Define population genetics

what does it help us to understand?

study of allele freq. over within a pop over time

NS and genetic drift

it is the number of individuals in a population with a certain genotype

divided by

the total number of individs in a population

# of each allele/total # of alleles

or

allele frequency= frequency of homozygous + 1/2 heterozygous

below are some genotype counts. Determine the corresponding genotype and allele frequency.

A₁A₁=60

A₁A₂=30

A₂A₂=10

Genotype frequncies: .6 ; .3 ; .1

Allele count A1: 150

Allele count A2: 50

Allele frequency A1: 150/200 = .75

Allele frequency of A2: 50/200 = .25

germ cells (ovary and testes): 2n=46

gametes (sperm and egg): 1n=23

zygote: 2n=26

what does Hardy-Weinberg describe?

also define HW

describes allelic and genotypic frequencies in EQUILIBRIUM

HWT: genotype/allele frequencies will remain constant from generation to generation in the absense of evolutionary processes like natural selection and genetic drift

Who contributed what to HW?

Where were they from?

Hardy: Cambridge Mathematician

Punnet: Cambridge geneticist

Weinberg: Germ physician and geneticist

(worked independantly)

Derive HWT

using A and B as your alleles

p=freq. of A

q=freq. of B

1. The probability (P) of an event is equal to its frequency. So p+q =1 because 100% of the time you will get either allele A or B.

2. Multiplication Rule: The P of two independant events occuting together= the product of their frequencies. So getting two of one allele with a frequency p= pp or p²

3. Either/Or Rule: If a population has two different alleles with frequencies "p" and "q", then the P of chosing both is 2*p*q*. The 2 is there because you could get this two different ways AB of BA)

how did they mathematically prove that a second generation would have the same allele frequencies as the first generation

?

1.We know the gametes that each genotype can produce.

AA can only give A

AB can give A or B

BB can only give B

2. We know the frequencies that these genotypes will appear at:

AA=p2

AB=pq

BA=pq

BB=q2

3. We can determine the frequencies of the offspring alleles

A= p2+pq

=p(p+q)

we know that p+q =1 (HW rule 1)

This applies for B too

1. Addition Rule: p+q=1 "the probabililty of an event is equal to it's frequency"

2. Multiplication Rule: "probability of 2 events happening=their product." Probability of AA = p x p =p2

3. Either or Rule: "If a pop has 2 diff alleles (A and B) with frequencies p and q, then the probability of gettin one of each = 2 x their product or

2xpxq

the two is there because there are two different ways to get AB: AB or BA

the lump curve is 2pq

the downward slope is p²

the upward slope is q²

*on the y axis is 0-1 of genotypic frequency

*the x axis describes the allele frequencies that coincide with a given genotypic frequency

What is the significance of the HW theorem?

1. relationships twix alleles and genotypes are specified after one genome

2. the allele-genotype relationship is a stable equilibrium over time

3. genetic variation can be maintained if it reaches HW

4. Allele frequency depends on mating patterns NOT on dominant recessive relationships (recessive traits won't just dissappear and there is not always a 3:1 ratio of phenotypes)

1. there are two types of lactate dehydrogenase in drosophila

 a fast LDH (small) and a slow LDH (big)

2. Heterozygotes have some of each

3. So we can take a fly, purify it's LDH proteins and put it through electrophoresis. If we see two bands then we must be dealing with the heterozygote. If we see one band at the bottom (where the small stuff goes) they we have a homozygote of LDHfast....etc etc

4. We can take a population of flies, figure out the frequency of each genotype and then determine the allele frequency based on what we see (experimental allele freq.)

5. Then we use the allele frequency based solely on genotype to see if the observed allele frequency is following HW (expected allele freq.)

We take 1012 flies.

figure out their genotypic frequencies of fLDH/fLDH, sLDH/sLDH, fLDH/sLDH

fLDH/fLDH = 546

fLDH/sLDH = 271

sLDH/sLDH = 195

what are the allelic freqs?

Is this in HWE?

Freq of

fLDH/fLDH = .54 = p²

fLDH/sLDH = .268 = 2pq

sLDH/sLDH =.193 = q²

observed allelic frequencies

Freq. of fLDH=.54+.5(.268)= .673=p

Freq. of sLDH= .193+ .5(.268)=.327=q

expected genotypic frequencies using observed allelic freq.

Freq. of fLDH/fLDH=p²= .673²=.453

Freq. of fLDH/sLDH=2pq=2(.673)(.327)=.440

Freq. of sLDH/sLDH= q²= .327²=.107

The expected genotypic frequencies don't match with the observed ones. HWE does not exist here, something else must be effecting allelic frequencies.

Ho is the null hypothesis. Says that observed and expected frequencies are not different

H₁ is the alternative hypothesis that says that observed and expected frequencies are different

1. Random Mating

2. Genotypes have= fertility

3. Therea are no survival differences between phenotypes (no NS)

4. No random genetic drift/samplin bias

5. Population size is approximately infinitely large

x² must be > x²_critical

where the critical value comes from a table

we usually use the .05 column

if this is true then there is a 95% chance of correctness

determine x² from the following:

fADH/fADH: observed=546: expected 458.4

fADH/sADH: observed=271: expected 445.3

sADH/sADH: observed 195: expected 108.3

using the next flashcard, can you regject the null hypothesis?

Do examples in slide set 2.2

29

33

find chi squared of the following expected and observed numbers