Download Meiosis Meiosis: Before and After

Mitosis is cell division that provides each
daughter cell with a full set of chromosomes.
Lecture 3
• Before mitosis, each chromosome consists
of two identical chromatids, attached at the
centromere
• Review Mitosis and Meiosis
• Review Monohybrid Cross
• Review backcross and testcross
• During mitosis, each chromosome divides
into two identical single-chromatid
chromosomes
• Dihybrid cross
• Probability
• Each daughter cell receives one of the two
chromatids/chromosomes.
Mitosis: Each daughter cell receives a chromatid
Meiosis
2 chromosomes
4 chromatids
2 chromosomes
2 chromatids
Meiosis: Before and After
• Before:
– diploid number of chromosomes
– (e.g. for humans, 46)
– each chromosome has two chromatids
• Provides each daughter nucleus with a single
haploid set of chromosomes
• The products of meiosis are typically
gametes (eggs and sperm)
• Before meiosis, there is a diploid number of
chromosomes and each chromosome
consists of two chromatids
• After meiosis, there is a haploid set of
chromosomes and each chromosome
consists of one chromatid
Meiosis Consists of
Two Divisions
• The first divides pairs of homologous
chromosomes
• The second divides sister chromatids
• After:
– haploid set of chromosomes (e.g. 23)
– each chromosome consists of one chromatid
1
Fertilization
II
Pair of homologous
chromosomes
• Gametes combine to form a zygote
• Chromosomes from gametes are
combined in the zygote’s nucleus
(zygote is diploid)
I
Blue – paternal (from dad)
Pink – maternal (from mom)
The first division separates pairs of homologous chromosomes
The second divides sister chromatids
Example of Monohybrid Cross
X
Green pods GG
Yellow pods gg
All green pods Gg
Backcross
Monohybrid Cross Diagram with Gametes
P
Gametes
F1
F1
Gametes
F2
GG
G
x
gg
g
Gg
Gg
x
½G ½g
¼ GG ½ Gg
• Cross between progeny and parental genotype
• Example:
P:
F1:
Backcrosses are:
Gg
½G ½g
¼ gg
GG x
G
G x GG
or G x
F1 produces two types of gametes: ½ G and ½
P produces only one type of gamete G or
Proportions of genotypes in progeny are ½ to ½
G x GG cross: ½ GG and ½ G (all green pods)
produces ½ G and ½
(½ green, ½ yellow)
G x
2
Test Cross: A cross to find out the
genotype of a dominant phenotype
• Individuals with dominant phenotypes may
be either homozygotes or heterozygotes
• A test cross is used to determine the
unknown genotype
• Unknown individual is crossed with a
homozygous recessive
Test Cross Example
F2 from monohybrid cross has Green Pods. Genotype??
• It could be either GG or G
• To find out: cross it with a
(yellow pod) plant
If the unknown plant is GG the cross is:
GG x
All the progeny from the test cross are G – green pods
If the unknown plant is G the cross is:
G x
Half of the progeny are G (green),and half are
(yellow)
Dihybrid Cross
Diagram of Dihybrid Cross with
Green/Yellow Pods and Tall/Short Height
Cross between 2 pure breeding varieties
that differ for 2 traits
Generation
Genotypes
Phenotypes
P
GGTT x ggtt
Green, Tall
Yellow, Short
Each trait is controlled by a separate gene (locus)
Each gene (locus) has two alleles
Gametes
Trait
Pod Color
Height
Alleles
G - green (dominant)
g - yellow
T - tall (dominant)
t - short
There are 16 (4 x 4)
Possible Gamete Combinations
GT
F1
gt
GgTt
Green, Tall
GgTt x GgTt
All combinations of
gametes are equally
likely because they
are independently
assorted
¼ GT
¼ Gt
¼ gT
¼ gt
Gamete1
Gamete2
Genotype
Phenotype
GT
GT
GGTT
Green, Tall
“
Gt
GGTt
Green, Tall
“
gT
GgTT
Green, Tall
“
gt
GgTt
Green, Tall
Gt
GT
GGTt
Green, Tall
Green, Short
“
Gt
GGtt
“
gT
GgTt
Green, Tall
“
gt
Ggtt
Green, Short
gT
GT
GgTT
Green, Tall
“
Gt
GgTt
Green, Tall
“
gT
ggTT
Yellow, Tall
“
gt
ggTt
Yellow, Tall
gt
GT
GgTt
Green, Tall
“
Gt
Ggtt
Green, Short
“
gT
ggTt
Yellow, Tall
“
gt
ggtt
Yellow, Short
3
Gamete1
Gamete2
Genotype
Phenotype
GT
GT
GT
GGTT
Green, Tall
1
“
Gt
GGTt
Green, Tall
2
“
gT
GgTT
Green, Tall
3
“
gt
GgTt
Green, Tall
4
Gt
GT
GGTt
Green, Tall
5
“
Gt
GGtt
Green, Short
“
gT
GgTt
Green, Tall
“
gt
Ggtt
Green, Short
gT
GT
GgTT
Green, Tall
7
8
“
Gt
GgTt
Green, Tall
“
gT
ggTT
Yellow, Tall
“
gt
ggTt
Yellow, Tall
gt
GT
GgTt
Green, Tall
“
Gt
Ggtt
Green, Short
“
gT
ggTt
Yellow, Tall
“
gt
ggtt
Yellow, Short
Gt gT gt
Expected Proportions in Dihybrid Cross
Green, Tall (Dominant for both)
Yellow, Tall (Dominant for one)
Green, Short (Dominant for other)
Yellow, Short (Recessive for both)
1
6
2
1
2
9
3
3
Punnett Squares
• Useful for simple problems, but not for
the more complex ones we will be
working with soon
• If you understand probabilities you do
not need to use a Punnett square !!!
We define an event as something
that may happen with a certain
probability
We use the following abbreviation for
the probability of an event:
Pr (event)
9/16
3/16
3/16
1/16
1
Probability & Statistics
• Probabilities of events
• Complex events
• Conditional probability
The probability of an event is the
proportion of times that it will happen
1. Probability of flipping a coin and getting
heads is 0.5
Pr (heads) = 0.5
2. Probability of a baby being a boy (for our
purposes) is 0.5
Pr (boy) = 0.5
4
Probability values are
always between 0 and 1
Killed by a shark: 1 in 350 million (0.0000000029)
1. A probability of 0 means the event will never
happen
2. A probability of 1 means the event will always
happen
3. Since events can’t happen less often than never,
or more often than always, all events have
probabilities between 0 and 1
Probabilities for Some Events
Happening to Someone this Year
Killed by a dog: 1 in 18 million (0.0000000556)
•
•
•
•
Killed by a shark
Killed by a dog
Killed in an airline crash
Killed by lighting
1 in 350 million
1 in 18 million
1 in 7.7 million
1 in 4.2 million
0.0000000029
0.0000000556
0.0000001299
0.0000002381
Probabilities for Some Events
Happening to Someone this Year
A guy dating a supermodel: 1 in 88,000 (0.0000113636)
•
•
•
•
•
•
Killed by a shark
Killed by a dog
Killed in an airline crash
Killed by lighting
Date a Supermodel
Killed in an auto accident
1 in 350 million
1 in 18 million
1 in 7.7 million
1 in 4.2 million
1 in 88,000
1 in 6,200
0.0000000029
0.0000000556
0.0000001299
0.0000002381
0.0000113636
0.0001612903
5
A single coin toss is a simple
event with a known probability
Probability of an Event
An event happens with a certain probability
Abbreviation for the probability of an event:
However we usually need to
know the probabilities of more
complex events that are
combinations of simple events
Probability of Event Not Happening
Pr (not A) = 1-Pr(A)
Example:
Pr (Heads) = ½
 Pr (not Heads) = 1 – ½ = ½
In some cases, we need to know the
probability that either of two mutually
exclusive events will occur
Pr (event)
Probability of flipping a coin and getting heads
is 0.5
Pr (heads) = 0.5
A single coin toss is a simple event
with a known probability
However we usually need to know
the probabilities of more complex
events that are combinations of
simple events
Venn Diagram of Mutually
Exclusive Events
By mutually exclusive, we mean events that
could not possibly happen at the same time
For example:
head and tails are mutually exclusive
what is
Pr (heads or tails) ?
6
Two Possible Paths…
We call such complex events
unions of simple events.
1/2
For unions, we add the
probabilities of the events:
1/2
Pr (either A or B) = Pr(A) + Pr(B)
Start here
Example 2
1/2
1/2
Pr (single dice roll is a 1 or a 2 )
Pr (Heads OR Tails) =
½+½=1
Six possibilities, all with Pr = 1/6
Calculate: Pr (single die roll is a 1 or a 2 )
Pr (dice comes up 1) = 1/6
Pr (dice comes up 2) = 1/6
Pr (dice comes up 1 or 2) =
1/6 + 1/6 = 2/6 = 1/3
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What is the Probability of rolling one die
and having it not come up either 1 or 2?
Pr (not (1 or 2)) = ?
Pr (not (1 or 2)) = 1 – Pr(1 or 2) =
1 – 1/3 = 2/3
In other cases we need to know the probability
of two events happening together
We call such complex events intersections of
simple events
For intersections, we multiply the probabilities
of the simple events
Pr (both A and B) = Pr (A) x Pr (B)
We can rephrase this as:
Example of intersection:
Pr (two babies are both boys)
=?
Pr(first baby is a boy AND second baby is a boy)
Pr (first baby is a boy) = 1/2
Pr (second baby is a boy) = 1/2
Pr (first baby is a boy and second is a boy) =
1/2 x 1/2 = 1/4
Venn Diagram
8
Venn Diagram
Conditional Probability
Used when occurrence of one event
changes the probability of another event
Example: A die is rolled, and comes up an
even number, what is the probability
the number is 4?
Venn Diagram
1/3
Conditional probability
Review of Probability
What is the probability of rolling a 4 given that you know an
even number was rolled ?
• Simple events – probability is given
P (4 | even) = Pr (4) / Pr (even) =
1
61
1
3
2
Pr(A) = 0.5
• Probability of (not A) = 1 – Pr (A)
• Union: event A or event B
Pr(A or B) = Pr(A) + Pr(B)
given
divide
• Intersection: event A and event B
Pr(A and B) = Pr(A) x Pr(B)
• Conditional: Event B given A
Pr(B | A) = Pr(B)  Pr(A)
9
Some Genetic Examples
Scenario:
In a monohybrid cross, the probability of an
F2 progeny having green pods is ¾, and
probability of having yellow pods is ¼
Problem 2:
Problem 1:
What is the probability of 3 progeny all
having green pods?
Pr (3 with green pods) =
Pr (green AND green AND green)
= ¾ x ¾ x ¾ = (¾)3 = 27/64
Problem 3:
What is the probability of having at least
one progeny with yellow pods among 3
progeny?
What is the probability of having two
progeny with green pods among 4
progeny?
Pr (at least one yellow pod) =
1 - Pr (3 green pods)
= 1 - 27/64 = 37/64
We will need to first learn "the rules of
counting".
How to Count Complex Events
• Product Rule - how many possible
results are there in experiments with
multiple parts?
• Permutations – how many different
ways can things be ordered?
• Combinations – how many different
unordered combinations are possible
Product Rule for Counts
• Suppose there are two parts to an
experiment
• The first part can have m distinct results
• With each possibility for the first part
there can be n distinct results for the
second part
• The total number of results is m x n
Example: Role a die and flip a coin:
m = 6, n = 2, 6 x 2 = 12 distinct results
10
Example of Product Rule for Counts
Permutations vs. Combinations
In the progeny of a cross there are 3
possible genotypes for one gene, and 2
possible genotypes for a second gene.
How many possible genotypes are
there:
3x2=6
A permutation is an ordered set. For example:
A, B, C and A, C, B are two permutations of the
same set of letters
A combination is an unordered set. For example:
A, B, C and A, C, B are the same combination,
but A, B, C and X, Y, Z are different
combinations
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