Using mathematical approaches to calculate changes in allele frequenciesthis is evidence of evolution HardyWeinberg equilibrium Hypothetical nonevolving population preserves allele frequencies ID: 933886
Download Presentation The PPT/PDF document "Hardy Weinberg: Population Genetics" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Hardy Weinberg: Population Genetics
Using mathematical approaches to calculate changes in allele frequencies…this is evidence of evolution.
Slide2Hardy-Weinberg equilibrium
Hypothetical, non-evolving population
preserves allele
frequenciesnatural populations rarely in H-W equilibriumuseful model to measure if forces are acting on a populationmeasuring evolutionary change
W. Weinberg
physician
G.H. Hardy
mathematician
Slide3Evolution of populations
Evolution =
change in allele frequencies
in a populationhypothetical: what conditions would cause allele frequencies to not change?very large population size (no genetic drift)no migration (no
gene flow in or out)no mutation (no genetic change)
random mating (no sexual selection)no natural selection (everyone is equally fit)
H-W occurs ONLY in non-evolving populations!
Slide4Populations & gene pools
Concepts
a
population is a localized group of interbreeding individualsgene pool is collection of alleles in the populationremember difference between alleles & genes!
allele frequency is how common is that allele in the population how many A vs. a in whole population
Slide5H-W formulas
Alleles:
p
+ q = 1Individuals: p
2 + 2pq + q2 = 1
bb
Bb
BB
BB
B
b
Bb
bb
Slide6Origin of the Equation
Assuming that a trait is recessive or dominant
Allele pairs AA,
Aa, aa would exist in a populationp + q = 1The probability that an individual would contribute an A is called pThe probability that an individual would contribute an a is called q
Because only A and a are present in the population the probability that an individual would donate one or the other is 100%p2
+ 2pq + q2
Male Gametes A(p)
Male Gametes a(q)
Female gametes A(p)
AA
p
2
Aa
pq
Female Gametes a(q)
Aa
pq
aa
q
2
Slide7Hardy-Weinberg theorem
Counting
Alleles
assume 2 alleles = B, bfrequency of dominant allele (B) = p frequency
of recessive allele (b) = q frequencies must add to 1 (100%), so:
p + q = 1
bb
Bb
BB
Frequencies are usually written as decimals!
Slide8Hardy-Weinberg theorem
Counting
Individuals
frequency of homozygous dominant: p x p = p2
frequency of homozygous recessive: q x q =
q2 frequency of heterozygotes: (
p x q) + (q x p) = 2p
q
frequencies of
all individuals
must add to 1 (100
%
), so:
p
2
+ 2pq +
q
2
= 1
bb
Bb
BB
Slide9Practice Problem:
In a population of 100 cats, there are 16 white ones. White fur is recessive to black.
What are the frequencies of the genotypes?
Slide10What are the genotype frequencies?
Use
Hardy-Weinberg
equation!
q
2 (bb): 16/100 = .16q (b): √.16 =
0.4p (B): 1 - 0.4 =
0.6
bb
Bb
BB
p
2
=.36
2pq
=.48
q
2
=.16
Must assume population is in H-W equilibrium!
Slide11Answers:
bb
Bb
BB
p
2=.36
2pq
=.48
q
2
=.16
Assuming
H-W equilibrium:
Expected data
Observed data
bb
Bb
BB
p
2
=.74
2pq
=.10
q
2
=.16
How do you explain the data?
p
2
=.20
2pq
=.64
q
2
=.16
How do you explain the data?
Slide12Tips for Solving HW Problems:Solve for
q
first.
Then solve for p.Don’t assume you can just solve for p2
if only given dominant phenotypic frequency. READ carefully!!! HW Math is fun
Slide13Homework:Answer all the questions on the “Hardy Weinburg
Practice Problems” handout
Complete the following
prelab questions:List the conditions for a Hardy-Weinberg Population.Write a hypothesis for expected allele outcome for Case 1.Write down the formula of how to determine the allele frequencies.Write a hypothesis for expected allele outcome for Case 2.Write a hypothesis for expected allele outcome for Case 3.