Day 48 Hardy-Weinberg
Hardy-Weinberg Equation
p^2 + 2pq + q^2 = 1
-The Hardy-Weinberg equation is used to test if a population is evolving or not
-A population is a group of the same species
-We can characterize a population by describing its gene pool
For example human hair texture is an incomplete dominant trait
Lets say that:
C= Curly
S= Straight
CS= Wavy
Because hair texture is an incomplete dominant trait we can tell what an individual's genotype is based on their phenotype
Lets describe the gene pool for hair texture at this high school
-Assuming there are 500 people at this school we will have 1,000 alleles for hair texture since we are all diploid
-We have 320 people with straight hair, 160 with wavy hair, and 20 with curly hair
-This gives us 800 alleles for straight hair (320 x 2= 640 + 160 from the heterozygotes = 800)
-800/1000 means that our gene pool is 80% straight hair
-The rest has to be for the curly allele so 20% for curly
If a population is in Hardy-Weinberg equilibrium then the allele frequencies will remain constant over time
-If mating is random then we can think of it as if all these alleles are in a pool and randomly thrown together
-In a random mating situation we can use the Hardy-Weinberg equation to figure out what the chances are of having each type of offspring
In our hair population we can figure out the chances of each genotype
-For the homozygous Straight hair alleles we take p x p = p^2 so that is .80 x .80 = .64
-If random mating takes place then 64% of our population should be homozygous for straight hair
-For the homozygous Curly hair we take q x q = q^2 so that is .20 x .20 = .04
-We get 4% with curly hair
-To get the percentage for heterozygous we have to remember that there are two possibilities for heterozygous, p x q and q x p. which is 2pq.
-So we take .8 x .2 = .16 and .2 x .8 = .16 we add both of these together to get 32% wavy hair
If these allele frequencies were to remain relatively the same generation after generation then the population would be in a Hardy-Weinberg Equilibrium. In that case we would say that the population is not evolving
In order for a population to be in a Hardy-Weinberg Equilibrium these 5 conditions must apply
1) No mutations
2) Random Mating
3) No natural Selection
4) Extremely Large Population Size
5) No Gene Flow
Time for a quick writing exercise!
-Write a paragraph explaining why each of these 5 conditions must be present for evolution to not occur
With our hair texture example we could tell how many heterozygous individuals there were because it shows in their phenotype. When it is unclear if an individual is heterozygous we have to guess
There is a disease called PKU (phenylketonuria) that is contracted when you are homozygous recessive for the disease.
-PKU means that you can not ingest any phenylalanine otherwise it results in mental disability.
-We know that the disease affects 1 in every 10,000 births so that would mean q^2 = .0001 so q = the square root of .0001 which is .01
-p = 1 - q which is 1 - .01 = 0.99
2pq = 2 x .99 x .01 = 0.0198 (almost 2%)
homozygous recessive are .01% of the population
Heterozygous is 2% of the population
Homozygous dominant are 98% of the population
Lets take a 10 minute break and when you get back start practicing by solving the Skills Exercise in your book on page 406 (1-5)
If we have time we will start talking about the History of Life