Lecture 2
• Probability problem from Wednesday
• Mitosis and Meiosis
• Monohybrid and Dihybrid Crosses
The Probability Problem
from Wednesday
• 1/1000 people have the disease
• The test is positive for 99% of people who
have the disease
• The test is also positive for 2% of people who
don’t have the disease (false positives)
• If you test positive, what is the probability that
you have the disease?
Out of every 1000 people…
• Only 1 (1/1000) has the disease (and is very
likely to test positive)
• 20 people (2%) test positive who don’t have
the disease
• 21 (1 + 20) test positive, but only 1 out of 21
has the disease
• Probability of having the disease if you
test positive: 0.048 (1/21)
1 with disease /21 testing positive = 0.048
Our Coverage of Mitosis and Meiosis
Mitosis and Meiosis
(Chapter 2 in textbook)
• Emphasis on how mitosis and meiosis
relate to Mendelian genetics
– focus on separation of chromosomes and
chromatids at each stage
• Not concerned with detailed
descriptions of each stage!
1
Most plant and animal cells are diploid (2n)– they have two
sets of chromosomes
Most plant and animal gametes are haploid (n)– they have
one set of chromosomes
Members of the same species have the same number of
chromosomes
In humans, there are 23 chromosomes per haploid set:
22 autosomes plus 1 sex chromosome (X or Y)
Chromosome with
1 chromatid
A Single Chromatid
Pair of homologous
chromosomes
Each
with 2 chromatids
A Pair
of Homologous
Chromosomes
Long Arm
Centromere
Short Arm
Think of Mitosis and Meiosis as
Solutions to Problems
Think of Mitosis and Meiosis as
Solutions to Problems
Starting with two sets of chromosomes
(one from dad, one from mom)
• Problem: During normal cell division
make sure every cell gets both sets of
chromosomes
• Solution: Mitosis
Chromosomes and Chromatids
Starting with two sets of chromosomes
(one from dad, one from mom)
• Problem: During production of gametes
(eggs and sperm), make sure every
gamete gets one complete set of
chromosomes (mix mom’s and dad’s)
• Solution: Meiosis
2
Chromatid Duplication and
Chromosome Division
Chromatid Duplication and
Chromosome Division
1 chromosome
1 chromosome
2 chromosomes
2 chromosomes
1 chromatid
2 chromatids
2 chromatids
2 chromatids
Mitosis: Each daughter cell receives a chromatid
Mitosis is cell division that provides each
daughter cell with a full set of chromosomes.
• Before mitosis, each chromosome consists
of two identical chromatids, attached at the
centromere
2 chromosomes
4 chromatids
• During mitosis, each chromosome divides
into two identical single-chromatid
chromosomes
2 chromosomes
2 chromatids
• Each daughter cell receives one of the two
chromatids/chromosomes.
Meiosis
• 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: Before and After
• Before:
– diploid number of chromosomes
– (e.g. for humans, 46)
– each chromosome has two chromatids
• After:
– haploid set of chromosomes (e.g. 23)
– each chromosome consists of one chromatid
3
Meiosis Consists of
Two Divisions
• The first divides pairs of homologous
chromosomes
• The second divides sister chromatids
II
Pair of homologous
chromosomes
I
Blue – paternal (from dad)
Pink – maternal (from mom)
The first division separates pairs of homologous chromosomes
The second divides sister chromatids
Meiosis with two pairs of chromosomes
Fertilization
The first division separates pairs of
homologous chromosomes
• Gametes combine to form a zygote
• Chromosomes from gametes are
combined in the zygote’s nucleus
(zygote is diploid)
The second divides sister chromatids
Mendel's Peas
Some traits that Mendel studied
• Varieties of peas that differed in
obvious traits
• Each variety of pea was inbred by
selfing and pure breeding (offspring
looked like parents)
• Mendel crossed the different varieties
and observed how the traits were
inherited
4
The Monohybrid Cross
• A cross between two varieties that
differ in one trait
• Parent are homozygous (two copies of
the same allele) for the gene that
controls the trait
• Each parent is homozygous for a
different allele
Generations in Cross
•
•
•
•
P – Parental generation
F1 – first generation of progeny
F2 – progeny of the progeny
backcross –progeny crossed with a
parent
Example of Monohybrid Cross
X
Green pods GG
Yellow pods gg
All green pods Gg
Inheritance of pod color
demonstrates dominance
• Often (but not always), phenotype of
heterozygote is the same as one of the
homozygotes
– Example: A pod color heterozygote (Gg) looks like
a green pod homozygote (GG)
• The allele that controls the phenotype in a
heterozygote is the dominant allele, the other
is the recessive allele
– Green pod allele is dominant, yellow pod allele
is recessive
Simple* Genotype Abbreviations
• Dominant alleles are abbreviated by upper
case letters
– G for green pod allele
• The recessive allele uses the same letter, but
lower case
– g for yellow pod allele
• Diploid genotypes are abbreviated with two
letters, with dominant alleles listed first
– GG for a green pod homozygote
– Gg for a heterozygote
– gg for a yellow pod homozygote
*These rules only hold for simple cases!
5
Summary of First Generation of
Monohybrid Cross
• P generation: each individual is
homozygous for a different allele
• Gametes of a homozygous parent carry
one copy of the allele the parent is
homozygous for
• F1 generation – starts with zygote,
heterozygous for alleles from parents
Second generation of
monohybrid cross is either…
• heterozygous individuals crossed with
each other, or
• heterozygous individuals self-fertilized
6
Mendel’s Principle of Segregation
• Each individual has two alleles
(example Gg)
• During reproduction, alleles separate
(“segregate”) and only one is passed
on to each offspring (each offspring gets
either G or g)
Monohybrid Cross Diagram with Gametes
P
Gametes
F1
GG
G
x
gg
g
Self-fertilization (“Selfing”)
• Selfed
lines breed true because they are homozygous
GG x GG crosses produce all GG progeny
gg x gg crosses produce all gg progeny
• In selfing, only heterozygotes produce more
heterozygotes, and half their progeny are homozygotes
Gg
Gg x Gg crosses produce ½ Gg progeny
F1
Gametes
F2
Gg
x
½G ½g
¼ GG ½ Gg
Gg
½G ½g
¼ gg
• Each generation the proportion of heterozygotes to
decreases by ½
• As the proportion of heterozygotes gets very small, it is
likely that by chance it will reach zero
• Eventually all plants are homozygotes (GG or gg); each
homozygous line is a different pure-breeding line
Backcross
• Cross between progeny and parental genotype
• Example:
P:
F1:
Backcrosses are:
GG x gg
Gg
Gg x GG
or
Test Cross: A cross to find out the
genotype of a dominant phenotype
• Individuals with dominant phenotypes may
be either homozygotes or heterozygotes
Gg x gg
F1 produces two types of gametes: G and g
P produces only one type of gamete
Proportions of genotypes in progeny are ½ to ½
Gg x GG cross: ½ GG and ½ Gg (all green pods)
Gg x gg produces ½ Gg and ½ gg (½ green, ½ yellow)
• A test cross is used to determine the
unknown genotype
• Unknown individual is crossed with a
homozygous recessive
7
Test Cross Example
F2 from monohybrid cross has Green Pods. Genotype??
• It could be either GG or Gg
• To find out: cross it with a gg (yellow pod) plant
If the unknown plant is GG the cross is:
GG x gg
All the progeny from the test cross are Gg – green pods
If the unknown plant is Gg the cross is:
Gg x gg
Half of the progeny are Gg (green),and half are gg (yellow)
Mendel’s Principle of Independent
Assortment
• Only applies to crosses with multiple
(two or more) genes
• Alleles of different genes assort
independently of one another during
gamete formation
• Independent assortment means that
alleles from different genes are inherited
independently
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
8
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
9
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
10
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) ?
11
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
12
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
13
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