Outline for today’s lecture (Ch. 14, Part I)
• Ploidy vs. DNA content
• The basis of heredity ca. 1850s
• Mendel’s Experiments and Theory
– Law of Segregation
– Law of Independent Assortment
• Introduction to Probability
Reminder: Homologous chromosomes
-Pair at meiosis
(all pairs)
-Same sequence (except
sex chromosomes)
“C” (DNA per chromosome)
Ploidy vs. DNA content in Meiosis
Diploid
Haploid
4
2
1
G1
S
G2
Meiosis I
Meiosis II
Diploid: Contains two chromosomes from a homologous pair
one from each parent
Haploid: Contains only one chromosome from a homologous pair
The Nature of Heredity, ca. 1859
• Observation: Offspring generally intermediate in
phenotype (“trait value”) between those of parents
– Obvious example: Human children with one African and one
Nothern European parent
• Proposed explanation: “Blending Inheritance”
– Genetic material miscible, like paint:
• Black + White = Gray
• Tall + Short = Medium
• Etc.
Blending Inheritance: A logical difficulty
• Variation reduced every generation
• Ultimate consequence is a homogeneous population
– At odds with reality
• How to explain variation?
– “Sports” (Mutation in modern parlance)
Gregor Mendel: The Origin of Genetics
• Austrian farm boy, entered Augustinian monastary in
1843
• Attended University of Vienna in early 1850s
– Learned two things about science
• Do experiments
• Analyze your data (i.e., mathematically)
• ~1857, began an experimental program to investigate
the basis of inheritance (i.e., heredity) with peas
Mendel’s Experiments
•
Peas were a fortuitous study organism for several reasons:
– Many variable characters (e.g., flower color, seed shape, seed
color, etc.)
– Many varieties that bred “true” for particular traits (e.g.,
purple flowers, round seeds, etc.)
– Easy to do controlled crosses, both “self” and outcross
Mendel’s Experiments – Choice of characters
Used only discrete characters, i.e., “either-or”, not continuous
1.0
frequency
frequency
•
0.5
1.0
0.5
0.0
0.0
ite
ck
h
a
l
B
W
Color
2.0
3.0
Height
4.0
Mendel’s Experiments – Breeding design
1.
2.
3.
4.
Start with lines that breed
true for different traits,
e.g., purple and white
flowers
First generation of a cross
is called P (“parental”)
P
Self
Self
Self
F1
Offspring are F1 (“filial”)
Grand-offspring are F2
Self
F2
Mendel’s Experiments – Breeding design
1.
2.
Cross two true-breeding P
lines (purple, white)
X
Self F1s
F1
Self
3.
Observe phenotypes of
MANY F2 offspring and
COUNT THEM
F2
Mendel’s Experiments – Results
1.
2.
Cross two true-breeding P
lines (purple, white)
F1s ALL PURPLE
F1
•
What do we expect if
“blending inheritance”?
X
Mendel’s Experiments – Breeding design
1.
2.
3.
Cross two true-breeding
lines (purple, white)
P
X
F1s ALL PURPLE
Self F1s
F1
Self
4.
F2s are NOT all purple –
–
705 purple
–
224 white
–
i.e., ~ 3:1 purple : white
F2
Mendel’s Experiments – Conclusions
1.
“Heritable Factor” (i.e.,
gene) for white flowers did
not disappear in the F1,
but only the purple
“factor” affected flower
color.
P
F1
Self
"Particulate" inheritance
1.
Purple is “dominant” and
white is “recessive”
X
F2
Mendel’s Experiments – Important Points
1.
Followed the pattern of
inheritance for multiple
generations (i.e., > 1)
–
2.
Many 19th century
botanists would have
said “some white
flowers reappeared in
F2”
Mendel was lucky!
X
F1
Quantitative Analysis
–
3.
What if the experiment
terminated after F1?
P
Self
F2
Mendel’s Experiments in modern genetic terms
1.
2.
Alternative versions of genes account for variation in
inherited characters
–
Alternative versions of genes are “alleles”
–
Alleles reside at the SAME genetic locus
Relationship between alleles, chromosomes, and
DNA
– DNA at a locus varies in sequence
– Sequence variants cause different phenotypes
(e.g., purple and white flowers)
Mendel’s Experiments in modern genetic terms
•
Diploid individuals have
homologous pairs of
chromosomes, one from
each parent
•
An individual inherits one
allele from each parent
•
Alleles may be same or
different
•
If different, the dominant
allele determines the
organism’s phenotype
“Flower-color locus”
Purple allele
White allele
Mendel’s Experiments in modern genetic terms
• The two alleles at a locus segregate during gamete
production
– Each gamete gets only one of the two alleles
present in somatic cells
– Segregation corresponds to the different
gametes in meiosis (I or II?)
Recall Meiosis I – Metaphase I
•
What about crossing-over?
Mendel’s “Law of Segregation”
• If an individual has identical alleles at a locus (i.e., is
true-breeding), that allele is present in all its gametes
All
• If an individual has two different alleles at a locus,
half its gametes receive one allele, half receive the
other allele
half
half
Genetic Terminology –
• If a diploid individual has two copies of the SAME
ALLELE at a locus (i.e., it got the same allele from mom
and dad), it is a HOMOZYGOTE
• If it has two different ALLELES at a locus (got a different
allele from mom than from dad) it is a HETEROZYGOTE
•
The genetic makeup at a locus (or loci) is the individual’s
GENOTYPE
• An organism's Traits comprise its PHENOTYPE
Mendel’s Law of segregation: a test
Genotype: PP x pp
Gametes: P
p
P
Genotype: Pp
Gametes: 1/2 P, 1/2 p
F1
X
Self
Genotype: 1/4 PP, 1/2 Pp, 1/4 pp
Phenotype: 3 purple, 1 white
F2
Mendel’s Law of segregation: a test
F1
X
•
Phenotype:
•
Genotype:
•
•
Ova (female gametes)
Sperm (male gametes)
•
Half of male gametes will be P. Of those, half will unite with
an ovum that is P.
•
•
•
Thus, the frequency of PP in the F2 is: (1/2)(1/2 ) = 1/4
Frequency of pp = (1/2)(1/2) = 1/4,
Frequency of Pp = 2(1/2)(1/2) = 1/2
Pp
Pp
1/2 P, 1/2 p
1/2 P, 1/2 p
The “Punnett Square”
•
Gamete genotypes of one
parent given as columns
Male Parent
Sperm genotype
Female
Parent
Pp
P
p
P
PP
Pp
p
pP
pp
•
•
•
Gamete genotypes of other
parent given as rows
Offspring genotypes given
as cells in the table
Each cell has equal
frequency (here = 1/4)
Egg genotype
Pp
The “Punnett Square”
•
Male Parent
Sperm genotype
Note that in this cross there Female
Parent
are TWO ways to get a
heterozygote
P from mom, p from Dad
p from mom, P from Dad
•
Frequency of heterozygotes
= 1/4 Pp + 1/4 pP = 1/2
P
p
P
PP
Pp
p
pP
pp
Pp
Egg genotype
•
•
Pp
The “Testcross”
•
Male Parent
Individuals homozygous for Female
a dominant allele have the Parent
same phenotype as
heterozygotes
To determine the genotype
of an individual, cross it to a
known homozygous
recessive
•
What is the phenotypic ratio
among these offspring?
•
What is the genotype of the
unknown individual?
pp
p
PEgg genotype
•
Sperm genotype
P
?
p
The Law of Independent Assortment or Why Mendel
was so Lucky
• Mendel's next step was to cross plants that bred true
for each of TWO traits, e.g....
• seed shape (Round or wrinkled, Round dominant; R/r)
• seed color (Yellow or green, yellow dominant; Y/y)
• Parental cross: RRYY x rryy
• F1 are Round, Yellow (RrYy)
• Self F1s...
P
F1
X
The "Dihybrid Cross" - Dependent Assortment
•
Male F1 parent = RrYy
Hypothesis: Loci ("Traits" to
Mendel) assort together
("dependently")
If a gamete has an R allele, it
also has a Y allele (recall P
generation was RRYY, rryy)
•
If a gamete has an r allele it
also has a y allele
•
What are the expected
frequencies of F2
phenotypes?
Female F1 parent = RrYy
•
RY
RY
ry
ry
The "Dihybrid Cross" - Dependent Assortment
•
•
•
Male F1 parent = RrYy
Hypothesis: Loci assort
together ("dependently")
If a gamete has an R allele, it
also has a Y allele (recall
parents were RRYY, rryy)
If a gamete has an r allele it
also has a y allele
What are the expected
frequencies of F2
phenotypes?
Female F1 parent = RrYy
•
RY
RY
RRYY
rRyY
ry
ry
RrYy
rryy
The "Dihybrid Cross" - Dependent Assortment
Male F1 parent = RrYy
• NOT WHAT MENDEL
OBSERVED!
Female F1 parent = RrYy
• Predict 3/4 round, yellow,
1/4 wrinkled, green
RY
RY
RRYY
rRYy
ry
ry
RrYy
rryy
The "Dihybrid Cross" - Independent Assortment
Male F1 parent = RrYy
• Four combinations
of alleles in gametes
• Expect traits in
9:3:3:1 ratio
• THIS IS WHAT
MENDEL OBSERVED
Female F1 parent = RrYy
• All are equally likely
RY
Ry
rY
ry
RRYY
RRYy RrYY
RrYy
RRYy
RRyy
RrYy
Rryy
RrYY
RrYy
rrYY
rrYy
RrYY
Rryy
rrYy
rryy
RY
Ry
rY
ry
Mendel's Laws
1.
The Law of Segregation - ONE LOCUS
•
2.
If the locus is heterozygous, half the gametes get one
allele, half the gametes get the other allele
The Law of Independent Assortment - MULTIPLE
LOCI
•
Alleles at each locus segregate independently of alleles at
other loci
•
(When is this not true? or Why was Mendel so lucky?)
Introduction to Probability Theory
•
Independent Events - if the outcome of one event does not
depend on the outcome of some other event
– e.g., rolls of a die, flips of a coin, segregation of loci on
different chromosomes
•
The probability of BOTH of two events happening is the
product of the probability of each event happening
independently.
– Formally, Pr(A and B) = Pr(A) x Pr(B)
– e.g., Pr(two heads on two flips) = Pr(1st flip heads) x Pr(2nd
flip heads)
Introduction to Probability Theory
• Probability of EITHER of two events happening is the
sum of the probability of each event happening
independently
– Formally, Pr(A or B) = Pr(A) + Pr(B)
– e.g., Pr(one head on two flips) = Pr(head,tail or tail,head)
Pr(1st flip tails)*Pr(2nd flip heads) = (1/2)(1/2) =1/4
Pr(1st flip heads)*Pr(2nd flip tails) = 1/4
–
1/4 + 1/4 = ½
– Pr(1-locus heterozygote) = Pr(Aa) + Pr(aA) = ¼ + ¼ = ½
For tomorrow...
• Mendelian Genetics, continued
• Pedigree analysis
• Read the rest of Ch. 14