Hardy Weinberg Equilibrium

p2 + 2pq + q2 = 1

Two scientists independently derived the basic principle of population genetics called the Hardy – Weinberg Principle. This principle states that:

If all factors remain constant, the gene pool in a population will have exactly the same

composition generation after generation. This condition is called genetic equilibrium.

If the genetic equilibrium of a population is upset, the population is said to be evolving.

Evolution

"the sum total of the genetically inherited changes in the individuals who are the members of a population's gene pool." 

Evolution is simply a change in frequencies of alleles in the gene pool of a population.

Population

A group of the same species living in the same place at the same time

Gene pool

all of the genes / alleles that occur in a population.

Ex) human gene pool for blood type are IA, IB, and i.

Allele frequency

– % or proportion of that allele in the population

Conditions

Evolution will NOT occur and Hardy-Weinberg equilibrium will be met if the following conditions are met:

Conditions

1. No Mutation

Conditions

2. The population is infinitely large

- laws of probability must apply

Conditions

3. All members of the population breed

Conditions

4. All mating is totally random

Conditions

 5. Everyone produces the same number of offspring

Conditions

6. There is no migration in or out of the population

Equation

Equation used to find genotype frequencies:

p² + 2pq + q² = 1

And

p + q = 1

p is the frequency of the dominant allele

q is the frequency of the recessive allele

p2 is the frequency of the homozygous dominant genotypes

q2 is the frequency of the homozygous recessive genotypes

Equation

2pq is the frequency of the heterozygotes

Example

Albinism is only expressed in the phenotype of homozygous recessive individuals (aa).   

The average human frequency of albinism in North America is only about 1 in 20,000.

Question

Calculate the frequencies of the alleles and all three genotypes in this population.

Solution

Synthetic Theory of Evolution: Sample Hardy-Weinberg Problem

Examples:

1. In a population, 21% of the individuals are homozygous dominant, 49% are heterozygous and 30% are homozygous recessive. What percentage of the next generation are predicted to be homozygous recessive?

2. 16% of a population is observed to have a continuous hairline (recessive). What percentage of the population possesses the dominant allele? If there are 500 members in the population, how many would be heterozygous?

3. A recessive genetic disorder occurs in 9% of the population. What percentage of the population will be carriers for the disorder? What percentage will be homozygous dominant?

Quiz – Theoretical Ideas

http://w3.dwm.ks.edu.tw/bio/activelearner/18/ch18summary.html

Disturbances to Equilibrium

There are some situations that may make H-W equilibrium of alleles more likely to change:

1) Mutations

Whether a mutation is good or bad, often depends on the environment. A harmful mutation can turn out to have a selective advantage if the environment changes over time.

2) Non-random Mating

Individuals are often attracted to one another because they value specific traits. Ex. In humans, wolves, elk

-will reduce genetic diversity, thus decrease frequency of some alleles

3) Inbreeding

4) Genetic Drift

- a reduction in the gene pool variation caused purely by chance. Usually in small populations. If a specific allele doesn’t reproduce (by chance) it may be lost entirely.

Genetic Drift Example

5 ) Gene Flow

Migration – is the movement of genes into (immigration) / out of (emigration) the population. Some genes may migrate more readily than others.

6 ) Bottleneck Effect

occurs when a part of the population is eliminated by chance.

7) Founder Effect

- occurs when the founders of a new population have a specific genotype. Ex. polydactyl hands in Amish in Pennsylvania.

8) Natural Selection

Selective Advantage: the most important reason for changes to H-W equilibrium

New mutations may arise that give the organism an advantage over others of the same species

These alleles become more common with time

Means that some alleles are helping individuals to survive and reproduce

I. Stabilizing Selection:

atypical phenotypes are eliminated, and an average is favored. Ex. birth weight or color.

II. Directional Selection

– an atypical phenotype is selected for because of a progression of change in the environment. Ex. horse evolution, peppered moth.

III. Disruptive Selection

two or more phenotypes are selected due to different characteristics within a habitat. Ex. fish that feed on bottom vs fish that feed on top.

Speciation

Divergence producing new species, two types:1.Allopatric speciation: physical

separation of species drives the splitting of one species into two (or more)

Eg. Grand Canyon SquirrelsDarwin’s Finches

May not be immediately obvious Eg. Anole lizards

in Cuba – not physically separated now, but were 5 million years ago

Allopatry Animation

2. Sympatry

Division of one species into two or more in absence of physical barriers

Disputed by some

H-W Equilibrium - Summary

Does not change unless a force is acting upon it

This force is often natural selection – leads to evolution