Chapter 23 – Part 1
Part 2 After Break
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Context
Evolution appears to be the typical situation
Sometimes evolution is not occurring
Hardy-Weinberg Equilibrium Conditions that specify if evolution is NOT happening Equilibrium = no evolution More of a theoretical case than a real test
But affords comparison to evolution
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Definitions
Population Genetics – study of how populations change genetically over time
Population – Group of same species individuals that can and do interbreed successfully
Gene pool – all of the alleles at all loci in all the members of a population
Fixed – only one allele exists for a locus in the population More fixed alleles = lower species diversity
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Hardy-Weinberg
If gene pools are NOT Evolving, can use Hardy-Weinberg Describes a population that is NOT evolving Allelic frequencies will remain constant Gene frequencies remain constant throughout the
generations
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Conditions for Hardy-Weinberg
1. No mutations
2. Random mating
3. No natural selections
4. Large population size
5. No gene flow Immigration or emigration Genes coming into or leaving the population
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Math in Biology?
p = Frequency of the dominant allele = f(A)
q = Frequency of the recessive allele = f(a)
There are only 2 alleles (dominant + recessive), so
p + q = 1
square both sides: (p + q)2 = 12
expand the binomial: p2 + 2pq + q2 = 1
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Hardy-Weinberg Math (Page 2)
p2 = pp = f(aa) = Frequency of homozygous dominant
pq = f(Aa) = frequency of heterozygote However, remember from Punnett Square, there were 2
heterozygotes for the F1 generation; So 2pq = f(Aa)
q2 = qq = f(aa) = frequency of homozygous recessive
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In Summary
Summary: p2 + 2pq + q2 = 1 f(AA) + f(Aa) + f(aa) = 1 f(Homo. Dom.) + f(Hetero.) + f(Homo. Recess.) = 1 Are there any other genotypes? Makes sense?
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Problem (Part 1)
1. A trait has two characters, dominant (A) and recessive (a). In a population of 500 individuals in Hardy-Weinberg equilibrium, 25% display the recessive phenotype (aa).
a) What is the frequency of the dominant allele in the population?
b) What is the frequency of the recessive allele in this population?
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Answer
f(aa) = 0.25 OR q2 = 0.25
q = √(0.25) = 0.5 OR f(a) = 0.5 So the frequency of the recessive allele = 0.5
From before: p + q = 1 AND q = 0.5, so p = 0.5 = f(A) So the frequency of the dominant allele = 0.5
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Part 2 of Problem
What are the frequencies of
a) homozygous dominant genotype?
b) Heterozygous genotype?
c) homozygous recessive genotype?
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Part 2 of Problem (Answer)
What are the frequencies of
a) homozygous dominant genotype?
Since p = 0.5, p2 = (0.5)2 = 0.25
b) Heterozygous genotype?
Since p = 0.5 & q = 0.5, 2pq = 2(0.5)(0.5) = 0.5
c) homozygous recessive genotype?
Yep, it was given, but if we must: q = 0.5, q2 = (0.5)2 = 0.25
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Part 3 of Problem
How many individuals have the
a) homozygous dominant genotype?
b) Heterozygous genotype?
c) homozygous recessive genotype?
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Part 3 of Problem (Answer)
How many individuals have the
a) homozygous dominant genotype?
500 members & p2 = 0.25, (0.25)(500) = 125
b) Heterozygous genotype?
500 members & p = 0.5, q = 0.5 2pq = 0.5
So 500 (0.5) = 250 heterozygotes
c) homozygous recessive genotype?
500 members & q2 = 0.25, (0.25)(500) = 125
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Part 4 of Problem
How many individuals have the
a) Dominant phenotype?
b) Recessive phenotype?
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Part 4 of Problem (Answer)
How many individuals have the
a) Dominant phenotype?
= (Homo. Dom.) + (Hetero.) = 125 + 250 = 375
b) Recessive phenotype?
= Homo. Recess. = 125
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