Lecture 1: Mendel’s Laws

1. Monohybrid cross2. Mendel’s Law I3. Dihybrid cross4. Test cross5. Mendel’s Law II

The garden of the Augustinian Monastery in Brno

Friars of the Augustinian monastery in Brünn, in 1860-ies

1822 - 1884

Gregor Mendel

Hypothetico-deductive method applied by Mendel (apparently unknowingly)

Observations

Hypothesis

Experimentalpredictions

Testing byexperiments

Theory

1902-1994

Garden pea as experimental organism

General features of model organisms:

short life cyclelarge number of offspringeasy (inexpensive) to handlesufficient variationknown genetic history

Specific feature of garden pea:

can be cross-pollinated (crossed)

can be self-pollinated (selfed)

Seven pairs of simple differences

For each character Mendel obtain a true-breeding (pure-breeding)line of plants that continuously (for 2 years of cultivation) showed only one character

Mendel’s basic experiment:monohybrid cross

When a similar experiment was done with each pair of characters, the results were the same:

F1 progeny resembles one of the parentsIn F2, the missing trait reappears in ¼ of the progenyThe ratio of two classes of progeny was 3 : 1

Mendel’s hypotheses derived from these observations that explained his experiments

1. Particulate nature of inheritance: factors = genes

2. Alleles, alternative forms of genes3. Two different alleles in F1

(heterozygote) and two identical alleles in P (homozygote)

4. Single alleles in gametes5. Dominant (R) and recessive (r)

alleles6. Equal frequency of R and r gametes

(1/2) in F17. Equal chance for each gamete of one

F1 parent to fuse with any other gamete of another F1 parent

P: R/R x r/r

Gametes R r

F1 All R/r

½ R ½ r

½ R ¼ RR ¼ Rr

½ r ¼ Rr ¼ rr

F2: By phenotype 2 classes: ¾ round (R/R, R/r, R/r) and ¼ wrinkled (rr) 3:1

By genotype 3 classes: ¼ R/R, ½ R/r and ¼ r/r 1:2:1

♀♂

To test his hypothesis of equal gamete formation in F1, Mendel designed a ‘test-cross’

P: round R/r x wrinkled r/r

Gametes ½ R and ½ r All r

½ R ½ r

r ½ Rr ½ rr

F ½ round (R/r)and ½ wrinkled (r/r)1:1 ratio

Instead of one class in F1, there are two classes in 1:1 ratio

This was possible only if R and r gametes were produced with the equal frequency of ½

Observations

Hypothesis

Experimentalpredictions

Testing byexperiments

Theory (“Law”)

The hypothesis of equal gamete formation now becomes theoryMendel’s Law of Equal Segregation (Law I)

Two alleles of the same gene segregate equally

- when two alleles segregate from each other into gametes, a half of gametes carries one allele, and a half of gametes carries another allele

Important terms to remember:

Monohybrid cross: a single pair of alleles are involved

Genotype (e.g. R/R or R/r): genetic constitution of organism

Phenotype (e.g. round or R/-): appearance of organism

Homozygosity: identical alleles (R/R or r/r) Homozygote, homozygous

Homozygous dominant (R/R), homozygous recessive (r/r)

Heterozygosity: different alleles (R/r)Heterozygote, heterezygous

Dihybrid cross

If two pairs of characters are involved, will these characters be transmitted together or independently?

P: round, green R/R; y/y x wrinkled, yellow r/r; Y/Y

Gametes R; y r; Y

F1 All double heterozygousdominant phenotype R/r; Y/y

F2 ?Round dominant to Wrinkled, Yellow dominant to Green

Let’s assume that the characters are transmitted together (which is not true, btw!), that is: R stays with y, while r stays with Y, as they were in parental gametes

P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y

Gametes R; y r; Y

F1 Round, yellow R/r; Y;y

Gametes ½ R;y ½ r;Y

F2 ½ R;y ½ r;Y

½ R;y ¼ R/R;y/y ¼ R/r; Y/y

½ r;Y ¼ R/r; Y/y ¼ r/r; Y/YThen the prediction is: three classes and the ratio is1:2:1

¼ round, green R/R;y/y ½ round, yellow R/r;Y/y ¼ wrinled, yellow r/r; Y/Y

Or we can assume that the characters are transmitted independently. Then how many different types of gametes will we see in F1? Not two but four types!

P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y

Gametes: R; y r; Y

F1: Round, yellow R/r; Y;y

Gametes: ¼ R;y ¼ R;Y ¼ r;y ¼ r;YWhy four types of gametes?

Probability of two independent events is a product of probabilities of the individual events.

According to Mendel Law I: there must be ½ of gametes carrying Y and ½ of gametes carrying y, and also ½ of gametes carrying R and ½ of them carrying r.

If the presence of, say, R is independent of Y, then the probability (frequency) of gametes to carry both R and Y is ½ x ½ = ¼ . Similar ¼ of gametes with contain R and y, etc. , the total of four types of gametes with equal frequency of ¼ for each type.

Or we can assume that the characters are transmitted independently. Then how many different types of gametes will we see in F1? Not two but four types!

P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y

Gametes: R; y r; Y

F1: Round, yellow R/r; Y;y

Gametes: ¼ R;y ¼ R;Y ¼ r;y ¼ r;Y

F2: ¼ R;y ¼ R;Y ¼ r;y ¼ r;Y

¼ R;y¼ R;Y ¼ r;y¼ r;Y

How many classes?

Punnett Square

Figuring out an outcome of a dihybrid cross using Punnettsquare

but a branch diagram can help you out

Or we can assume that the characters are transmitted independently. Then how many different types of gametes will we see in F1? Not two but four types!

P: Round, green R/R; y/y x Wrinkled, yellow r/r; Y/Y

Gametes: R; y r; Y

F1: Round, yellow R/r; Y;y

Gametes: ¼ R;y ¼ R;Y ¼ r;y ¼ r;Y

F2 (phenotypes):¾ yellow Y/- 9/16 round, yellow R/-; Y/-

¾ round R/- ¼ green y/y 3/16 round, green R/-; y/y

¾ yellow Y/- 3/16 wrinkled, yellow r/r; Y/-

¼ wrinkled r/r ¼ green y/y 1/16 wrinkled, green r/r; y/y

Then the prediction is: four classes and the ratio is 9 : 3 : 3 : 1and that was confirmed by the actual experiment

Mendel’s logic:

• assuming independent packaging (assortment) of alleles into gametes, we predict four equally frequent (1/4) classes of gametes in double heterozygous F1 and four phenotypes among F2 progeny observed with the 9:3:3:1 ratio.• the experiment has confirmed the phenotypic ratio, hence it is likely that the independent assortment hypothesis is correct• to further prove it, he had to design an experiment and predict its outcome based on the independent assortment hypothesis• if the prediction failed, the hypothesis was wrong• if the prediction held true, the hypothesis was correct, and would become not mere a hypothesis but a theory.

P: Round, Yellow R/r; Y/y x wrinkled, green r/r; y/y

Gametes: ¼ R;y¼ R;Y all r; y ¼ r;y ¼ r;Y

F2 Genotypes Phenotypes Actually observed

¼ R/r; y/y round, green 49 ¼ R/r; Y/y round, yellow 56¼ r/r; y/y wrinkled, green 53 ¼ r/r; Y/y wrinkled, yellow 51

As predicted, the test-cross produced four classes of progenywith equal ratio (1 : 1 : 1 : 1)

Test-cross to verify equal frequencies of gametes in the double heterozygote

The hypothesis of independent packaging of alleles has been confirmed and thus become

Mendel’s Law of Independent Assortment (Mendel’s Law II)

Different pairs of alleles assort independently

- during gamete formation assortment of alleles of one gene is independent of assortment of alleles of another gene

1:2:1 1:2:1 F2 genotype F2 phenotype

1/4 Y/Y 1/16 R/R;Y/Y round, yellow

1/4 R/R 2/4 Y/y 2/16 R/R;Y/y round, yellow

1/4 y/y 1/16 R/R;y/y round, green

1/4 Y/Y 2/16 R/R;y/Y round, yellow

2/4 R/r 2/4 Y/y 4/16 R/r;Y/y round, yellow

1/4 y/y 2/16 R/r;y/y round, green

1/4 Y/Y 1/16 r/r;Y/Y wrinkled, yellow

1/4 r/r 2/4 Y/y 2/16 r/r;Y/y wrinkled, yellow

1/4 y/y 1/16 r/r;y/y wrinkled, green

9 classes 4 classes

Branch diagram to calculate the genotypic ratio in the dihybrid cross

Trihybrid cross looks even more complicated …

… but again, use a branch diagram! The actual ratio is not for memorization

Note: In testcross (heterozygote to homozygous recessive), number of both phenotypic and genotypic classes is 2n