Download lecture 03 - Hardy-Weinberg - Cal State LA

Measuring genetic variability
Studies have shown that most natural populations have some
amount of genetic diversity at most loci
locus = physical site where a gene resides on a chromosome
plural is loci
For instance, you can measure the number of different alleles
of a given protein using gel electrophoresis
Protein electrophoresis
A gel is a porous slab of jello-like
material, which large molecules like
proteins can slowly move through
By running a current across the gel,
one end becomes positively charged
Proteins with a negative charge will
move towards the + end of the gel
+
Protein electrophoresis
Why might proteins carry a negative charge?
Some amino acids are negatively charged in solution
(glutamate, aspartate)
Some are positively charge (lysine, arginine, histidine)
By adding up the total number of + and – charged amino acids,
you can figure out the total (or net) charge of a protein
The net charge of Lys-Asp-Asp-Ser-Thr-Arg-Glu-Glu
+ + -
Protein electrophoresis
The net charge of Lys-Asp-Asp-Ser-Thr-Arg-Glu-Glu
+ + -
-2
- but different alleles may change the total charge on a protein:
Consider a different allele of this protein:
Lys-Asp-Thr-Ser-Thr-Arg-Glu-Glu
+ + -
This allele has a net charge of -1
-
Sampling variation in a population
(1) Sample many individuals
(2) Grind them up and load a drop of
the mush onto each lane of a gel
(3) Run a current across the gel
(4) Stain the gel by adding a chemical
that will turn dark when a particular
enzyme reacts with it
+
-
Variation in a population: Allozyme electrophoresis
Different protein alleles that show up
on such a gel are termed allozymes
This individual was homozygous for
the most common allele
-
+
Variation in a population: Allozyme electrophoresis
Different protein alleles that show up
on such a gel are termed allozymes
This individual was heterozygous:
-
+
Variation in a population: Allozyme electrophoresis
What is the frequency of “a” allele
in this population?
A
a
a
+
Variation in a population: Allozyme electrophoresis
What is the frequency of “a” allele
in this population?
A
a
a
total # of a alleles: 10
total # of alleles:
12
frequency of a: 10/12 = 83.3%
+
Population Genetics
Integrates Darwinian evolution by natural selection with
Mendelian principles of inheritance
Shows how changes in the frequency of alleles in a population
affect the frequency of the traits they control
Evolution: change in allele frequency over generations
How do alleles behave in a sexually reproducing,
diploid population?
Population Genetics
In a population where adults mate randomly every generation,
does the frequency of alleles change over time?
Assume a population where there are two alleles of a gene,
A and a
- frequency of allele A in the gene pool is 60%, or 0.6
- in other words, 60% of sperm and 60% of eggs made
by adults in this population carry the A allele
- frequency of allele a in the gene pool is 40%, or 0.4
What will be the frequencies of the various genotypes
(AA, Aa, aa) after one round of random mating?
odds that an A sperm will meet an A egg:
(frequency of
A sperm)
0.6
X
X
(frequency of
A egg)
0.6
= frequency of
AA zygote
=
0.36
Egg
Sperm
Zygote
Probability
A
A
AA
0.6 x 0.6 = 0.36
A
a
Aa
0.6 x 0.4 = 0.24
Aa
a
A
aA
0.4 x 0.6 = 0.24
a
a
aa
0.4 x 0.4 = 0.16
0.36 + 0.48 + 0.16 = 1
AA
Aa
aa
These probabilities are the genotype
frequencies of the next generation
So what will the allele frequencies be after this generation
reproduces? (will the frequencies change?)
Calculate new gamete frequencies, as before:
AA is 36% of the population (0.36), so 36% of gametes are A
Aa is 48% of the population, so 24% of gametes are A and
24% are a
aa is 16% of the population, so 16% of gametes are a
New allele frequencies:
A: 0.36 + 0.24 = 0.6
a: 0.24 + 0.16 = 0.4
Hardy-Weinberg Equilibrium
The allele frequencies for the A and a alleles do not change
from generation to generation
- they are in equilibrium
- hence, the population does not evolve
This illustrates an example that is true in general:
allele frequencies do not change from generation to generation
The general case is stated algebraically as the
Hardy-Weinberg equilibrium principle
Hardy-Weinberg Equilibrium
The frequency of A in the population is called p
The frequency of a in the population is called q
frequencies
in the
parental
gametes
When there are only 2 alleles, p + q = 1
What are the odds of each genotype after a round of mating?
AA
pxp
p2
Aa
(p x q) + (q x p)
2pq
aa
qxq
q2
Hardy-Weinberg Equilibrium
AA
pxp
p2
Aa
(p x q) + (q x p)
2pq
aa
qxq
q2
so, we’ve gone from allele frequencies in the parental gene pool
to genotype frequencies among the offspring
What happens when these offspring reproduce?…
Calculate new gamete frequencies, as before:
AA has frequency = p2, so p2 gametes will carry the A allele
Aa has frequency = 2pq, so ½ (2pq) or pq gametes will carry A
Hardy-Weinberg Equilibrium
AA has a frequency = p2, so p2 gametes will carry the A allele
Aa has a frequency = 2pq, so ½ (2pq) or pq gametes will carry A
New allele frequency:
A: p2+ pq
The frequency of A can be re-stated as:
p2 + pq = p(p + q)
= p(1)
=p
Since p + q = 1
Hardy-Weinberg Equilibrium
Thus, we can draw 2 conclusions from the Hardy-Weinberg
equilibrium principle:
#1) frequency of an allele stays the same over generations
- it doesn’t matter what the particular allele frequencies are
- it doesn’t matter how many alleles there are for a gene
#2) when allele frequencies are given as p and q,
the genotype frequencies will be:
p2 + 2pq + q2
The Hardy-Weinberg principle predicts that evolution will not
happen in a population -- unless one of the underlying
5 assumptions is violated
Hardy-Weinberg Assumptions
The 5 assumptions:
1) There is no natural selection
- all individuals survive and reproduce equally
- if individuals of some genotypes survive and reproduce
more than others, then allele frequencies may change
from one generation to the next
2) There is no mutation
- alleles don’t change to other existing alleles or new alleles
Hardy-Weinberg Assumptions
The 5 assumptions:
3) There is no migration
- no individuals moved into or out of the population
- if individuals with certain genotypes leave the population,
then the allele frequencies may change
Hardy-Weinberg Assumptions
The 5 assumptions:
4) There were no chance events that caused some individuals
to pass on more alleles to the next generation
- this is termed genetic drift
- commonly happens in small populations
- genetic drift causes evolution by changing allele
frequencies
-
Hardy-Weinberg Assumptions
The 5 assumptions:
5) Individuals mate at random
- individuals are not more likely to mate with others of
their own genotype
examples: a) big individuals do not prefer big individuals
b) habitat choice: mate where you like to hang
When individuals mate non-randomly, genotype frequencies
change over generations and the model is violated
Use of Hardy-Weinberg
How do scientists use Hardy-Weinberg equilibrium theory?
- useful as a null model-- something to be disproven
-
Go out into the field, sample allele and genotype frequencies
- if allele frequencies change over time, or if genotype
frequencies cannot be predicted from allele frequencies,
then the null model (H-W equilibrium) is not correct
Use of Hardy-Weinberg
If null model is wrong, one of the assumptions is being violated
- indicates that selection, mutation, or other force is acting
on a population
- functions as a spotlight, drawing attention to potential cases
where a population may be evolving
You can’t easily go out into the field and tell if a population is
under natural selection or experiencing high migration....
Selection
Happens when individuals with certain phenotypes survive
or reproduce at higher rates than others
- bottom line: differential reproductive success
- when phenotype is derived largely from genotype,
evolution can happen
selection on phenotype
Selection and Allele Frequencies
When selection increases the reproductive success of certain
genotypes, do allele frequencies change over generations?
Take the earlier example: frequency of allele A was 60%, and
the frequency of allele a was 40%, in a population
that makes 1,000 zygotes
AA
360
Aa
480
aa
160
(actual # of individuals)
Selection and Allele Frequencies
When selection increases the reproductive success of certain
genotypes, do allele frequencies change over generations?
Take the earlier example: frequency of allele A was 60%, and
the frequency of allele a was 40%
AA
Aa
aa
360
480
160
Now assume that genotypes differ in their rates of survival
(due to effects on phenotype)
- all AA survive
- only 75% of Aa survive
- 50% of aa survive
Selection and Allele Frequencies
AA
360
x 100%
360
+
Aa
480
x 75%
360
+
aa
160
x 50%
80
= 800 survivors
When this generation makes gametes, what will the allele
frequencies be?
First calculate genotype frequencies…
Total individuals of each genotype / total # of individuals
AA
Aa
aa
360/800 = 0.45
360/800 = 0.45
80/800 = 0.1
Selection and Allele Frequencies
Total individuals of each genotype / total # of individuals
AA 360/800 = 0.45
Aa 360/800 = 0.45
aa 80/800 = 0.1
Calculate allele frequencies, when these individuals make gametes
Frequency of A allele = frequency of AA + ½ frequency of Aa
= (0.45) + ½ (0.45)
= 0.45 + 0.225
= 0.675
Frequency of allele A was originally 0.6
- selection changed allele frequencies
- thus, the population evolved in response to selection
Artificial selection experiments
Laboratory experiments using fruit fly Drosophila melanogaster
have shown that many forms of “artificial” selection cause
rapid evolution by changing allele frequencies in
experimental populations
- scientists change the conditions of experimental populations
- after many generations, check to see if allele frequencies
have changed, relative to control populations
Artificial selection experiments
Change conditions of 2 experimental populations: add ethanol
After 50 generations,
allele frequencies
had changed
relative to
control
populations
flies fed
ethanolspiked food
Selection and Genotype Frequencies
In the previous case, selection changed allele frequencies
Can selection change genotype frequencies, instead?
Consider this population:
Frequency of A = 0.5
a = 0.5
Genotype:
frequency:
AA
0.25
250
after one round
of random mating:
Aa
0.5
500
aa
0.25
250 (# out of 1,000
individuals)
Selection and Genotype Frequencies
Genotype: AA
frequency: 0.25
250
Aa
0.5
500
aa
0.25
250
Now introduce selection: only 50% of homozygotes survive
AA
# of adults: 125
Aa
500
aa
125
(750 survivors)
New genotype frequencies:
(total # of each genotype / total # of individuals in population)
AA
Aa
aa
125 / 750 = 0.167
500 / 750 = 0.667
125 / 750 = 0.167
Selection and Genotype Frequencies
New genotype frequencies:
(total # of each genotype / total individuals in the population)
AA 125 / 750 = 0.167
Aa 500 / 750 = 0.667
aa125 / 750 = 0.167
New allele frequencies, when these individuals produce gametes…
Frequency of A allele = frequency of AA + ½ frequency of Aa
= (0.167) + ½ (0.667)
= 0.167 + 0.334
= 0.5
This was the initial frequency of the A allele!
Selection and Genotype Frequencies
Despite strong selection against homozygotes, allele frequencies
didn’t change
population did not evolve
Conclusion #1 of Hardy-Weinberg wasn’t violated by selection
.... what about conclusion #2: can you still predict genotypes
from the new allele frequencies?
Selection and Genotype Frequencies
Can you still predict genotypes from the new allele frequencies?
New allele frequencies:
A = 0.5
a = 0.5
New genotype frequencies:
AA
125 / 750 = 0.167
Aa
500 / 750 = 0.667
aa
125 / 750 = 0.167
Frequency of the A allele:
0.5
Predicted frequency of the AA genotype:
(0.5)2 = 0.25
Actual frequency of the AA genotype:
125/750 = 0.167
Selection and Genotype Frequencies
Frequency of the A allele:
0.5
Predicted frequency of the AA genotype:
(0.5)2 = 0.25
Actual frequency of the AA genotype:
125/750 = 0.167
Selection took the population out of Hardy-Weinberg equilibrium
Conclusion #2 (genotypes are predicted from allele frequencies)
is violated
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