Hardy-Weinberg & Genetic Equilibrium
• Hardy-Weinberg principle – allele frequencies in a
population will remain constant unless one or more
factors cause those frequencies to change.
• Genetic equilibrium – condition in which allele
frequencies remain constant.
Hardy-Weinberg
• Conditions for maintaining genetic equilibrium from
generation to generation.
– There must be random mating.
– The population must be very large.
– There cannot be any movement into or out of the
population.
– There cannot be any mutations.
– There cannot be any natural selection.
Hardy-Weinberg Equations
This is the
Hardy
Weinberg
Equation…
2
2
p +2pq+q
I have
absolutely
no idea
what
you’re
talking
about…
2
2
p +2pq+q
• Hardy-Weinberg states:
• P= the frequency of the dominant allele or
the % of A are in a population
• Q= the frequency of the recessive allele or the
% of a in a population
• So p + q = 1
What are Ps and
Qs???
Let’s break
it down…
2
2
p +2pq+q
I’m
scared!!
p2
2
2
p +2pq+q
The letter P
stands for
all the
dominant
alleles in a
population.
So p2 is all
the
organisms
with 2
dominant
alleles
q2
2
2
p +2pq+q
The letter q
stands for
all the
recessive
alleles in a
population.
So q2 is all
the
organisms
with 2
recessive
alleles
Well, that covers
all the recessive
and dominant
alleles… so what
about 2pq??
2
2
p +2pq+q
When
organisms are
HETEROZYGOUS
they have both
a recessive and
a dominant
allele
2pq
2
2
p +2pq+q
Oh yeah
heterozygous!
Would you
review it all?
2
2
p +2pq+q
• P= all the dominant alleles so p2 is all the
organisms with 2 dominant alleles
• Q= all the dominant alleles so q2 is all the
organisms with 2 dominant alleles
• 2pq is all the organisms who have 1
dominant allele and I recessive allele.
We’ll do three Hardy Weinberg
problems together.
These problems are similar to
those you would see on a test or
exam.
Have your pencils and calculators
ready as we break these
problems down step by step.
If you follow along carefully you
will have all the information you
need to solve these types of
problems on your own.
2
2
p +2pq+q
Question: The allele for green amoebas
is recessive. Blue is dominant. Use the
Hardy-Weinberg equation to estimate
the percent of this amoeba population
that is heterozygous.
Step one: Don’t panic!! Count the
recessive ones
I think I am
ready to
try a
problem!!!
(an easy
one…)
2
2
p +2pq+q
Question: The allele for green amoebas
is recessive. Blue is dominant. Use the
Hardy-Weinberg equation to estimate
the percent of this amoeba population
that is heterozygous.
There are 16
altogether and
I can see that 4
of them are
recessive like
me!
2
2
p +2pq+q
Question: The allele for green amoebas is recessive. Blue is dominant. Use
the Hardy-Weinberg equation to estimate the percent of this amoeba
population that is heterozygous.
4/16=25% or .25 so q2= .25
Now that you know q2 you
can find out q by using your
calculator to find the square
root of .25
Did you get .5? Right!!!
2
2
p +2pq+q
Question: The allele for green amoebas is recessive. Blue is dominant. Use
the Hardy-Weinberg equation to estimate the percent of this amoeba
population that is heterozygous.
You know that p+q=1
(always!) so now that you
know q=.5 you can find p.
Did you figure out that p is
also .5? Good! You now all
have all the information you
need to answer the question
2
2
p +2pq+q
Question: The allele for green amoebas is recessive. Blue is dominant. Use
the Hardy-Weinberg equation to estimate the percent of this
amoeba population that is heterozygous.
The question is asking you for
the heterozygous frequency so
you need to use 2pq to solve
this one.
2pq is 2(.5x.5)
Did you get .50? Good! So 50%
of this population is
heterozygous.
Ready for
another
one?
2
2
p +2pq+q
Do I
have a
choice?!
2
2
p +2pq+q
Question: In a certain population of 1000
amoebas, 640 are blue and the rest are
green. The green trait is recessive to blue.
How many individuals would you expect to
be homozygous for blue colour?
q2 (green amoebas) is 360/1000
= 0.36
Use your calculator to find the sq.
root of .36
Did you get it? q = 0.6
You know p+q=1 so now you can
figure out p !
It does gets
easier with
practice!
Remember :
p+q=1
2
2
p +2pq+q
Question: In a certain population of
1000 amoebas, 640 are blue and the
rest are green. The green trait is
recessive to blue. How many individuals
would you expect to be homozygous for
blue colour?
p+0.6 = 1 therefore p = 0.4
The homozygous dominant frequency is
p2 = 0.4x0.4 = 0.16
So 160 individuals would be
homozygous for the blue colour.
Did you get
it?
2
2
p +2pq+q
Question: Within a population of
amoebas the color blue (B) is dominant
to the color green (b). And, 40% of all
amoebas are green. With this
information you can calculate:
The percentage of amoebas in the
population that are heterozygous.
And
The frequency of homozygous dominant
individuals.
Let’s try
one more!
2
2
p +2pq+q
Question: Within a population of amoebas the color blue (B) is
dominant to the color green (b). And, 40% of all amoebas are
green. With this information you can calculate:
The percentage of amoebas in the population that are
heterozygous.
And
The frequency of homozygous dominant individuals.
First find p and q.
Green is recessive and 40% are green , so you know q2 = 0.4.
2
2
p +2pq+q
Question: Within a population of amoebas the color blue (B) is dominant to the color
green (b). And, 40% of all amoebas are green. With this information you can calculate:
The percentage of amoebas in the population that are heterozygous.
And
The frequency of homozygous dominant individuals.
• Use your calculator to find the square root of q2
• q = 0.632 (round it off) Did you get it?
• Remember p + q = 1
• p +0.63=1 so p= 0.37.
• Now we have all the information we need to answer the
questions.
2
2
p +2pq+q
Question: Within a population of amoebas the color blue (B) is dominant to the
color green (b). And, 40% of all amoebas are green. With this information you
can calculate:
The percentage of amoebas in the population that are
heterozygous.
I see!
And
The frequency of homozygous dominant individuals.
• The first question asks about heterozygous
amoebas. So calculate 2pq.
• 2 (0.37x0.63)
• Did you get 0.47? That makes the answer 47%
2
2
p +2pq+q
Question: Within a population of amoebas the color blue (B) is dominant to the
color green (b). And, 40% of all amoebas are green. With this information you
can calculate:
The percentage of amoebas in the population that are
heterozygous.
And
The frequency of homozygous dominant individuals.
• The second part asks about homozygous
amoebas. So calculate p2.
• That would be 0.372
• Did you get 0.14? That’s right! So 14% would be
homozygous dominant
2
2
p +2pq+q
Any
questions?
No, it’s making sense.
I’ll just keep
practicing!