Beginning of Genetics: Transmission of Traits from one generation to the next.

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Peas and Probability

The proportion of the types of gametes and their union can be described by probability rules

Speaker Notes:

Individuals are result from the union of a male gamete and a female gamete. The particular union that takes place can be predicted from the proportions of types within the males gametes and the proportions of diverse types among the female gametes.

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Reading Assignment

The reading for today’s lecture is chapter 13 up to 13.2 plus ‘Solving Genetics Problems’ p.291.

Speaker Notes:

Pea natural history

From wild species varieties were developed by selection.
Varieties of peas are called “true-breeding” if all the offspring have the same traits as their parent, i.e., characters of the variety.

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Speaker Notes:

Alternative states among the varieties of pea studied by Mendel.

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Speaker Notes:

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Pea

Peas normally self-fertilize. The pollen matures and fertilizes the stigma of the same flower.
Mendel started his experiments by changing this normal pattern. He used pollen from one variety to fertilize a different variety.

Speaker Notes:

Apomixis is the most effective way to maintain traits from one generation to the next.

In the pea, a cross requires human manipulation.

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Speaker Notes:

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Pea Varieties

Variety A
- Axial flowers
- Yellow seeds
- Round seeds
- Inflated pods
- ….

Variety B
- Axial flowers
- Green seeds
- Wrinkled seeds
- Inflated pods
- ….

There are many varieties we consider only two today.

Speaker Notes:

Mendel made crosses among a number of different varieties.

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Two ways of crossing A & B

The cross between 2 varieties can be done two ways, ♂A with ♀B or ♂B with ♀A. The two crosses are called a pair of ‘reciprocal crosses’.

Speaker Notes:

How did people figure out they could take the flowers apart and use the parts to fertilize another plant?

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Offspring Phenotypes
of cross between varieties A & B

454 offspring (individual peas and plant that grew from the pea.)
All axial flowers
All round seeds
All yellow seeds
All inflated pods
The progeny from a cross between 2 true-breeding lines is known as the F1.

Speaker Notes:

Mendel kept records of the number of individuals within each type. Those counts were crucial to his theory.

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This fact is not surprising for axial flowers or inflated pods as the parents did not differ in those traits.

Are traits associated with variety B (wrinkled seed shape & green seed color) gone forever or are they present, but masked, in the F1 individuals?

All F1 individuals look like variety A.

Speaker Notes:

After mixing the two types could coexist, one type could convert the other type, or a new type could be created.

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F1 allowed to self –
Offspring of selfed F1 is called F2

F2 Seed Color: Mendel observed 416 YELLOW and 140 GREEN seeds.
F2 Seed shape: Mendel observed 423 ROUND and 133 WRINKLED seeds.

Speaker Notes:

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As the original types reappear in F2, one infers that neither the Green nor the Wrinkled causative agent was destroyed (in the F1). The green and wrinkled characters were probably just masked by the Yellow and Round characters, respectively.

If the F1 still has both characters, while only manifesting one, then one might expect the YELLOW F2 plants to be of 2 types, either like the parental A variety or like the F1.

Green & Wrinkled were not destroyed in F1

Speaker Notes:

How would you test if there were two types of F2 plants with YELLOW seeds?

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Mendel allowed the F2 to self to form an F3 generation.

The F2 YELLOW seeds were of two types. Some YELLOW seeds produced all YELLOW progeny in the F3 (i.e. were pure), others produced mostly YELLOW seeds with some GREEN mixed in (like F1).
In the F3 all the GREEN F2 seeds produce ONLY GREEN seeds in the F3 (so GREEN is always true-breeding or pure).

Speaker Notes:

So in the F2 there are 3 types altogether; yellow with all YELLOW progeny, YELLOW with both YELLOW and GREEN progeny and GREEN (which always have only GREEN progeny).

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Mendel’s Hypothesis

Mendel explained the F2 and F3 results by hypothesizing there were two factors, yellow and green, and that each plant had two factors. The original varieties (parents) had either 2 green or 2 yellow. The F1 plant had one yellow and one green factor.

Speaker Notes:

We used the term factor for modern term allele or gene.

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Mendel’s Idea in Color 1

Parents

When two different alleles (the name for the factors) are together in an individual, the allele seen in the phenotype is called dominant, the invisible allele is called recessive. This is Mendel’s Law of Dominance, his 1st law.

Speaker Notes:

The concepts can be represented by many symbols including colored balls.

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Mendel’s Idea in Color 2

Parents

Gamete’s

Selfing

Only one allele is included in a gamete. Each of the alleles in the F1 has an equal chance of being the one included.

Speaker Notes:

While the individuals one sees always have two factors, the gametes they produce only have one of the two. The rows and columns represent the types of gametes that can be produced and their proportions.

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From colors to letters
Rules for naming genes

Seed shape is controlled at a LOCUS, a place on a chromosome. A locus is symbolized with letters. Different characters (color, shape, etc) are controlled by separate loci each of which needs a distinct symbol.
ALLELES are the specific genetic material at a locus. The dominant allele is shown as a capital letter, the recessive allele as lower case. Alleles should be italicized.
G = yellow allele, g = green allele
R = round allele, r = wrinkled allele

Speaker Notes:

The conventions used for symbols make the system easier to understand.

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Conventional Symbols

Parents

Gametes

GG gg

G g

half G g half

G g

Each parent is homozygous, because the allele from the mother is the same as that from the father.

The F1 is heterozygous, it has a different from its mother as that from its father.

♀

♂

Speaker Notes:

Homozygous means the allele from the mother is the same as the allele from the father. Heterozygous means the two alleles are different.

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Expectations of offspring

Each individual offspring results from the union of a male gamete and a female gamete. If there are multiple types of gametes, the probability that a particular gamete is involved in a particular fertilization is proportional to the frequency of that type in the gamete pool, separately for each sex, of course.

Speaker Notes:

List all the types of male gametes. Write down the proportion of each type. The proportions must add to 1.

List all the types of female gametes. Write down the proportion of each type. The proportions must add to 1

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Expectations
for each offspring

Offspring possibilities and probabilities

Gamete unions Genotypes Phenotypes

GG = ½•½ = ¼ GG = ¼

Gg = ½•½ = ¼

gG = ½•½ = ¼

gg = ½•½ = ¼ gg = ¼ GREEN = ¼

YELLOW = 3/4

Gg = ½

Two possible males gametes times two possible female gametes = 4.

Possible types and expected proportions.

Speaker Notes:

From gametic unions to genotypes to phenotypes. That direction always works, the reverse does not always work.

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Expectations
for Multiple Offspring

Let us consider 3 F2 offspring. What are the possible outcomes for three offspring?

Outcomes probability

YELLOW, YELLOW, YELLOW = ¾•¾•¾ = 27/64

YELLOW, YELLOW, GREEN = ¾• ¾•¼ = 9/64

YELLOW, GREEN, YELLOW = ¾• ¼•¾ = 9/64

GREEN, YELLOW, YELLOW = ¼• ¾•¾ = 9/64

YELLOW, GREEN, GREEN = ¾• ¼• ¼ = 3/64

GREEN, YELLOW, GREEN = ¼• ¾• ¼ = 3/64

GREEN, GREEN, YELLOW = ¼• ¼• ¾ = 3/64

GREEN, GREEN, GREEN = ¼• ¼• ¼ = 1/64

27/64

9/64

Speaker Notes:

There is a difference between a specific order of colors and a question like two yellow and 1 green.

To answer what is the probability of getting 2 GREEN and 1 YELLOW add up all the ordered possibilities that add up to 2 GREEN and 1 YELLOW, i.e. 9/64 as shown to right.

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The probability of a particular ordered outcome (YGY) is the product of the probabilities of each independent event, ¾·¼·¾ =9/64

If you are asked what is the probability of 2 YELLOW and one GREEN, list all the outcomes that fulfill the desired condition, namely YYG, YGY, GYY. Add together the probabilities of each particular outcome to get probability of the condition.

Probabilities

Speaker Notes:

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Outcome Proportions

The observed total number(s) in each category can be compared to the numbers expected in each category with the χ2 (Chi-squared) test.

Next lecture the use of the χ2 (Chi-squared) test will be explored.

Speaker Notes:

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Problem

If you expect 3/4ths YELLOW and 1/4th GREEN, what proportion of the pods with 4 peas do you expect to have 3 YELLOW peas and only one GREEN pea?

Speaker Notes:

In this problem you will learn that the most likely outcome does not happen 100% of the time.

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Vocabulary

Locus
Allele
Phenotype
Genotype
Proportion
True breeding
Expected proportion

Dominant
Recessive
Heterozygous
Homozygous
Reciprocal cross
F1, F2 & F3
gametic genotype

Speaker Notes: