Download Evolution and Alleles

Evolution and Alleles
Reginald Punnett
Wilhelm Weinberg
G. H. Hardy
Udny Yule
Population Genetics - definitions
► Gene
pool – all genes including all of the
different alleles in a population.
► Relative (allele) frequency – the number
of times an allele occurs in a gene pool
compared with the number of times other
alleles for the same gene occur.
► In genetic terms evolution is any change
in the relative frequency of alleles in a
population.
Natural selection and single gene traits
► Sometimes
single gene traits have only 2
phenotypes.
 Ex.: Widow’s peak, tongue rolling, PTC tasting…
► Natural
selection on single gene traits can
lead to changes in allele frequencies and
thus to evolution.
 Ex.: Organisms of one color may produce fewer
offspring than those of another color.
Natural selection and polygenic traits
► Normal
distributions of polygenic traits form
a bell curve. Ex.: height.
► Natural selection can affect this curve in 3
ways.
• Directional selection.
• Stabilizing selection.
• Disruptive selection.
http://www.sparknotes.com/biology/evolution/naturalselection/section1.html
Directional Selection
► When
individuals at one end of the curve
have higher fitness.
http://www.sparknotes.com/biology/evolution/naturalselection/section1.html
Stabilizing selection
► When
individuals near the center of the
curve have higher fitness than individuals at
either end – the bell curves remains but
becomes more narrow.
http://www.sparknotes.com/biology/evolution/naturalselection/section1.html
Disruptive selection
► When
individuals at the upper and lower
ends of the curve have higher fitness than
those near the middle.
► If the pressure is strong enough, the
curve can split in two.
http://www.sparknotes.com/biology/evolution/naturalselection/section1.html
Genetic drift
►A
type of genetic change distinct from natural
selection.
► Occurs in small populations.
► Individuals with a particular allele may leave more
descendants than other individuals just by chance.
(Remember – the laws of probability predict
results more accurately with larger sample size.)
► Over time a series of chance occurrences can
cause an allele to become common in a
population.
► This random change is called genetic drift.
Founder effect – a situation in which allele
frequencies change as a result of the migration of
a small subgroup of a population.
Evolution and Alleles are Related
► Reginald
Punnett: Brachydactyly (short
fingers) is a dominant trait!
► Udny
Yule (statistician): If it is dominant,
shouldn’t 75% of the population have it?
► G.H.
Hardy (mathematician) did the math.
► Confusion
genetics.
between family genetics and population
Punnett Squares for Families
Predicted Offspring
But what about Populations?
What if there were only 30% A and 70% a in
the population?
The equation
► The
whole population is made up of
AA + 2Aa + aa = 1
0.09 + 2(0.21) + 0.49 = 1
G.H. Hardy’s Equation
► Let
p = A = the frequency of allele A
► Let q = a = the frequency of allele a
► So
p2 + 2pq + q2 = 1
AA = pp
Aa = pq
aa = qq
Quadratic Equation gives genotype
proportions.
►p
+q=1
Or the frequency of dominant allele plus frequency
of recessive allele = 100%
► If
there is random mating:
► p2
(p+q)2 = 1
+ 2pq + q2 = 1
► These are the predicted frequencies of the
genotypes of the selected trait.
What did Hardy and Weinberg say?
Allele frequencies will stay the same from generation
to generation IF:
► There are no mutations.
► Mating is random.
► Populations are infinitely large.
► The is no movement in or out of
► There is no selection.
the population.
This is known as genetic equilibrium.
How can we use this?
► What
if we know that 4% of the population has
cystic fibrosis?
► That means that:
► aa = a2 = 0.04
► So a = √0.04 = 0.2 and A = 0.8
► Heterozygous folks in pop. = 2Aa = 0.32
► Odds of mating between any Aa folks = 0.32 x 0.32
= 0.10
► But only ¼ of their children would be aa, so 0.10 x
0.25 = 0.025 in the population would be aa.
► (In reality it is only 0.00001 or .001%.)
Fishy Frequencies
Procedure 1
1) Get a random population of 10 fish from the “ocean.”
2) Count gold and brown fish and record in your chart;
you can calculate frequencies later.
3) Eat 3 fish, chosen randomly, without looking at the
plate of fish
4) Add 3 fish from the “ocean.” (One fish for each one
that died). Be random. Do NOT use artificial selection.
5) Record the number of gold and brown fish.
6) Again eat 3 fish, randomly chosen
7) Add 3 randomly selected fish, one for each death.
8) Count and record.
9) Repeat steps 6, 7, and 8 two more times.
10) Fill in the class results on your chart.
►
Fishy Frequencies
Procedure 2
1) Get a random population of 10 fish from the “ocean.”
2) Count gold and brown fish and record in your chart;
you can calculate frequencies later.
3) Eat 3 gold fish; if you do not have 3 gold fish, fill in the
missing number by eating brown fish.
4) Add 3 fish from the “ocean.” (One fish for each one
that died). Be random. Do NOT use artificial selection.
5) Record the number of gold and brown fish.
6) Again eat 3 fish, all gold if possible.
7) Add 3 randomly selected fish, one for each death.
8) Count and record.
9) Repeat steps 6, 7, and 8 two more times.
10) Fill in the class results on your chart
►
Calculations
Example of calculations
IF…….
gold brown q2
q
p
p2
3
7
.30 .55 .45 .20
2pq
.50
Note: gold is recessive so gold fish are qq = q2
.30 = 30% in decimal form