Transcript probability laws

GREGOR MENDEL
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Austrian monk
Studied at the University of Vienna
Discovered the basic principles of heredity
Worked with breeding garden peas
– Self pollinating
– Perfect flowers
– Artificially cross pollinated
Mendel’s Pea Plants
• True breeding – all
offspring same variety
• Hybridization – crossing 2
contrasting true breeding
varieties
• P generation – parental
generation (true
breeding)
• F1 – first filial (hybrids)
• F2 – second filial (from
self pollinating F1s)
Mendel tracked heritable
characters for 3 generations
MENDEL’S LAWS
1. Alternative versions of genes (alleles) account
for variations in inherited characters.
2. For each character, an organism inherits two
alleles, one from each parent.
3. If the 2 alleles differ, then one, the dominant
allele is fully expressed in the organism’s
appearance; the recessive allele has no
noticeable effect on the organism’s
appearance
4. The 2 alleles for each character segregate
during gamete production.
Law of Segregation
• Letters represent alleles
(upper case for dominant
alleles & lower case for
recessive alleles)
• P generation – true
breeding plants, matching
alleles (PP or pp)
• Gametes contain only
one allele
• Fusion of gametes →
hybrid F1s
• When hybrids produce
gametes, the 2 alleles
segregate
• Half the gametes
receive the P allele and
half receive the p allele
• Punnett squares show
possible combinations
of alleles in gametes
• Each square is a
possible offspring
VOCABULARY
TEST CROSS
PROBABILITY LAWS
1. CHANCE HAS NO MEMORY
2. RULE OF MULTIPLICATION: the chance
of 2 independent events occurring together
is the product of their individual
probabilities.
3. RULE OF ADDITION: the probability of an
event that can occur in 2 or more different
ways is the sum of the separate
probabilities.
PROBABILITY PRACTICE
1) If a coin is tossed 7 times and lands heads all
seven times, what is the chance of getting
heads again?
2) A couple has 3 girls; what is the chance that
their fourth child will be another girl?
3) In a deck of 52 cards, what is the chance of
drawing:
a) Any red card?
b) Any ace?
c) Any heart?
PROBABILITY PRACTICE
1. From a normal deck of cards, what is the
chance of drawing the Jack of Hearts?
2. When tossing 2 dice, what is the probability of
getting a “6” up on both?
3. What is the probability of 2 parents, with
genotypes AabbCc x AaBBCc, having a child
with the genotype AaBbCc?
AaBbRr x Aabbrr
• What fraction of the offspring will have the
following genotypes?
– aabbrr
- AaBbRr
- aaBbrr
• What fraction of the offspring will have at
least two recessive phenotypes?
a) list all possible genotypes
b) calculate probabilities (rule of multiplication)
c) pool probabilities (rule of addition)
AaBbRr x Aabbrr
Predict the gametes
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Formula 2n (n = # of heterozygous pairs)
AA → 20 →1 gamete type (A)
Aa → 21 → 2 gametes (A or a)
AABb → 21 →2 gametes (AB or Ab)
AaBb → 22 → 4 gametes (AB, Ab, aB, ab)
AaBbDd → 23 → 8 gametes
AaBbDdFf → 24 →16 gametes
AaBbDd
AaBbDdFf
Incomplete Dominance
• Alleles for red and
white, neither is
dominant.
• Hybrids are a blend of
the two alleles and are
phenotypically pink
• There is NO allele for
pink, therefore NO true
breeding pink flowering
plants.
• Codominance: both
alleles equally
expressed. Human
blood type, cow
coloring
MULTIPLE ALLELES
EPISTASIS
• Gene at one locus alters the
phenotypic expression of a
gene at a second locus
• Gene for fur color: (B) black
(b) brown
• 2nd gene deposition of
pigment: (C) color (c) white
Polygenic Traits
• Skin color and
height in humans
• Additive effect of
2 or more genes
on 1 phenotype
• Quantitative
characters –
variation along a
continuum
• Dots represent
“units” of
darkness
NATURE and NURTURE
The product of a genotype is a range of
phenotypic possibilities over which there
may be variation due to environmental
influence. Norm of reaction
- Hydrangea flower color and pH (blue-pink)
- Human blood typing: little range (genotype
mandates phenotype.
- Human blood counts: vary with altitude,
fitness, infectious agents
Norms of reaction broadest for polygenic traits
like skin color. Multifactorial characters: both
genetic & environmental influences.
Mendelian Inheritance in Humans
• Recessive Disorders
– Cystic fibrosis
– Tay-Sachs disease
– Sickle-cell disease
- PKU
• Dominant Disorders
– Achondroplasia
– Huntington’s disease
• Multifactorial Disorders
-Polydactyly
SICKLE CELL DISEASE
• Pleiotrophy – one
disorder, multiple
effects
• Incomplete
dominance
• Heterozygotes –
sickle cell trait,
advantage
(resistant to
malaria)
PEDIGREES
INHERITANCE PATTERN?
FETAL TESTING
THE
CHROMOSOMAL
BASIS OF
INHERITANCE
The Chromosomal Basis of
Mendel’s Laws
Segregation
R & r alleles
Segregate
Only one long
chromosome
In each
gamete
Fertilization
recombines
the R & r
alleles
Independent
Assortment
Long and short
chromosomes;
Arranged in 2
equally likely
ways
They assort
independently
Fertilization
9:3:3:1 ratio
THOMAS HUNT MORGAN
• Worked with Drosophila
• Wild type – phenotype most common in the
wild. Red eyes, gray, normal wings
• Mutant phenotypes – white eyes, ebony,
vestigial wings
• Discovered sex linkage
• Sex linked genes – on sex chromosomes
Sex Linked Inheritance
• Sex linked genes: on the
X or Y chromosome
• X & Y NOT homologous
• X-linked genes: males
being XY have only one
copy/allele, females XX
have two copies/alleles
• X-Linked recessive –
more common in males
• X-Linked dominant – more
common in females
SEX DETERMINATION
• Humans – sex
determined by
presence or absence
of Y chromosome;
XX-female; XY-male
• Fruit flies – # of X
chromosomes; XXfemale; XY-male;
XXY-female
• Birds – females are
heterogametic
Transmission of Sex-Linked
Recessive Traits
Father w/ trait
transmits to all
daughters
Carrier passes
trait to ½ sons
½ daughters
Sons afflicted
Carrier w/ afflicted
male; 50% of
children afflicted
LINKAGE
• Law of Linear Order: genes on the same
chromosome are linked and are inherited
in a block.
• Drosophila – 2 linked genes; inherited
together
– body color (G gray, g ebony)
– wing size (L long, l vestigial)
• Test cross by Morgan produced
unexpected results
CROSSING OVER
MAPPING
• Linkage map – genetic map based on
recombination frequencies
• Map units – one map unit = 1%
recombination frequency
• Cytological maps – locate genes with
respect to chromosomal features like
stained bands
Recombination frequencies:
used to construct genetic map
The probability of a crossover between 2 loci is proportional
to the distance separating the loci
Sex linked Disorders in Humans
• Duchenne Muscular Dystrophy
• Hemophilia
• Red/Green Color blindness
X Inactivation
NONDISJUNCTION
leads to aneuploidy (trisomy, monosomy, polyploidy)
CHROMOSOMAL MUTATIONS
Human Chromosomal Disorders
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Down Syndrome (Trisomy 21)
Turner Syndrome (XO, monosomy X)
Klinefelter syndrome (XXY)
XYY, XXX
Cri du chat (cry of the cat) deletion in #5
CML (chronic myeloid leukemia) translocation
of # 22
• Down Syndrome due to translocation of #21
Genomic Imprinting
• Prader-Willi Syndrome:
– Mental retardation, obesity, short
stature, small hands & feet
(father)
• Angelman Syndrome:
– Spontaneous laughter, jerky
movements, other motor and
mental symptoms (mother)
• Same cause – partial deletion
of chromosome #15
• Genomic Imprinting – gene on
one chromosome silenced