1. Evolution and Alleles Reginald Punnett Wilhelm Weinberg G. H. Hardy
Udny Yule

2. 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.

3. 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.

4. 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.

5. Directional Selection
When individuals at one end of the curve have higher fitness.

6. 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.

7. 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.

8. 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.

9. Founder effect – a situation in which allele frequencies change as a result of the migration of a small subgroup of a population.

10. 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 between family genetics and population genetics.

11. Punnett Squares for Families

12. Predicted Offspring

13. But what about Populations?
What if there were only 30% A and 70% a in the population?

14. The equation
The whole population is made up of
AA + 2Aa + aa = 1
(0.21) = 1

15. G.H. Hardy’s Equation Let p = A = the frequency of allele A
Let q = a = the frequency of allele a
So p pq + q2 = 1
AA = pp
Aa = pq
aa = qq

16. 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: (p+q)2 = 1
p pq + q2 = 1
These are the predicted frequencies of the genotypes of the selected trait.

17. 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 the population.
There is no selection.
This is known as genetic equilibrium.

18. 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 = in the population would be aa.
(In reality it is only or .001%.)

20. 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.

21. 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

22. Calculations Example of calculations IF……. gold brown q2 q p p2 2pq
Note: gold is recessive so gold fish are qq = q2
.30 = 30% in decimal form