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.
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Trihybrid cross
2
• 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
Product law
3
• Product law used to calculate odds of an
outcome from independent events
– Flip a coin: heads or tails, 50:50 chance (1/2)
– Flip a coin 3 times, get 3 heads; the next flip, there’s
still a 50:50 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
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
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Branch diagram for figuring trihybrid cross
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Crossing 2 individuals
heterozygous for all 3 traits:
Ww 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
Alterations to Mendel
•
•
•
•
•
•
•
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Incomplete or partial dominance
Codominance
Multiple alleles
Lethal alleles
Gene interactions
Sex-linked, sex-limited, & sex-influenced
Effect of environment
Extranuclear inheritance
6
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: 1:2:1
www.people.virginia.edu/ ~rjh9u/snapdragon.html
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Partial dominance-2
• Partial dominance is not a common visual phenotype
– 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.
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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
1:2:1 ratio
http://boneslab.chembio.ntnu.no/Tore/Bilder/BlodMN.jpg
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Multiple alleles
10
• 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
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
12
• In genetic crosses, information is obtained by
examining the phenotype of the offspring.
– In some instances, the genotype 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_Iss21_dec18_02/img/obesity-mice.jpg
Lethal alleles-2
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– 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
– 2:1 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.
Complex inheritance and dihybrid crosses
14
• 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 3:1 ratio, co-dominant trait
shows 1:2:1 ratio
– Phenotypic classes in offspring no longer 9:3:3:1
• Actually come out 3:6:3:1:2:1
• Complex inheritance produces odd ratios.
Really good practice problems
15
• http://www.biology.arizona.edu/mendelian_gen
etics/mendelian_genetics.html
• Do all the problems from the links “Monohybrid
cross” and from “Dihybrid cross”.