Transcript Mendel’s Second Experiment - Father Michael McGivney

Mendel’s Second Experiment
The Inheritance of
Two Traits:
 Does the inheritance
of one characteristic
influence the
inheritance of another
characteristic?
 For example: Does
pea shape influence
pea color?

Mendel performed a
Dihybrid Cross

He crossed two pea plants that differed in
two traits.

P generation:
P generation:


Pure round & yellow (RRYY)
Pure wrinkled Green (rryy)
What do you think the results were?
The F1 generation will be
heterozygous for both traits: RrYy
Mendel's Experiments
Moving On to Two Traits at a Time
Keep T and t for tall
and short plants,
respectively.
 Add R and r for round
and wrinkled seeds,
respectively.
 A double
heterozygote male
produces four types
of gametes.

Cross with a Female Double
Heterozygote

A double
heterozygote
female produces
four types of eggs.
Crossing the Double Heterozygotes

The male passes
on his alleles, two
per gamete
Crossing the Double Heterozygotes

The female passes
on her alleles, two
per egg.
Double Heterozygote Cross:
Assessing the Resultant Genotypes
At least one T yields
tall stature.
 At least one R yield
round seeds.
 Thus, there are 9
ways (gray) to
produce tall, roundseeded offspring.

Double Heterozygote Cross:
Assessing the Resultant Genotypes
Again, at least one T
yields tall stature.
 And one R is required
for round seeds, so rr
must produce
wrinkled seeds.
 Thus, there are 3
ways (lighter gray) to
produce tall, wrinkly
seeded offspring

The Third Phenotype
in a Double Heterozygote Cross



Two t alleles yield short
stature.
At least one R produces
round seeds.
Thus, there are 3 ways
(lightest gray) to produce
short offspring with round
seeds.
The Fourth Phenotype
in a Double Heterozygote Cross
Two t alleles yield
short stature.
 Two r alleles produce
wrinkled seeds.
 There is only 1 way
to produce short
offspring with
wrinkled seeds.

http://trc.ucdavis.edu/biosci10v/bis
10v/media/ch08/dihybrid_v2.html
The F1 generation were all round and yellow

What happens
when you cross
F1 with a F1?
The F2 generation:
9 round and yellow
3 round and green
3 wrinkled and yellow
1 wrinkled and green
These results represent a phenotypic ratio of 9:3:3:1
Law of Independent Assortment



The inheritance of
alleles for one trait does
not affect the
inheritance of alleles for
another trait.
This means that different
pairs of alleles are passed
to the offspring
independently of each
other.
A pea plant’s ability to
produce white flowers
instead of purple ones does
not influence the same
plant’s ability to produce
round peas instead of
wrinkled peas
http://www.sumanasinc.com/webcontent/ani
mations/content/independentassortment.html
The Rules of Probablity
Probablity scale ranges from 0-1
 An event that is certain to occur has a
probability of 1, while an even that is
certain NOT to occur has a probability of
0.
 E.g. chances of rolling 3 on a die: 1/6
 The probabilities of all possible outcomes
for an event must add up to 1.

The Rule of Multiplication

How do we determine the chance that two or
more independent events will occur together in
some specific combination?
– Compute the probability for each independent event,
then multiply these individual probabilities to obtain
the overall probability of these events occurring
together.
– E.g. What is the chance that two coins tossed
simultaneously will land heads up?
 1/2 x 1/2 = 1/4
– If an F1 plant has a genotype Pp, what is the
probability that a particular F2 plant will be pp?

If a parent has a genotype YyRr, what is
the probability of an F2 plant having the
genotype YYRR?
The Rule of Addition

What is the probability that an F2 plant from a
monohybrid cross will be heterozygous?
– There are two ways F1 gametes can combine to
produce a heterozygous result. The dominant allele
can come from the ovum and the recessive allele
from the sperm or vice versa.

By the rule of addition, the probability of an
event that can occur in two or more different
ways is the sum of the separate probabilities of
those ways.
– 1/4 + 1/4 = 1/2
Using rules of probability to
solve genetics problems

Imagine a trihybrid cross
– P: purple flower
p: white flower
– Y: yellow seed y: green seed
– R: Round seed r: wrinkled seed
PpYyRr x Ppyyrr What fraction of offspring will
exhibit the recessive phenotype for at least two
of the three traits?
 Solution: List all possible genotypes:

– ppyyRr, ppYyrr, Ppyyrr, Ppyyrr, ppyyrr
– Next use rule of multiplication to calculate the
individual probabilities for each of the genotypes
– Use rule of addition to pool the probabilities for
fulfilling the condition of at least two recessive traits.
Solution: PpYyRr x Ppyyrr
ppyyRr
x
x
=
ppYyrr
x
x
=
Ppyyrr
x
x
=
PPyyrr
x
x
=
ppyyrr
x
x
=
____________________________________
Chance of at least 2 recessive traits =
Test Crosses
A test cross can be used for both monohybrid
and dihybrid crosses to determine the genotype
of an unknown individual.
 It involves crossing the unknown genotype with
a homozygous recessive individual.
 The results will determine the unknown
genotype.

Examples: Monohybrids


In a monohybrid test cross involving height, if all offspring
are tall, one can deduce that the original genotype was TT
(homozygous).
If 50% of the off spring are tall and the other 50% dwarf,
one can deduce that the original genotype was Tt
(heterozygous)
Examples: Dihybrids




In test cross involving shape and color, if it produces plants
that show the dominant phenotype for both traits that is
round and yellow, one can conclude that the original
genotype was RRYY.
If the original plant is heterozygous (RrYy), the cross will
produce a 25% chance for each combination.
25% Round and Yellow
25% Round and Green
25% Wrinkled and Yellow 25% Wrinkled and Green
Beyond Mendel’s Laws
Incomplete Dominance
 Co-Dominance
 Multiple Alleles

Incomplete Dominance


Occurs when neither of
the alleles for a certain
trait is dominant.
This gives rise to an
intermediate expression
found in individuals that
are heterozygous. Ex.
White flowers and Red
flowers are homozygous,
Pink flowers are
heterozygous.
Co-Dominance
Both alleles for a trait are
dominant and are both expressed
in a heterozygous individual.
 Which of the following offspring
would represent co-dominance
from the mating of a pure black
rooster and a white hen?
 Black chicken
 White chicken
 Grey chicken
 Black and White
chicken.

Multiple Alleles
Occurs when a gene
has more than two
alleles.
 Ex. Human blood has
3 alleles: A, B, O

Phenotype (blood
type)
Genotype
A
IA IA or IA i
B
IBIB or IB i
AB
IAIB
O
ii