Genetics & Probability

Mendel’s laws: segregation independent assortment

reflect same laws of probability that apply to tossing coins or rolling dice

What is Probability? Probability is the likelihood that a particular event

will occur.

It does not ALWAYS happen (think Deal or No Deal)

Can be written as a decimal, percentage, ratio, or fraction

How do we use the principles of probability in our daily lives?

Ex.Horse racingNCAA March MadnessSuperbowl Coin TossLas Vegas $$$$$

Probability & genetics

Calculating probability of making a specific gamete is just like calculating the probability in flipping a coin probability of tossing heads?

50% probability making a gamete…

PP

P

P

Pp

P

p

50%

100%

Determining probability

Number of times the event is expected Number of times it could have happened

What is the probability that you picked an odd number when picking from 1-10? There are five odd numbers between 1 and 10.

Or you can express it as a fraction: 5/10. Since it's a fraction, why not reduce it? The probability that you will pick an odd number is 1/2.

Probability can also be expressed as a percent...1/2=50% Or as a decimal...1/2=50%=.5

Chance that 2 or more independent events will occur together probability that 2 coins tossed at the

same time will land heads up

Or .25 or 25% or 1:4 probability of Pp x Pp pp

Rule of multiplication

1/2 x 1/2 = 1/4

1/2 x 1/2 = 1/4

Terminology and Directions

ALLELES = (WARNING - THIS WORD CONFUSES PEOPLE; READ SLOW) alternative forms of the same gene. 

Hair Texture Gene- Straight (S) or Curly (s)

One form of the gene codes for curly hair. 

A different code for of the same gene makes hair straight. 

So the gene for hair texture exists as two alleles --- one curly code (s), and one straight code (S).

Alleles

Dominant (Capital Letter) Shows up more in a

population, Expresses itself when it is present

Recesive (Small Letter) Shows up less in a

population, only shows when there is no dominant trait.

GENOTYPE = the genes present in the DNA of an organism. 

We will use a pair of letters (ex: Tt or YY or ss, etc.) to represent genotypes for one particular trait. 

There are always two letters in the genotype -one letter (gene) from mama organism -one letter (gene) from papa organism

Phenotypes

PHENOTYPE = how the trait physically shows-up in the organism. 

Wanna know the simplest way to determine an organism's phenotype ? 

Look at it.  Examples of phenotypes: blue eyes, brown fur, striped fruit, yellow flowers.

VOCAB

Now, turns out there are three possible GENOTYPES – two big letters (like "TT"), one of each ("Tt"), or two lowercase letters ("tt").

Since WE LOVE VOCABULARY, each possible combo has a term for it.

Hetero/ Homo

Two capital (TT) or

Two lowercase (tt) in the GENOTYPE

Called HOMOZYGOUS ("homo" means "the same"). 

Sometimes the term "PUREBRED" is used instead of homozygous.

Heterozygous

When the GENOTYPE is made up of one capital letter & one lowercase letter (ex: Tt) it's called HETEROZYGOUS ("hetero" means "other").  Just to confuse you, a heterozygous

genotype can also be referred to as HYBRID.

Let's Summarize:

Genotype = genes present in an organism (usually abbreviated as two letters)

AA = homozygous = pure Aa = heterozygous = hybrid aa = homozygous = pure

Quick Review

Genotype= genes of the organism “Letters” ex. TT or Tt or tt.

Phenotype= the physical appearance of a trait in an organism What it physically looks like.

The Letters are chosen for the Dominant trait of the allele.

Homozygous and Heterozygous

When we have two capital or two lowercase letters in the GENOTYPE (ex: TT or tt) it's called HOMOZYGOUS ("homo" means "the same").  Sometimes the term "PUREBRED" is

used instead of homozygous. When the GENOTYPE is made up of one

capital letter & one lowercase letter (ex: Tt) it's called HETEROZYGOUS ("hetero" means "other").  Just to confuse you, a heterozygous

genotype can also be referred to as HYBRID.

Dominant and Recessive

Dominant (Capital Letter) Shows up more in a population, Expresses itself when it is present

Recesive (Small Letter) Shows up less in a population, only shows when there is no dominant trait.

Punnet Square

Baby steps of Punnet Squares

1. Determine and write down the genotypes of the parents

2. Draw a punnet square of appropriate size3. Split the letters of the parents and put

them on the outside4. Do the punnet square5. Summarize the results by showing

genotypic and phenotypic ratios

Punnet Square Practice Steps 1 -Determine the genotypes of the

parents and write them down Tall (T) is dominant to short pea plants (t).

Cross a short pea plant with one that is heterozygous for tallness. What are the parents genotypes? tt x Tt

Cross a short pea plant with one that is heterozygous for tallness. What are

the parents genotypes?

tt x Tt

T

t

t t

3. Draw a p-square4. Split the letters of the

parents and put them on the outside

5. Do the punnet square

Tt Tt

tt tt

Summarize the results by showing genotypic and phenotypic ratios

Genotypic Ratio (letters) TT- 0 or 0/4 or 0% Tt- 2 or 2/4 or 50% tt- 2 or 2/4 or 50%

Phenotypic (looks) Tall- 2 or 2/4 or 50% Short- 2 or 2/4 or 50%

Tt Tt

tt tt

T

t

t t

Decide what the genotypes of the parents are In humans, brown eyes, B, are dominant to

blue eyes, b. If the father has brown eyes and is homozygous dominant for the trait, BB, and the mother has blue eyes and is homozygous recessive for the trait, bb, what are the possible genotypes and phenotypes of their offspring.

Father-homozygous dominant-BB Mother-homozygous recessive-bb

Then, write the genotype for one parent across the top of the punnett square, and the genotype for the other parent along the left side of the square.

B B

b

b

Fill in the boxes inside with whatever letter are on top and to the left of them

B B

b

b

The genotypes inside the boxes represent the possible gene combination of their offspring

Each box is a 25% or ¼ chance

So, the genotypes of all the offspring in this genetic cross would be Bb

Because there is at least one dominant allele the phenotype (appearance) would also be dominant all offspring would have brown eyes

B B

b

b Bb

BbBb

Bb

Try another punnett square

Two brown eyed parents, who are both heterozygous for the trait, Bb, mate. What are the chances they will have a blue eyed child?

Step 1

•What are the genotypes of the 2 parents?

Step 3

B b

b

B

Step 4

B b

b

B BB

bbBb

Bb

Step 5

Genotypes of offspring BB-1/4 or 25% Bb-1/2 or 50 % Bb-1/4 or 25%

Phenotypes of offspring Brown eyes (BB and Bb)-

3/4 or 75% Blue eyes (bb)-1/4 or

25% Probability of blue eyed

child=1/4 or 25 %

B b

b

B BB

bbBb

Bb

Biology

What is a dihybrid cross?

Work 2 genes at once

Find the expected offspring for both traits

They are a little more work than the monohybrid cross, but…

So much fun!!

Steps to solving a dihybrid problem 1. Read the problem and find the two

separate traits. Sample problem: In Springfield, red hair (H) is

dominant to blue hair (h) and having four fingers (F) on your hand is dominant to having five fingers (f). If Side Show Bob and Mrs. Van Houten get married and decide to have a little brother for Millhouse, what is the chance that the newborn will have red hair and five fingers if Side Show is heterozygous for red hair and heterozygous for four fingers and Mrs. Van Houten has blue hair and is homozygous for four fingers?

Genotypes

2. Find the two parents and write down their genotypes.

HhFf x hhFF

What do they Want?

3. Read the question and see what you have to look for. Do they want you to find a ratio, percent, fraction, or do they want you to list all possibilities?

Math Class

4. Once you have found all the information, you can start to set up the problem by finding the gametes for each parent by using FOIL.

FOIL stands for First, Outside, Inside, Last

FOIL

Here is an example of how to use FOIL:

(a + b) * (c + d) First = (a + b) * (c + d) = ac Outside = (a + b) * (c + d) = ad Inside = (a + b) * (c + d) = bc Last = (a + b) * (c + d) = bd So our pairs are: ac, ad, bc, bd

Parent Genotypes

Now try it with the parents alleles Side Show = HhFf So, HF, Hf, hF, hf Mrs. Van Houten = hhFF So, hF, hF, hF, hF

DiHybrid (Double Cross)

5. Once you have the gametes, you have to line them up in a punnett square.

You are going to need a bigger square!

Put the gametes of one parent across the top of the square and the other down the side of the square

HF Hf hF hf

hF

hF

hF

hF

6. Now you have to do the actual cross.

This is a single box example. Remember to always put the

two like alleles back together, The same letters go together,

and The capital letter should go

first Keep the same sequence of

alleles (letters)

HhFF

HF

hF

Fill in the rest of the box!

HhFF HhFf hhFF hhFf

HhFF HhFf hhFF hhFf

HhFF HhFf hhFF hhFf

HhFF HhFf hhFF hhFf

HF Hf hF hf

hF

hF

hF

hF

Genotypic Ratio

7. Find the genotypic ratio

HhFF = 4/16 (25%) HhFf = 4/16 (25%) hhFF = 4/16 (25%) hhFf = 4/16 (25%)

Phenotypic Ratio

8. Find the phenotypic ratio

Red hair, four fingers = 8/16 (50%)

Blue hair, four fingers = 8/16 (50%)

Answer the Question

9. Now, don’t forget to answer the question!

If Side Show Bob and Mrs. Van Houten get married and

decide to have a little brother for Millhouse, what is the chance that the newborn will have red hair and five fingers if Side Show is heterozygous for red hair and heterozygous for four five fingers and Mrs. Van Houten has blue hair and is homozygous for four fingers?

0%

Review: Dominant/Recessive

One allele is dominant over the other (capable of masking the recessive allele)

PP = purple pp = white Pp = purple

Review Problem: Dominant/Recessive

In pea plants, purple flowers (P) are dominant over white flowers (p) show the cross between two heterozygous plants.

P

p

P p

pp

Pp

Pp

PP- PP (1); Pp (2); pp (1)- ratio 1:2:1

- purple (3); white (1)- ratio 3:1

GENOTYPES:

PHENOTYPES:

Incomplete Dominance

Incomplete dominance is when one allele is not completely dominant over the other.

The alleles do not blend, but the phenotype is a blending of the two traits.

Incomplete Dominance

Ex. Flower Color in 4 O’clocks

RR = red rr = white Rr = pink

Problem: Incomplete Dominance Show the cross between a pink and a

white flower.

- Rr (2); rr (2)- ratio 1:1

- pink (2); white (2)- ratio 1:1

R r

r

r

rrRr

rrRr

GENOTYPES:

PHENOTYPES:

Codominance

Codominance are when the alleles are neither dominant or recessive.

In cases of codominance, both traits are expressed in the offspring

Symbols are always written as capital letters.

Example of Codominance

In chickens-they are either white, black or black and white

The colors are comdiminant

Another Example of Codominance

•White and red are codominant.

•Cows are white, red or red and white

Codominance

The heterozygous condition, both alleles are expressed equally

Sickle Cell Anemia in Humans

NN = normal cells

SS = sickle cells NS = some of each

Problem: Codominance

Show the cross between an individual with sickle-cell anemia and another who is a carrier but not sick.

N S

S

S

NS

NS

SS

SS

- NS (2) SS (2)- ratio 1:1

- carrier (2); sick (2)- ratio 1:1

GENOTYPES:

PHENOTYPES:

Multiple Alleles

There are more than two alleles for a trait

Blood type in humans Blood Types?

Type A, Type B, Type AB, Type O

Blood Alleles? A, B, O (in book – IA, IB, I)

Rules for Blood Type

A and B are codominant AA = Type A BB = Type B AB = Type AB

A and B are dominant over O AO = type A BO = type B OO = type O

Blood Also Shows Codominance

Problem: Multiple Alleles Show the cross between a mother who has type

O blood and a father who has type AB blood.

- AO (2) BO (2)- ratio 1:1

- type A (2); type B (2)- ratio 1:1

GENOTYPES:

PHENOTYPES:

O O

A

B

AO

BO

AO

BO

Problem: Multiple Alleles Show the cross between a mother who is

heterozygous for type B blood and a father who is heterozygous for type A blood.

-AB (1); BO (1); AO (1); OO (1)- ratio 1:1:1:1

-type AB (1); type B (1) type A (1); type O (1)- ratio 1:1:1:1

GENOTYPES:

PHENOTYPES:

A O

B

O

AB

OO

BO

AO

Sex-Linked Inheritance

Traits that are only found on the X or Y chromosome

Colorblindness and Hemophilia are examples of sex-linked traits.

These genes are recessive and found only on the X chromosome.

Sex-linked Punnet Squares

Constructed the same way as a regular Punnet Square.

Alleles are placed next to the X chromosome.

Sex-linked Punnet Squares

XB Xb

XBXb XbXb

XBY XbY

Xb

Y

Definition

Some traits are determined by the combined effect of two or more pairs of alleles. These traits are called polygenic traits.

Each gene contributes a small but additive effect to the trait.

Other names for polygenic traits are multi-factorial traits, or quantitative traits.

Polygenic traits are continuous

Because so many alleles contribute to the final phenotype, a variety of phenotypes can occur!

For example, height is a polygenic trait. If you look around, you will notice there are not two set heights, but rather a continuum of height among your classmates.

Another example of a polygenic trait: Hair Color

Hair color is controlled by alleles on chromosomes 3, 6, 10, and 18.

The more dominant alleles that appear in the genotype, the darker the hair!