Population Genetics

Mind Your P’s and Q’s

I. Introduction

• A. Old definition– 1. Change in the look

of the species over time in response to a changing environment

– 2. Difficult to work with experimentally

– 3. Hard to measure slow and gradual change

B. New Defintion of Evolution

• 1. changing allelic frequencies over time

• 2. represents a marriage of genetics and evolutionary theory

• 3. new area of biology is born• 4. population genetics• 5. allows evolution to be

quantified• 6. independently arrived at by two

investigators-Hardy and Weinberg

C. Definitions of Population Genetics

• 1. Species– a group of

organisms made up of different populations whose individuals have the ability to interbreed and produce fertile offspring

2. Population

• a. localized group of individuals belonging to the same species

• b. Members of the same population tend to be more closely related to eachother than to other populations

• c. result of inbreeding and proximity

• d. A population is the smallest unit of living organisms that can undergo evolution.

3. Gene pool

• a. sum of all of the alleles present in a population

• b. each individual organism donates two alleles for each gene as they are diploid

• c. walk down to gym and release genes

• d. If homozygous for the gene-allele is said to be fixed

4. Allelic frequencies

• a. P = the frequency of the dominant allele in the gene pool

• b. Q = the frequency of the recessive allele in the gene pool

• c. Calculate the p and q values from the population on the right.

5. Genotypic frequencies

• a. Construct punnet square• b. Fishing example• c. Values total 1

6. Example

• need an example to illustrate-population of students with freckles• freckles is the dominant allele and the condition of no freckles is the recessive allele• F = freckles f = no freckles• 500 individuals in our population and let’s have 20 individuals with no freckles, 160

heterozygous with freckles, and 320 of the individuals with homozygous dominant for the trait.

• we can calculate the percentage of recessive and dominant alleles in the gene pool• 500 individuals donate 1000 alleles to the gene pool• 20 individuals are ff = 40 alleles are there any other recessive alleles to be concerned

with?• 160 Ff = 160 recessive alleles from this source brings up the total to 200 alleles for the

recessive condition• if the recessive is 200 alleles, it must be that the dominant type makes up the rest of

the 1000 which is 800• verify• -320 FF = 640 alleles• -160 Ff = 160 alleles and the grand total is 800 alleles

7. PKU

• one in 10,000 babies is born with this condition

• knowing this number we can predict all of the other frequencies

• this represents q2 = .0001 take the square root of both sides and you have q = .01 or 1%

• p would then be equal to .99 or 99%

• what are the chances of being a carrier for this trait?

II. Hardy Weinberg Equilibrium

• A. Definition• B. Conditions• 1. Must have very

large population sizes

2. Must be no migration into or out of the population

3. Must be no mutation-or if mutations occur-they must be equal in the forward as well as in the backward direction

4. Must be random mating

5. Must be no natural selection

6. No natural selection essentially means that all organisms have the same fitness

C. Value of H-W equilibrium

• 1. Static allelic and genotypic frequencies• 2. Represents a situation of no evolution• 3. Idealized situation• 4. Can compare natural populations to idealized• 5. Zero in on source of evolutionary pressures

III. Forces driving microevolutionary change

Example of microevolution

A. Natural selection

• Hair color comes in two varieties the dominant white color (R) and the recessive red color (r)

• Make up the gene pool with 50 red pieces of plastic representing the recessive and 50 white which represent the dominant allele

• What are the initial p and q values for this population • 1. p = .5• 2. q = .5

2. Genotypic frequencies

• a. Homozygous dominant• b. Heterozygous• c. Homozygous recessive

3. Conditions change-new predator arrives

• the predator is a hawk who has keen vision

• he can see the red rabbits very well and completely depletes their number every generation

• this would represent total selection against the red color

• 13 WW 25WR 12RR

• 12 red rabbits are annihilated this generation

4. Recalculate p and q

• compute the number of surviving rabbits = 38 rabbits• how many alleles are in the gene pool = 38 x 2 = 76• of those 76 alleles, how many are the recessive type• this number is simply the single copy of the recessive allele that each

heterozygote possesses• 25/76 = 33% is equal to the new q value• if q is equal to 33%, the new p is equal to 67%• renew the gene pool to 100 alleles reflecting the new p and q values• draw again

Sample problem• A liver disease is caused by a

recessive allele. One person in one hundred possesses the condition.

• What are the values of p and q in this population?

What is the percentage of carriers

in the population?

Sample problem• Tall is dominant to short. A group of

individuals left to colonize an island probably wishing to get away from the rat race. Two short women and a short man join three heterozygous tall men on the raft.

• a. What are the p and q values for the pioneering group?

• b. After several years of inhabiting the island, its population grows to 2500 people. If H-W conditions were in effect, how many homozygous tall people would you find in the population?

• c. A decree is handed down from the governing body which rules that all short people have to leave the island tomorrow because it is getting too crowded. What are the new p and q values of the population?

•

B. Mutations

• 1. occur very infrequently• 2. in a large population, the

values of p and q are not shifted rapidly due to mutation

• 3. this is the source of evolutionary change as it produces the raw material on which natural selection operates

• 4. new alleles arise as mutations

C. Migration• 1. another name for migration is gene flow-either immigration or

emigration• 2. usually the numbers of individuals who move out or into a population do

not change the p and q• 3. the inertia of a large population mass buffers changes brought about by

gene flow• 4. obviously migration has a homogenizing effect on two separate

populations if enough occurs Time_Fall_1993.jpg• 5. populations evolving under different local conditions will look very

different

D. Population size

• 1. population size can produce a sampling error

• 2. coin flip• 3. any population that is over

10,000 individuals is relatively free from sampling error

• 4. if a population becomes very small, the p and q values of the population can change by chance alone

• 5. chance change in p and q values due to small population size is called genetic drift.

Sample calculations

• a. allele “a” makes up 1% of the gene pool or q = .01• b. in a population of 1,000,000 people the gene pool is

2,000,000• c. there would be 20,000 recessive alleles in the pool• d. in a population of 100 individuals the gene pool is 200

alleles• e. there are two recessive alleles in this pool• f. you can see how it is easier to lose the two alleles than the

20,000 alleles

Example of genetic drift

5. Founder effect

6. Bottleneck effect

Example of bottleneck effect

Another analogy

E. Nonrandom mating-assortative mating

1. inbreeding

• a. Inbreeding depression

• b. Increase in homozygosity

2. Sexual selection

IV. Different types of selection

• A. Directional selection

B. Disruptive selection

C. Stabilizing selection

D. Clinal variation

• 1. Bergmann’s rule• 2. Allen’s Rule

Another example of clinal variation

E. Frequency dependent selection-scale eating cichlids

F. Heterosis or hybrid vigor

Sickle cell vs. malaria