The evolution of populations & Hardy- Weinberg Equilibrium FRIDAY, SEPTEMBER 5, 2014

The evolution of populations & Hardy-Weinberg EquilibriumFRIDAY, SEPTEMBER 5, 2014

Warm-up What do you think is the most important component in order for evolution to occur? (Hint: think about the definition of evolution).

Homework Be a leader assignment… due Monday, September 8!◦Directions: Solve your problem on a separate sheet of paper and staple it to your given worksheet slip. Hand it in on Monday.

◦Be prepared to show your group how you solved the problem!

Lamarck vs. Darwin

Inheritance of acquired characteristics Natural selection

Evolution is change in the genetic composition of a population from generation to generation

But what is a more concise definition for evolution that will help us determine quantitatively if evolution is occurring??

Evolution is the change in allele frequencies over time

How can we measure allele frequencies?

How can we track changes in allele frequencies over time?

Genetic variation exists in the population (this is key for evolution to occur!)

Certain alleles produce traits that are more adaptive, i.e., promote greater survival and reproduction

These alleles get passed on to the next generation

Evolution is the change in allele frequencies in a population over generations Population: group of individuals of the same species that live in the same area and interbreed, producing fertile offspring. Gene pool: genetic makeup of a population

Evolution is the change in allele frequencies in a population over generations

Mechanisms that cause allele frequency change:◦ Natural selection◦ Genetic drift◦ Gene flow◦ Mutation◦ Non-random mating

Only natural selection causes adaptive evolution

Mini genetics review

Alleles are different versions of that geneExample:

Combinations of alleles

Example for a population in which alleles for a gene are ‘R’ or ‘r’ Homozygous recessive: rr Homozygous dominant: RR Heterozygous: Rr

Skittles gene pool

Now, how do we measure changes in allele frequencies in populations over time?

First, we must know the starting point

What are the allele frequencies in the population right now? We cannot measure change unless we know the initial state.

Use Hardy-Weinberg Principle to quantify evolution

Godfrey Harold "G. H." Hardy Wilhelm Weinberg

The idea is to track allele frequencies

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

What is the frequency of allele A?What is the frequency of allele a?

The idea is to track allele frequencies

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

The frequency for allele A = 13/20 or 0.65The frequency for allele a = 7/20 or 0.35

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

Generation 1

?

Generation 2

Hardy-Weinberg Principle Allele frequencies of alleles and genotypes in a population will remain constant from generation to generation if all assumptions are met

A gene pool that remains constant is said to be in Hardy-Weinberg equilibrium

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

Generation 1

?

Generation 2

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

Generation 1

A0.65

a0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12

Generation 2

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

f(A) = 0.65f(a) = 0.35

A0.65

a0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12

f(A) = ?f(a) = ?

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

f(A) = 0.65f(a) = 0.35

A0.65

a0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12

f(A) = 0.65f(a) = 0.35

Allele frequencies did not change, thus no evolution.

The Hardy-Weinberg Principle

Allele frequencies in a population will remain constant if ALL of the following conditions are met:

1. The population is infinitely large2. Individuals mate randomly3. No gene flow4. No natural selection5. No mutations

If all conditions are met, then NO evolution. Allele frequencies will remain constant. This is the null hypothesis.

The Hardy-Weinberg equation: p2 + 2pq + q2 = 1A

0.65a

0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12

Understanding the equation

AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

p2 + 2pq + q2 = 1p is the frequency of the dominant allele (A) = 0.65q is the frequency of the recessive allele (a) = 0.35


p = f(AA) + ½ f(Aa)p = 0.5 + ½ 0.3 = 0.65

q = f(aa) + ½ f(Aa)q = 0.2 + ½ 0.3 = 0.35


AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

Using p and q from generation 1, solve for frequencies of predicted genotypes in generation 2 using HW


A0.65

a0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12


p = f(AA) + ½ f(Aa)p = 0.5 + ½ 0.3 = 0.65

q = f(aa) + ½ f(Aa)q = 0.2 + ½ 0.3 = 0.35

Generation 2p = f(A) = 0.65q = f(a) = 0.35


A0.65

a0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12

Generation 2p = f(A) = 0.65q = f(a) = 0.35


p = f(AA) + ½ f(Aa)p = 0.5 + ½ 0.3 = 0.65

q = f(aa) + ½ f(Aa)q = 0.2 + ½ 0.3 = 0.35

p2 = the predicted frequency of genotype AA = 0.422pq = the predicted frequency of genotype Aa = 0.46q2 = the predicted frequency of genotype aa = 0.12

The Hardy-Weinberg equation: p2 + 2pq + q2 = 1

What is the frequency of alleles B and b?

Allele Frequencies

a) red = 0.36, white = 0.16

b) red = 0.6, white = 0.4

c) red = 0.5, white = 0.5

d) Allele frequencies cannot be determined unless the population is in equilibrium.

Red short-horned cattle are homozygous for the red allele, white cattle are homozygous for the white allele, and roan cattle are heterozygotes. Population A consists of 36% red, 16% white, and 48% roan cattle. What are the allele frequencies?

Allele Frequencies

a) red = 0.36, white = 0.16

b) red = 0.6, white = 0.4

c) red = 0.5, white = 0.5

d) Allele frequencies cannot be determined unless the population is in equilibrium.

Red short-horned cattle are homozygous for the red allele, white cattle are homozygous for the white allele, and roan cattle are heterozygotes. Population A consists of 36% red, 16% white, and 48% roan cattle. What are the allele frequencies?

Let’s see another example

We sampled 200 individuals from a population:

128 individuals have the AA genotype

53 individuals have the Aa genotype

19 individuals have the aa genotype

What are the genotype frequencies?



128 individuals have the AA genotype (0.64)

53 individuals have the Aa genotype (0.26)

19 individuals have the aa genotype (0.10)

What are the allele frequencies?

Genotype frequencies






p = AA + ½(Aa) = 0.64 + ½(0.26) = 0.77

q = aa + ½(Aa) = 0.10 + ½(0.26) = 0.23


Allele frequencies






p = AA + ½(Aa) = 0.64 + ½(0.26) = 0.77

q = aa + ½(Aa) = 0.10 + ½(0.26) = 0.23p + q = 0.77 + 0.23 = 1.0p2 + 2pq + q2 = (0.77)2 + 2(0.77)(0.23) + (0.23)2 = 1.0


Allele frequencies

Let’s work through another example

Albinism (aa) occurs on average 1 in 20,000 individuals in North America.

What is the frequency of the A and a allele in this population?

Let’s work through another exampleAlbinism (aa) occurs on average 1 in 20,000 individuals in North America. What is the frequency of the A and a allele in this population?


q2 = f(aa) = 1/20,000 = 0.00005√ q2 = √ 0.00005q = 0.007 (frequency of a in the population)

p = 1 – qp = 1 – 0.007 p = 0.993 (frequency A in the population)

p2 + 2pq + q2 (0.993)2 + 2(0.993)(0.007) + (0.007)2 = 1.0

p2 = 98.6% (AA)2pq = 1.4% (Aa)q2 = 0.005% (aa)

The Hardy-Weinberg Principle Allele frequencies in a population will remain constant if ALL of

the following conditions are met:1. The population is infinitely large2. Individuals mate randomly3. No genetic migration and mutation4. No natural selection5. No mutation

If ALL conditions are met, then there’s NO evolution. Allele frequencies will remain constant.


AA

AA

AA

AA AA

Aa

Aa

Aa

aa

aa

f(A) = 0.65f(a) = 0.35

A0.65

a0.35

A0.65

AA0.42

Aa0.23

a0.35

Aa0.23

aa0.12

What will happen if these assumptions are not met?1. The population is infinitely large2. Individuals mate randomly3. No genetic migration and mutation4. No natural selection

f(A) = 0.65f(a) = 0.35

Exit TicketWhat is the Hardy-Weinberg formula, and what does each component represent?

Work on Clover Study

Documents

The evolution of populations & Hardy- Weinberg Equilibrium FRIDAY, SEPTEMBER 5, 2014