11.2 Applying Mendel’s Principles

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11.2 Applying Mendel’s

Principles

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Lesson Overview Applying Mendel’s Principles

Probability and Punnett Squares

• Mendel carefully categorized and counted all of the offspring of each pea plant cross.

• When he crossed two plants that were hybrids for stem height (Tt),

• About three-fourths (3/4) of the offspring were tall

• About one-fourth (1/4) were short

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• The principles of probability can be used to explain the results of his genetic crosses.

• Probability: the likelihood that a particular event will occur.

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• Example: Coin flip

• Two possible outcomes: heads up or tails up

• The chance, or probability, of either outcome is equal.

o 1 in 2, ½, or 50%

• If you flip a coin three times, what is the probability that it will land heads up all three times?

• Each flip is an independent event, with a 1 in 2 chance of landing heads up.

• The probability of flipping 3 heads in a row is 1/2 × 1/2 × 1/2 = 1/8

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• There is a 1 in 8 chance of flipping heads three times in a row.

• Past outcomes do not affect future ones.

• Just because you’ve flipped a coin heads-up does not mean that you’re more or less likely to have a coin land heads-up on the next flip.

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Using Segregation to Predict Outcomes

• Alleles randomly

segregate during gamete formation.

• The principles of

probability can be used to predict the outcomes of genetic crosses.

• Mendel’s crosses

produced a mixture of tall and short plants.

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Using Segregation to Predict Outcomes If each F₁ (first generation)

plant had one tall allele and one short allele (Tt),

•1/2 of the gametes they produced would carry the short allele (t).

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Because the t allele is

recessive, the only way to produce a short (tt) plant is for two gametes carrying the t allele to combine.

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Each F₂ gamete has a one in two, or 1/2, chance of carrying the t allele.

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Using Segregation to Predict Outcomes There are two gametes,

so the probability of both gametes carrying the

t allele is:

½ x ½ = ¼

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Roughly one-fourth of the F₂ offspring should be short.

The remaining

three-fourths should be tall.

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This predicted ratio (3 dominant to 1 recessive) showed up consistently in

Mendel’s

experiments.

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For each of his seven crosses, about 3/4 of the plants showed the trait controlled by the dominant allele.

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About 1/4 of the

plants showed the trait controlled by the recessive

allele.

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Not all organisms with

the same characteristics have the same

combinations of alleles.

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• Both the TT and Tt allele combinations resulted in tall pea plants.

• The tt allele combination produced a short pea

plant.

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Organisms that have two identical alleles for a

particular gene (TT or tt) are said to be

homozygous.

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Organisms that have two different alleles for the same gene (such as Tt) are

heterozygous.

Pg. 535 Figure 2.2

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Probabilities Predict Averages

• Probabilities predict the average outcome of a large number of events.

• The larger the number of offspring, the closer the results will be to the predicted values.

• If an F₂ generation contains just three or four offspring, it may not match Mendel’s ratios.

• When an F₂ generation contains hundreds or thousands of individuals, the ratios usually come very close to

matching Mendel’s predictions.

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Genotype and Phenotype

• Every organism has a genetic makeup as well as a set of observable characteristics.

• Phenotype refers to the physical characteristics that genes control.

• Genotype refers to the genetic makeup.

• All of the tall pea plants had the same phenotype.

• They did not, however, have the same genotype.

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Genotype and Phenotype

• There are three different genotypes among the F2 plants: Tt, TT, and tt.

• The genotype of an organism is inherited,

whereas the phenotype is formed as a result of both the environment and the genotype.

• Two organisms may have the same phenotype but different genotypes.

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For the example below, name the:

Dominant allele - Recessive allele - Genotypes -

Phenotypes -

Homozygous (purebred) - Heterozygous (hybrid) -

Genotype: Genotype: Genotype:

Phenotype: Phenotype: Phenotype:

Quick Review

B ^b ^b ^b

B B

*Letter used is usually the first letter of the dominant trait

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Genetics Practice Problems

1. For each of the following, indicate if it is a genotype or a phenotype

Green leaves ___________________________ red hair __________________________ Gg _______________________

HH ____________________________ left handedness _________________________ nn ________________________

2. For each genotype below, indicate whether it is heterozygous (het) or homozygous (hom). If it is homozygous, indicate homozygous dominant with HomD and Homozygous recessive with HomR.

AA ____________ Bb ____________ Cc ____________ Dd ____________ EE ____________ ff ____________

Gg ____________ HH ____________ ii ____________ JJ ____________ kk____________ Ll ____________

Mm ____________ nn____________ oo ____________ PP ____________ Qq ____________ rr ____________

3. For each of the genotypes below determine what phenotypes would be possible.

Purple flowers are dominant to white Brown eyes are dominant to blue

PP _____________ BB ___________

Pp _____________ Bb ____________

pp ______________ bb _____________

Round seeds are dominant to wrinkled Bobtails are recessive (to long tails) RR ______________ TT ____________

Rr ______________ Tt ____________

rr _______________ tt _____________

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Using Punnett Squares

• Punnett Square: simple diagram that helps you predict the outcome of a genetic cross.

• Uses mathematical probability to predict genotype and

phenotype combinations.

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Monohybrid (One-Factor) Cross:

How To Make a Punnett Square

A monohybrid (aka one-factor) cross only looks at one trait.

Step 1: Write the genotypes of the two parent individuals.

Example: Cross between a male and female osprey (bird), both heterozygous for large beaks (B).

Genotypes:

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Step 2: Determine what alleles would be found in all of the possible gametes that each parent could produce.

Ex: What gametes could be produced (by male and female)?

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Step 3: Draw a table with enough spaces for each pair of gametes from each parent.

(One allele per space.)

•Enter the genotypes of the gametes produced by both parents on the top and left sides of the table.

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How To Make a Punnett Square Step 4:

Fill in the table by

combining the alleles.

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Step 5:

•Determine the genotypes and phenotypes of each offspring.

•Calculate the ratio or percentage of each genotype.

•Calculate the ratio or percentage of each phenotype.

Ex:

•Possible genotypes =

•Ratio of genotypes =

•Ratio of large beaks to short beaks =

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Quick Review

Which set of parents is most likely to have blue-eyed babies?

Parent 1=Bb Parent 2=BB Parent 3=bb Parent 4=Bb

Cross Parent 1 and 2 Cross Parent 1 and 4 Cross Parent 3 and 4

Chances of a child with blue eyes:

______ out of ________

or _________%

______ out of ________

or _________%

______ out of ________

or _________%

Punnett squares show you the probability of a genotype. What does probability mean?

Example: flipping a coin!

What percent do you think should be heads?

Actual (out of 4): Heads _____/4_ = _____% Tails _____/4_ = _____%

Terms: P = _____________, F1 = _______________, F2 = _______________

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Practice with Punnett Squares

1. In peas, round is dominant to wrinkled.

a. The genotype for round could be _________ or _________.

b. The genotype for wrinkled is _________.

c. What percent of offspring should be round if you cross RR x Rr?

d. What percent of offspring should be wrinkled with the same cross?

2. In pea plants, tall is dominant to short.

a. If a heterozygous tall plant is crossed with another heterozygous tall plant, what percent of the offspring should be short?

b. If a heterozygous plant is crossed with a homozygous recessive plant, what percent of the offspring should be short?

3. In pea plants, purple flowers are dominant to white flowers. If a white flowered plant is crossed with a plant that is heterozygous for the trait, what percentage of the offspring will have purple flowers?

4. In guinea pigs, the allele for long hair is recessive to short hair. What percentage of the offspring should have short hair if a pure breeding short haired guinea pig is crossed with a long haired guinea pig?

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Independent Assortment

Does having one trait affect the chances of having another?

Does the segregation of one pair of alleles affect other pairs?

•Mendel watched two genes as they

were passed from one generation to the next.

•These studies are called dihybrid, or two-factor, crosses, because they

involve two different genes.

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The Dihybrid (Two-Factor) Cross: F1

Mendel crossed true-breeding (homozygous) plants.

•Parent 1 was homozygous for round seed shape and yellow seed color

•Parent 2 was homozygous

recessive for both seed shape and color

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• Parent 1 (round, yellow) had the genotype RRYY, which is homozygous

dominant.

• Parent 2 (wrinkled,

green) had the genotype rryy, which is

homozygous recessive.

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What did he find?

•All of the F₁ offspring had round, yellow peas.

•The alleles for yellow and round peas are dominant to alleles for green and wrinkled peas.

•Genotype of each offspring was _________, heterozygous for both seed shape and seed color.

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Was any of this new information?

Not really, so…

•Mendel then crossed the F₁ plants to produce F₂ offspring.

Out of 556 total F₂ offspring:

•315 were round and yellow

•32 were wrinkled and green

•209 had combinations of

phenotypes not seen in the parents (yellow and wrinkled or green and round).

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What does this mean?

• The alleles for seed shape segregated independently of those for seed color.

Just because a pea was yellow did not mean it had to be

round, and vice versa.

• Genes that segregate independently do not influence each other’s inheritance.

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• Possible phenotypes?

• How many plants are predicted to have each phenotype? (phenotypic ratio)

• Possible genotypes?

• How many plants are predicted to

have each genotype? (genotypic ratio)

• Mendel’s results were very close to the 9:3:3:1 phenotypic ratio predicted.

• Principle of independent assortment:

genes for different traits can segregate independently during gamete

formation.

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A Summary of Mendel’s Principles

• Biological characteristics are determined by genes.

• Genes are passed from parents to offspring.

• If a gene has two or more alleles (forms), some may be dominant and others may be recessive.

• Dominant traits/alleles may

mask the presence of recessive alleles.

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• In most sexually reproducing organisms, each adult has 2 copies of each gene.

• One from each parent.

• May be same or different alleles.

• Genes segregate from each other when forming gametes.

• Gametes have a 1 in 2 chance of getting either allele.

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Alleles for different genes usually segregate independently of each other.

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• In early 1900s, American geneticist Thomas Hunt Morgan used fruit fly as a model organism in his genetics experiments.

• Chose fruit flies because they can produce lots of offspring quickly.

• Morgan and other biologists tested all of Mendel’s principles.

• Found they applied to other organisms, not just pea plants.

• Basic principles of Mendelian genetics can be used to study inheritance of certain human traits and calculate the probability of traits appearing in each generation.