (60, 20, 20)
• but after one generation of random mating the
  expected genotype frequencies were achieved.
• 49, 42, 9

11
Application of Hardy-Weinbergfrequency of
carriers in a population

• Phenylketonuria
• defect in phenylalanine metabolism (recessive
  trait)
• 1 in 10,000 newborn Caucasians have the phenotype
  (genotype q2)
• How many carriers are in the population?
• What is the frequency of 2pq?
• Using Hardy-Weinberg (assumptions)
• Calculate the allele frequencies
• ?(1/10,000) 0.01 q
• Therefore p 1 - 0.01 0.99
• Calculate the genotype frequencies
• 2x 0.01 x 0.99 0.0198 or 2 in 100 are carriers

12
Frequencies of Genotypes in Populations

• Hardy Weinberg Principle null hypothesis
• Assumptions
• NO Selection
• NO Mutation
• NO Assortative Mating (i.e.Non-Random Mating)
• NO Migration
• NO Chance Events such as Genetic Drift
• As a Null Model
• If Selection
• Changes in genotype frequencies resulting in
  changes in allele frequencies
• If Mutation
• Changes in allele frequencies resulting in
  changes in genotype
• If Non-Random Mating
• Changes in genotype frequencies but allele
  frequencies would remain the same

13
Frequencies of Genotypes in Populations
Selection
14
Application of Hardy-Weinbergas a null model or
null hypothesis

• Selection
• Differences in relative fitness among the
  genotypes
• Fitness is the number of descendants an
  individual leaves in next generation.
• Results in unequal contribution to the gene pool
  by the genotypes
• Genotype frequencies will deviate from
  Hardy-Weinberg expectations.