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9/23/05 Mendel Revisited

In typical genetical parlance the hereditary factorthat determines the round/wrinkled seed differenceas referred to as “the gene” for round or wrinkledseeds

What we mean more precisely is that this genecontrols the difference in seed form between theround and wrinkled strains that Mendel worked with

Does Mendel’s work suggest that this is the onlygene in the pea genome that can affect this particulartrait?

If not, then why is round vs. wrinkled referred to asa single-gene trait?

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Inheritance of a single trait: round or wrinkled seeds♦ Mendel crossed a true-breeding line that had round seeds with

a true-breeding line with wrinkled seedsPARENTAL♦ All of the progeny seeds resulting from this cross were

round. These progeny are called the F1 (for first filial)generation. [Subsequent generations are indicated as F2, F3,and so on.]

♦ Mendel then did a reciprocal cross and obtained the sameresult

♦ What was the significance of the results of the reciprocalcrosses?

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♦ Mendel planted the F1 seeds and allowed the F1 plants toself-pollinate

♦ In this F2 generation, he observed♦ 5474 round and 1,850 wrinkled seeds, which represents a

ratio of round: wrinkled equal to 2.96 to 1.♦ This is essentially a 3 to 1 ratio.♦ In other words, about 3/4 of the F2 seeds were round and 1/4

were yellow. No seeds of intermediate phenotype wereobserved.

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♦ Mendel had made the striking observation that

even though the wrinkled form had disappeared inthe F1 generation, it reappeared in the F2generation.

♦ THERE WAS NO IRREVERSIBLE BLENDINGOF THE TRAITS

♦ To describe this result, he designated the roundphenotype as the dominant phenotype since itappeared in the F1 and the wrinkled phenotype asrecessive.

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Mendel repeated these experiments with the sixother traits and obtained similar results:1. The results of reciprocal crosses were the same2. One form of the trait was always dominant. The

F1 progeny only showed the dominant trait anddid not exhibit any intermediate phenotype.

3. In the F2 generation, the ratio of plants with thedominant and recessive phenotypes was 3 to 1.

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FROM THESE AND OTHER DATA

♦ Mendel proposed that the hereditary determinants foreach trait are discrete and do not become blendedtogether in the F1, but maintain their integrity fromgeneration to generation.

♦ Mendel also proposed that, for each trait examined, thepea plant contains two copies of the hereditarydeterminant (gene) controlling the trait, one copycoming from each parent

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Write up genotypes of crossesOMIT for students

MENDEL USED A SIMPLE SYMBOLISM TO CONNECT THEORY ANDOBSERVATIONS.♦ Mendel developed a simple symbolism to show how his principle of

segregation could be used to explain his observations.♦ He designated the genotype or genetic composition of a given pea

plant in the following manner.♦ Each pair of genes, was symbolized by a different letter.♦ The dominant form of the gene was indicated by an upper-case letter

and the recessive form by a lower-case letter.♦ These alternative forms of a gene are called alleles.♦ Returning to the experiments on seed form, the dominant round allele

is designated by R and the recessive wrinkled allele by r (Figure 4).♦ The genotype of the true-breeding parental round line is RR

indicating that it carries two copies of the round allele in each cell.♦ Such pure lines are said to be homozygous (homo -meaning

“identical”) for the round allele.♦ The genotype of the parental wrinkled line is rr indicating it is

homozygous for the recessive wrinkled allele.♦ The F1 round progeny contain a dominant allele for round contributed

by the round parent and a recessive allele for wrinkled contributed bythe wrinkled parent. T

♦ he F1 plants are Rr or heterozygous (hetero- meaning “different”)for the two different alleles.

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Using genetic symbolism, how is the 3 to 1 (dominant torecessive) F2 ratio explained?

Mendel’s principle of segregation• Mendel proposed that during gamete formation in the F1, the

paired Rr alleles would separate into different gamete cellsand that about 1/2 of the gametes would carry the dominant Rallele and 1/2 would carry the recessive r allele.

• This would be true for both the male and female gametes,• Mendel assumed that the male and female gamete cell would

combine at random.• So, a given R or r male gamete would have an equal chance of

fertilizing an R-bearing or an r-bearing ovule.

Two elements of chance are indicated here:• the chance that a gamete is R vs. r• the random (with respect to genotype)

combination of male gametes with female gametes

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Because of the element of chance in theseprocesses, we need to use the rules ofprobability to make predictions about thegenotypic and phenotypic composition ofthe F2 progeny

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A probability is a measure of the likelihoodor chance, that an event will have aparticular outcome.

A probability is usually expressed as afraction between 0 and 1.

1 - the event is certain to occur

0 - the event is certain not to happen

In all other cases the chance that a particularevent will occur increases as the probabilityapproaches 1

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The product (both-and) rule of probability:the probability of two independent events bothoccurring is the product of each of theirrespective probabilities

To use the product rule, the events must beindependent: the occurrence of one eventcannot affect in any way the probability ofthe other event occurring

This rule can be applied to multipleindependent events

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What is the outcome of such chance events?Mendel recognized that the basic rules ofprobability could be used to predict thelikelihood of each genotype (RR, Rr and rr)for a given F1 progeny.

• What is the chance that an F2 progenyshows the recessive phenotype? Accordingto the product (both-and) rule ofprobability, the probability that a givenzygote received an r allele from both themale and females gametes is 1/2 X 1/2 or1/4.

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The sum (either-or) rule of probability

The probability of either one of twomutually exclusive events occurring is thesum of their respective probabilities

In other words we are determining theprobability of one event or another event(either-or rule)

This rule applies to multiple events

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What is the chance that an F2 progenyshows the dominant phenotype?• Here we have to use the product (both-

and) and the sum (either-or) rules ofprobability.

• To show a dominant phenotype thegenotype of the F2 can be either RR or Rr.

• The probability of a dominant phenotype = (1/2)(1/2) + 2(1/2)(1/2) =3/4

RR Rr

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If a large number ofindependent fertilization eventsare examined these phenotypeprobabilities translate into thefraction of progeny that shouldbe of each phenotype:

• 3/4 of the F2 progeny shouldshow the dominant phenotypeand 1/4 the recessive.• Here then is Mendel’s 3 to 1ratio

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Mendel’s analysis predicted two classes of F2 roundprogeny

How to confirm that the round F2s consists of twodifferent genotypes in the proper ratio?

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• To confirm these predictions Mendel planted the F2 seeds andallowed the F2 plants to self-pollinate.

• He then examined the phenotypes of the F3 seeds.• As predicted, F2 plants showing the recessive phenotype always bred

true.• There were two classes of F2 progeny with the dominant phenotype.

One class bred true when self-pollinated.• The other class produced seeds with the dominant and recessive

phenotypes in a 3 to 1 ratio:

Fraction of F2 Phenotypeof F2

Phenotype ofF3 progeny

Genotype ofthe F2 plant

1/4 dominant all dominant

1/2 dominant 3/4 dominant1/4 recessive

1/4 recessive all recessive

1. For example, Mendel selfed 519 round plants from the F2 generationof the crosses described above.

2. He observed that 193 bred true (producing only round progeny) and372 plants produced both round and wrinkled seeds, giving a ratio ofhomozygotes to heterozygotes of 1.93 to 1 (~2 to 1).

ARE you OKAY with this?

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MENDEL EXTENDED HIS EXPERIMENTS BY EXAMININGTRAITS TWO AT A TIME♦ Mendel also was interested in knowing whether his

principle of segregation held true when the parentallines differed with respect to two or more traits.

♦ He crossed a parental line that had round, green seedswith a parental line with wrinkled, yellow seeds.

♦ As expected, all F1 seeds showed the dominant yellowand round phenotypes.

♦ Mendel then allowed the F1 plants to self-pollinate andexamined the phenotype of the F2 seeds.

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♦ Mendel observed four phenotypic categories in the F2generation.

Phenotype of F2 Number of F2(556 total)

Fraction of totalprogeny

yellow, round 315 9/16yellow, wrinkled 101 3/16green, round 108 3/16green, wrinkled 32 1/16

HOw to analyze this data so it makes sense in thecontext of the previous experiments

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He analyzed in the following way:♦ First he looked at the data for seed color only and noted

that the ratio of yellow (315 + 101 F2 plants) green (108 + 32 F2 plants) 416 to 140 or 3 to 1.♦ Likewise, the ratio of round (315 + 108) to wrinkled (101 + 32) seeds was 423 to 133 or 3.18 to 1.♦ For each trait, the F2 seeds exhibited the 3:1

(dominant: recessive) ratio that he had observedpreviously when analyzing the traits individually.

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How to explain the 9:3:3:1 distribution of progeny?

If the traits are combining at random, then the product rule ofprobability can be used to calculate the expected frequency ofround, yellow plants (both dominant phenotypes):

3/4 (round) X 3/4 (for yellow) = 9/16 (both round and yellow).

This is exactly what Mendel observed. The frequency of theother phenotypic categories can be explained in a similar fashion

♦ Mendel examined other combinations of traits (two at a time)and obtained similar results for each pair of traits:

♦ the phenotypes were combined at random in the F2 progenyto give a 9:3:3:1 ratio of progeny.

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MENDEL’S PRINCIPLE OF INDEPENDENT ASSORTMENTTo explain the random combination of phenotypes in theF2 progeny Mendel proposed that during gameteformation, the segregation of one gene pair occursindependently of the segregation of other gene pairs.

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• This principle of independent assortment makes very specificpredictions about the composition of gametes produced by an F1plant.

• The genotype of the F1 round, yellow plants can be symbolized asRrYy to indicate that the plant is heterozygous for the dominant andrecessive alleles for two different traits.

• Mendel’s principle of segregation predicts that 1/2 of the gametesproduced by such a plant should carry the dominant R allele and 1/2should carry the recessive r allele; likewise 1/2 of the gametes shouldbear the Y and 1/2 the y allele.

• Mendel’s principle of independent assortment means that whether agamete receives the dominant R allele or the recessive r allele has nobearing on whether the same gamete receives the dominant Y orrecessive y allele (see figure below)

• Mendel predicted then that a RrYy plant would produce four differenttypes of gametes in equal numbers:

1/4 YR = 1/2 chance of Y X 1/2 chance of R1/4 Yr = 1/2 Y X 1/2 r1/4 yR = 1/2 y X 1/2 R1/4 yr = 1/2 y X 1/2 r

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MENDEL USES A TESTCROSS TO CONFIRM HIS PREDICTIONSTo provide additional evidence for his principle of independentassortment, Mendel need to demonstrate that an F1 plant which isheterozygous for two different gene pairs produces four different typesof gametes in a 1:1:1:1 ratio. He did this by performing a testcrossbetween the F1 plant and a plant that had the recessive forms of the traitsunder examination:

F1 round, yellow plant X wrinkled, green plant RrYy rryy

This punnet square shows the expected progeny phenotypes and ratios ifthe F1 round, yellow parent produces the four types of gametes in equalproportions:

Gametes from F1 parent 1/4 RY 1/4 Ry 1/4 rY 1/4 ryGametefromtester rystrain

1/4 RrYy

round,yellow

1/4 Rryy

round,green

1/4 rrYy

wrinkled,yellow

1/4 rryy

wrinkled,green

A testcross is informative about gamete ratios because the tester straincontributes only recessive alleles to the progeny.Therefore the gamete composition of the F1 parent can be directlyinferred from phenotypic composition of the progeny.

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Figure 2-15 of your text illustrates how a Punnet Square can beused to explain the 9:3:3:1 F2 progeny ratios starting with thegamete composition of the F1 parents predicted by Mendel’sprinciple of independent assortment.

Note that genotype frequencies can be determined fromthis chart.

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What is the probability of this genotype: RRYy• could draw up the Punnett square, fill in all the square

and count up the number of squares with this genotype

Group portrait of the Cambridge University Natural Science Club. R. C.Punnett is in the second row, far right. Ernest Rutherford, the physicist,

is in the top row, far left.From the web site DNA from the Beginninghttp://vector.cshl.org/dnaftb/

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The disadvantages of using a Punnett Square• it is the hard way to do this calculation (that is,

determining the probability of this genotype: RRYy)• easier to consider that since the genes are assorting

independently, ou can use the product rule ofprobability chance RR (1/2 X 1/2) X Yy [2 (1/2)(1/2)]

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If you are dealing with multiple genes a punnettsquare not useful

Sample probability question• different chromosomes = independent assortment• independent assortment = independent rule = product rule of

probability

A friend of yours is trying to generate a strain of fruitflies that ishomozygous for four autosomal mutations (aabbccdd). Eachgene is on a different chromosome. He generates male andfemale AaBbCcDd heterozygotes. Next he mates a male and afemale fly:

AaBbCcDd X AaBbCcDd

He collects 200 progeny flies and carefully examines theirphenotypes. He is disappointed to discover that none of the 200progeny exhibits all four recessive phenotypes although he doesfind a couple of flies with 3 of the recessive phenotypes.Assuming that he scored the progeny phenotypes correctly,where did your friend go wrong? You must illustrate youranswer with the appropriate calculation.

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Mendel’s work provided a powerful conceptualframework for thinking about heredity. He was the firstindividual to describe the basic rules of transmissiongenetics, that is, the mechanisms involved in the passageof genes from one generation to the next. All of theratios of progeny that Mendel observed in his F1 and F2generations could be explained as the consequence ofthree simple processes:

• Segregation of discrete, paired alleles into separategamete cells

• Independent assortment (segregation) of the pairedalleles controlling different traits

• Random fertilization of gametes

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Thinking about conditional probabilty: how does arestriction on the outcome of a cross affect theprobability of a specifc genotype?

the 1/3 -- 2/3 issue

F1 Aa X Aa A is dominant allele

F2 progeny AA Aa aa

Take individual F2 progeny one by one and self to determinegenotype:AA F2’s breed tureAa F2’s produce 3/4 (A-) 1/4 aa

Fraction of F2 Phenotypeof F2

Phenotype ofF3 progeny

Genotype ofthe F2 plant

1/4 of total F2 progeny(1/3 of round F2progeny)

dominant all dominant RR (bred true)

1/2 of total F2 progeny(2/3 of roundF2progeny)

dominant 3/4 dominant1/4 recessive

Rr

1/4 of total progeny recessive all recessive rr (bred true)

What is the probability that an F2 offspring isheterozygous?

What is the probability that an F2 with the dominantphenotype is heterozygous?

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Optional Challenge problem:

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Optional Challenge problem (related to previousproblem):

Did Mendel fudge his data?

When assessing the ratio of F2 homozygotes toheterozygotes, Mendel always reported the expected 2:1ratio. But if he only scored 10 progeny of each F2,the ratio of Rr to RR would turn out to be 1.7 to 1instead of 2 to 1. Do the calculations to show where the1.7 to 1 comes from.

will post answer next week