Transcript Mendelian Genetics II: Probability

Announcements
•Please don’t interrupt other classes (including other Genetics
labs) to check flies in Brooks 204 (see schedule on the door).
•Bring calculators for next week’s lab.
•Homework: practice on problems 6,7,8,12 - do not turn in.
Turn in answers to problem set 1, next page, in
lab next week.
Problem Set 1: due 9/10, 9/11 in lab
1. In guinea pigs, rough coat (R) is dominant over smooth coat (r). A
rough coated guinea pig is bred to a smooth one, giving eight
rough and seven smooth progeny in the F1.
a) What are the genotypes of the parents and their offspring?
b) If one of the rough F1 animals is mated to its rough parent, what
progeny would you expect?
2. In summer squash, white fruit (W) is dominant over yellow (w), and
disk-shaped fruit (D) is dominant over sphere-shaped fruit (d). The
following problems give the phenotype of the parents and their
offspring. Determine the genotypes of the parents in each case:
a) White, disk x yellow, sphere gives 1/2 white, disk and 1/2 white, sphere.
b) White, sphere x white, sphere gives 3/4 white, sphere and
1/4 yellow, sphere.
c) Yellow, disk x white, sphere gives all white, disk progeny.
2 pts each answer for total of 10 pts
Review of last lecture
1. Regulation of the cell cycle - 3 main checkpoints
2. Meiosis: 2 sequential divisions: one reductional,
one equational. Sources of genetic variation:
recombination via crossing over in pachytene of
prophase I and independent assortment, metaphase I.
3. Mendel and his peas - brief intro
4. Monohybrid cross - Punnett square method
Monohybrid Cross:
Punnett Square Method
(1) Define symbols:
D = tall allele
d = dwarf allele
(2) State the cross
(3) Diagram the gametes
(4) Complete the squares
(5) Summarize the results:
Genotype
Phenotype
Reciprocal crosses
•Results were the same regardless of which parent was
used, e.g.
–tall pollen pollinating dwarf eggs
–dwarf pollen pollinating tall eggs
•Therefore the results were not sex-dependent
•Mendel proposed “unit factors” to explain his results
Outline of Lecture 4
I.
Mendel’s first three postulates
II.
Monohybrid Testcross
III. Dihybrid Cross
Basic Mendelian
genetics
IV. Independent Assortment
V.
Trihybrid Cross
VI. Molecular basis of Mendel’s postulates
VII. Probability
I. Mendel’s postulates
Postulate 1. Unit factors in pairs
•Genetic characters are controlled by unit factors in pairs.
•In other words, genes are present in two associated copies in
diploid organisms.
•For example, DD plants have two alleles for tallness, dd plants
have two alleles for dwarfism.
Postulate 2. Dominance/recessiveness
•In the case of unlike unit factors, one can be dominant and
the other can be recessive.
•In other words, when two different alleles of a gene are
present, one may show its effect while the other may be
masked.
•For example, Dd plants have a tall allele D and a dwarf allele
d, but are phenotypically tall.
Postulate 3. Segregation
•During the formation of gametes, unit factors
segregate randomly.
•In other words, when sperm and eggs are formed,
one of each allelic pair is randomly distributed to to
each gamete.
•For example, a Dd plant makes pollen or eggs, each
randomly receives either the D allele or the d allele.
Practice: Axial/Terminal Pods
•In garden peas, an allele T for axial flowers is
dominant to an allele t for terminal flowers.
–In the F2 generation of a monohybrid cross,
what is the expected ratio of axial : terminal?
–Among the F2 progeny, what proportion are
heterozygous?
–Among the F2 progeny with axial flowers, what
proportion are heterozygous?
II. Monohybrid Test Cross (Backcross)
• How can you determine genotype from individual
expressing dominant phenotype? - DD or Dd?
• Cross individual with dominant phenotype to a
homozygous recessive individual.
?
?
III. Dihybrid cross - phenotypes
1.Which traits are dominant?
2. Did the phenotypes of the P1 generation affect the F1 or F2 generations?
Analysis of dihybrid cross phenotypes
(forked-line/probability method)
Trait 1
Trait 2
Combined traits
Dihybrid Cross: P1 cross
Since yellow and round are dominant,
Let G = yellow, g = green, W = round, w = wrinkled.
Confirm on your own using a Punnett square!
Dihybrid Cross: F1 cross
Dihybrid Cross: Summary
9
3
3
1
Dihybrid Testcross:
How to determine the genotype of an individual with
2 traits of dominant phenotype
All yellow
Mixed
All Round
IV. Independent assortment
Mendel’s Fourth Postulate:
An Interpretation from the Dihybrid cross
• During gamete formation, segregating pairs of unit
factors assort independently.
• In other words, segregation of 2 alleles at one genetic
locus has no effect on the segregation of 2 alleles at
another locus (unless linked).
• For example, the assortment of yellow and green
alleles has no effect on the assortment of round and
wrinkled alleles, and vice versa.
Independent Assortment
• Results in extensive genetic variation
• Number of possible gametes = 2n where n is the
haploid number
• For humans, 223 = 8 million
• Each individual represents one of (8 X 106)2 = 64 X
1012 possible genetic combinations from her parents
V. Gamete Formation: Trihybrid cross
What size of Punnett square needed for analysis?
Trihybrid Cross - Phenotypes
Forked-line Method
27:9:9:9:3:3:3:1
VI. Molecular Basis of Mendel’s
Postulates: Chromosome behavior
• 1879: Walter Flemming discovers chromosomes in
living cells.
• 1900: DeVries, Correns, and Tschermak repeat,
rediscover Mendel.
• 1902: Sutton and Boveri and others link behavior of
chromosomes to Mendelian segregation and
independent assortment; propose chromosomal
theory of heredity.
Theodor Boveri
• Hypothesis: Removal of
chromosomes should
result in some change
to organism.
• Did this in sea urchin
embryos, saw abnormal
embryos.
1862-1915
Walter Sutton (1877-1916)
• Studied grasshopper testis and ovary cells, observed
that haploid numbers of chromosomes mixed to form
diploid set.
• Noted that this chromosome behavior correlated with
Mendel’s genes, and proposed that genes are carried
on the chromosomes.
Correlation Between Unit Factors
and Genes on Chromosomes
• Unit factors in pairs ~ genes on homologous
chromosomes in pairs
• Segregation of unit factors during gamete formation ~
genes on homologs segregate during meiosis
• Independent assortment of segregating unit factors ~
genes on nonhomologous chromosomes assort
independently
• Stronger evidence for the chromosomal theory of heredity
came from experiments of T.H. Morgan and others with
fruit flies from 1909 onwards.
VII. Laws of probability help explain
genetic events
Genetic ratios are most properly expressed as probabilities:
ex. 3/4 tall: 1/4 dwarf
The probability of each zygote having the genetic potential
for becoming tall is 3/4, etc..
Probabilities range from 0 (an event is certain NOT to
happen), to 1.0 (an event is certain to happen).
How do we calculate the probability of 2 or more
events happening at the same time?
Product law
• For simultaneous outcomes (AND)
• What is the chance that you will roll snake eyes with
two dice? (1 and 1)
– Chance of rolling 1 with first die = 1/6
– Chance of rolling 1 with second die = 1/6
– Chance of rolling two 1’s = 1/6 X 1/6 = 1/36
• We used product law when calculating probabilities
by the forked-line method.
Sum law
• For outcomes that can occur more than one way
(OR)
• What is the chance that you will roll either a 1 or a 6
with one die?
– Chance of rolling 1 = 1/6
– Chance of rolling 6 = 1/6
– Chance of rolling 1 or 6 = 1/6 + 1/6 = 2/6 = 1/3
Genetic Example
What is the probability (p) of green, wrinkled seeds (ggww)
from a dihybrid cross?
Parents: GgWw X GgWw
Possible gametes: GW, Gw, gW, gw so p(gw) = 1/4
One gw must come from each parent (gw and gw), so
p(ggww) = p(gw and gw) = 1/4 X 1/4 = 1/16