Lecture 1: Mendel’s Laws
1.
2.
3.
4.
5.
Monohybrid cross
Mendel’s Law I
Dihybrid cross
Test cross
Mendel’s Law II
Gregor Mendel
The garden of the Augustinian Monastery in Brno
1822 - 1884
Friars of the Augustinian monastery
in Brünn, in 1860-ies
Hypothetico-deductive method applied
by Mendel (apparently unknowingly)
Observations
Testing by
experiments
Hypothesis
Theory
Experimental
predictions
1902-1994
Garden pea as experimental organism
General features of model
organisms:
¾short life cycle
¾large number of offspring
¾easy (inexpensive) to handle
¾sufficient variation
¾ known 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:
¾ F1 progeny resembles one of the parents
¾ In F2, the missing trait reappears in ¼ of the progeny
¾ The 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 genes
3. Two different alleles in F1
(heterozygote) and two identical
alleles in P (homozygote)
4. Single alleles in gametes
5. Dominant (R) and recessive (r)
alleles
6. Equal frequency of R and r gametes
(1/2) in F1
7. Equal chance for each gamete of one
F1 parent to fuse with any other
gamete of another F1 parent
P:
R/R
Gametes
F1
♂
x
r/r
R
r
All R/r
♀ ½R
½r
½R
¼ RR ¼ Rr
½r
¼ Rr ¼ rr
F2: By phenotype 2 classes: ¾ round (R/R, R/r, R/r) and ¼ wrinkled (rr)
By genotype 3 classes: ¼ R/R, ½ R/r and ¼ r/r
3:1
1:2:1
To test his hypothesis of equal gamete formation in F1,
Mendel designed a ‘test-cross’
P:
round R/r
Gametes
r
F
x
wrinkled r/r
½ R and ½ r
All r
½R
½r
½ Rr
½ rr
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
The hypothesis of equal gamete formation now becomes theory
Mendel’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
Observations
Testing by
experiments
Hypothesis
Experimental
predictions
Theory (“Law”)
Important terms to remember:
ƒ Monohybrid cross: a single pair of alleles are involved
ƒ Genotype (e.g. R/R or R/r): genetic constitution of
organism
ƒ Phenotype (e.g. round or R/-): appearance of organism
ƒ Homozygosity: identical alleles (R/R or r/r)
Homozygote, homozygous
ƒ Homozygous dominant (R/R), homozygous recessive (r/r)
ƒ 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
Gametes
F1
F2
x
wrinkled, yellow r/r; Y/Y
R; y
r; Y
All double heterozygous
dominant phenotype R/r; Y/y
?
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
R; y
Gametes
F1
r; Y
Round, yellow R/r; Y;y
½ R;y
Gametes
F2
½ r;Y
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/Y
Then 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
Gametes:
F1:
Gametes:
R; y
x
Wrinkled, yellow r/r; Y/Y
r; Y
Round, yellow R/r; Y;y
¼ R;y
¼ R;Y
¼ r;y
¼ r;Y
Why 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
R; y
Gametes:
F1:
r; Y
Round, yellow R/r; Y;y
Gametes:
F2:
¼ R;y
¼ R;Y
¼ r;y
¼ r;Y
¼ R;y
¼ R;Y
¼ r;y
¼ r;Y
¼ R;y
¼ R;Y
¼ r;y
¼ r;Y
How many classes?
Figuring out
an outcome of
a dihybrid
cross using
Punnett
square
Punnett Square
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
R; y
Gametes:
F1:
r; Y
Round, yellow R/r; Y;y
¼ R;y
Gametes:
¼ R;Y
¼ r;y
¼ r;Y
F2 (phenotypes):
¾ round R/-
¼ wrinkled r/r
¾ yellow Y/-
9/16 round, yellow R/-; Y/-
¼ green y/y
3/16 round, green R/-; y/y
¾ yellow Y/-
3/16 wrinkled, yellow r/r; Y/-
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 : 1
and 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.
Test-cross to verify equal frequencies of gametes in the double
heterozygote
P:
Round, Yellow R/r; Y/y
Gametes:
F2
¼ R;y
¼ R;Y
¼ r;y
¼ r;Y
x
wrinkled, green r/r; y/y
all r; y
Genotypes
Phenotypes
Actually observed
¼ R/r; y/y
¼ R/r; Y/y
¼ r/r; y/y
¼ r/r; Y/y
round, green
round, yellow
wrinkled, green
wrinkled, yellow
49
56
53
51
As predicted, the test-cross produced four classes of progeny
with equal ratio (1 : 1 : 1 : 1)
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
Branch diagram to calculate the genotypic ratio in the dihybrid cross
1:2:1
1/4 R/R
2/4 R/r
1/4 r/r
1:2:1
F2 genotype
F2 phenotype
1/4 Y/Y
1/16 R/R;Y/Y
round, yellow
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 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
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
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