Transcript Hardy-Weinberg

Hardy-Weinberg
It’s Not That Hard!
Foothill High School Science Department
What You Will Learn
• Who were Hardy & Weinberg?
• The nomenclature
–what do the words mean?
• How to calculate
–It really is not that hard.
• How you can use it.
Foothill High School Science Department
Who Were They?
Professor
Godfrey Harold Hardy
Mathematician
1877-1947
Foothill High School Science Department
Who Were They?
Dr. Wilhelm Weinberg
Physician
Geneticist
1862-1937
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What Did They Figure Out?
Hardy & Weinberg did not know each other,
but they were both interested in population
genetics.
They independently figured out how field
observations could be used to calculate the
frequency (how many) of alleles in populations of
organisms
Foothill High School Science Department
Remember the Punnett Square?
Let’s Review
Remember Mendel’s Peas?
TT,Tt
Remember Some Were
Tall & Some Were
RememberShort?
Height Was
Controlled By “Alleles” in
“Genes”?
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tt
Remember the Punnett Square?
Remember the old F1 Cross?
P1 = Tt
P2 = Tt
And Then P1 and P2 Got Married
And Then They Had Baby
Peas!
Foothill High School Science Department
Remember the Punnett Square?
P1 = Tt
Tt
P2 = Tt
Tt
What Does This Have To
Do With
Hardy-Weinberg?
Actually – Everything
It Is Hardy-Weinberg!
TT
Tt
Tt
tt
Here is how it works!
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Hardy-Weinberg
The Hardy-Weinberg Equation
Calculates Allele Frequencies In POPULATIONS
OF ORGANISMS.
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Hardy-Weinberg Language
Hardy-Weinberg
Could
WeLeft
Convert
Since
The
Hand
Is of
An
Algebraic
The
Language
of
Side
the
Equation
Representation
of
Represents
The
the Punnett
AllelePopulation,
Frequency It
Whole
Square
into
In Populations
of of
Sums
Up
To
100%
Mathematical
the Organisms
Population!
Language?
TT
Tt
Tt
tt
Watch!
T2
+
+
2Tt
+
t2
= 1 or 100%
Foothill High School Science Department
Hardy-Weinberg Language
We used Tall and Short Pea
plants (TT, Tt, tt)
But
We could have been
demonstrating color,
smoothness, locations, or
any other trait
TT
Tt
Tt
tt
That would require different letters for each trait.
However, Hardy-Weinberg applies to all traits!
Foothill High School Science Department
Hardy-Weinberg Language
To Solve This Problem,
Hardy-Weinberg Assigns A
Single Letter
To Represent Each
Different Allele
p = The Dominant Allele
TT
Tt
Tt
tt
q = The Recessive Allele
Foothill High School Science Department
Hardy-Weinberg Language
Let’s Recode Our
Punnett Square to
Hardy-Weinberg
Notation
p2
+
+
2pq
+
q2
pp
TT
pq
pq
Tt
pq
Tt
qq
qq
tt
= 1 or 100%
Foothill High School Science Department
Hardy-Weinberg Equation
TT
Tt
pp
pq
pq
qq
=
Tt
tt
p2 + 2pq + q2 = 1
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Calculating Hardy-Weinberg
Therefore:
All The “p” alleles +
All The “q” alleles =
ALL THE ALLELES!
Therefore:
p+q=1
pp
pq
Therefore:
The Genotypes of the
Offspring = ALL the
Possible Genotypes!
Key
Equations
pq
qq
Therefore:
p2 + 2pq +q2 = 1
You Already Know
1.
2.
This Punnett Square represents the Whole Population
Therefore, It Represents ALL the Alleles in the Population
Foothill High School Science Department
Calculating Hardy-Weinberg
w
w
Sheep
White
White
is
Dominant
ww
of Sheep
Black isNumber
Recessive
0.2
= 10
Number of BLACK Sheep = 1
2/10
Foothill High School Science Department
Calculating Hardy-Weinberg
w
OK
Hardy Weinberg Formula
p2 + 2pq + q2 = 1
ww = qq = q2
q  q2
w
ww
q2
q  q2
0.2
q  0.2
q = 0.447
q = 0.44721359549995793928183473374626
Calculating Hardy-Weinberg
q = 0.447
p+q=1
q = 0.447
p + 0.447 = 1
p = 0.553
p = 1 – 0.447
p + q = 1.000
Foothill High School Science Department
Calculating Hardy-Weinberg
q = 0.447
p = 0.553
pp
pq
p2 = pp = 0.553
0.306 x 0.553
0.247 x 0.447
pq = 0.553
q2 = qq = 0.447
0.200 x 0.447
+ 0.247
1.000
pq
qq