Variation and probability

1
Variation and probability

• Gamete production is source of variation and
  genetic diversity, an advantage of sex.
• As a result of segregation and independent
  assortment, lots of combinations possible.
• 2n possibilities exist for diploids where n
  haploid number of chromosomes
• In humans, this is 8 million different gametes
• Crossing over during meiosis creates even more
  combinations of genetic information
• This diversity important in evolution, survival.

2
Trihybrid cross

• Mendel also crossed peas and looked at
  inheritance of 3 traits simultaneously.
• These showed independent assortment also.
• A Punnett square to determine the phenotypic
  ratios would be unwieldy
• It would require an 8 x 8 matrix 64 squares
• Because independent events are involved, one can
  use the product law
• Multiply each probability.
• Simplest way forked-line method branch diagram

3
Product law

• Product law used to calculate odds of an outcome
  from independent events
• Flip a coin heads or tails, 5050 chance (1/2)
• Flip a coin 3 times, get 3 heads the next flip,
  theres still a 5050 chance of getting a head.
• The chance of getting 4 heads in a row
• ½ x ½ x ½ x ½ 1/16 the product law.
• Odds of round, yellow seeds in a cross of Ww GG x
  Ww gg ¾ x 4/4 3/4

4
Sum Law

• The sum law outcomes of events are independent,
  but can be accomplished in more than one way.
• Flip a penny and a nickel odds of 1 heads and 1
  tails?

There are 4 possible outcomes from this flip. 1
head, 1 tail can be from the penny being heads
(odds 1/4), but also from the nickel (1/4) ¼ ¼
½
5
Branch diagram for figuring trihybrid cross
Crossing 2 individuals heterozygous for all 3
traitsWw Gg Pp x Ww Gg Pp What proportion of
the offspring are expected to have round, green
peas and purple flowers, where W is round, w is
wrinkled G is yellow, g is green and P is
purple and p is white? W_ gg P_
¾ x ¼ x ¾ 9/64
6
Alterations to Mendel

• Incomplete or partial dominance
• Codominance
• Multiple alleles
• Lethal alleles
• Gene interactions
• Sex-linked, sex-limited, sex-influenced
• Effect of environment
• Extranuclear inheritance

7
Incomplete or partial dominance
One allele only partially masks the other. Half
as much enzyme makes half as much
pigment. Phenotypic ratio is the same as
genotypic 121
www.people.virginia.edu/ rjh9u/snapdragon.html
8
Partial dominance-2

• Partial dominance is not common
• A molecular phenotype showing partial dominance
  is more common
• One allele instead of 2 is producing enzyme, so
  on a gel, a protein band is half as intense.

9
Codominance

• M and N blood groups LM LN
• Glycoprotein on blood cell surface
• If one of each allele, both expressed.
• Phenotype indicates genotype.
• Heterozygote cross shows 121 ratio

http//boneslab.chembio.ntnu.no/Tore/Bilder/BlodMN
.jpg
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Multiple alleles

• In peas, Mendel following the inheritance of two
  contrasting traits, e.g. purple vs. white flowers
• Often, more than two alleles for a trait exist.
• Study of multiple alleles requires a population!
• In diploid organisms, an individual can only have
  a maximum of two alleles. (2 different alleles)
• In populations, many different alleles may be
  present.
• Classic example the ABO blood group system

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ABO Blood groups
Series of sugars added to cell lipid creates
trait. Genotypes include AA, AO type A BB, BO
type B OO type O AB type AB where A
and B are co-dominant, O is recessive. In AB and
O, the genotype is known from the phenotype.
http//science.uwe.ac.uk/StaffPages/na/abo_ho2.gif
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Lethal alleles

• In genetic crosses, information is obtained by
  examining the phenotype of the offspring.
• In some instances, the phenotype is lethal
• Lethality may present itself late in life
  (Huntington Disease) or may result in no
  offspring.
• Example

Fur color in mice Agouti on left, yellow on
right.
http//www.cumc.columbia.edu/news/in-vivo/Vol1_Iss
21_dec18_02/img/obesity-mice.jpg
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Lethal alleles-2

• If certain genotypes are lethal, results of a
  cross may be quite confusing.
• Agouti x agouti all agouti
• Yellow x yellow 2/3 yellow, 1/3 agouti
• Agouti x yellow ½ yellow, ½ agouti
• 21 ratio is tip-off that something odd happens
• Homozygous for yellow is lethal, so that genotype
  is NOT represented.
• For lethality, yellow allele acts as recessive.
• For coat color, yellow allele acts as dominant
• A agouti, Ay yellow. Heterozygote is yellow.

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Complex inheritance and dihybrid crosses

• Book example inheritance of simple trait and
  multiple allele trait albinism and ABO
• Crossing of heterozygotes
• Mm (albinism) and AB (blood type)
• Assume independent assortment
• Simple trait shows 31 ratio, co-dominant trait
  shows 121 ratio
• Phenotypic classes in offspring no longer 9331
• Actually come out 363121
• Complex inheritance produces odd ratios.

15
Really good practice problems

• http//www.biology.arizona.edu/mendelian_genetics/
  mendelian_genetics.html
• Do all the problems from the links Monohybrid
  cross and from Dihybrid cross.