Biology 345 Organic Evolution

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Probability of inheriting a specific allele
Remember The specific allele which ends up
being inherited from a parent to an offspring is
random. Since a parent has two alleles, and
each allele is equally likely to be inherited by
an offspring, the probability that an offspring
will get a specific allele 0.5. This is
equally true for both parents.
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Probabilities for second filial
generation (Crossing first filial generation)
Example 1 Suppose you breed a pair of plants
with pink flowers. What are the possible
genotypes and phenotypes of the offspring? RR
(Red), RW (Pink), and WW (White) Question What
is the probability of getting these genotypes?
Phenotypes? Answer P(RR) P(R) ? P(R) ?
0.50.5 0.25 P(WW) P(W) ? P(W) ? 0.50.5
0.25 P(RW) P(R) ? P(W) ? P(W) ? P(R) ?
0.50.5 0.50.5 0.25 0.25 0.5 P(Red)
P(RR) 0.25 P(White) P(WW) 0.25 P(Pink)
P(RW) 0.5
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Example 2 What if we did the same thing with eye
color? The genotype probabilities are exactly
the same! P(BB) P(B) ? P(B) ? 0.50.5
0.25 P(bb) P(b) ? P(b) ?
0.50.5 0.25
P(Bb) P(B) ?
P(b) ? P(b) ? P(B) ? 0.50.5 0.50.5
0.25 0.25 0.5 But the phenotypic
probabilities are different P(Blue) P(bb)
0.25 P(Brown) P(BB) P(Bb) 0.25 0.5
0.75
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Crosses Involving Two Genes
A cross that involves two independent traits is
termed dihybrid cross. Example Suppose Gene 1
has alleles A and a (A is dominant over a) Gene 2
has alleles B and b (B is dominant over b) The
genes are on different chromosomes Here is a
doubly heterozygous individual
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Probabilities in gametogenesis
What is the probability of each gamete?
P(AB) P(A) P(B) 0.5 0.5 0.25 P(Ab)
P(A) P(b) 0.5 0.5 0.25 P(aB) P(a)
P(B) 0.5 0.5 0.25 P(ab) P(a) P(b) 0.5
0.5 0.25
Note Each gamete is equally probable
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Crossing two double heterozygotes AaBb AaBb
What are the possible genotypes of the offspring?
AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabb
What are the probabilities of an offspring being
each genotype?
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Probabilities of genotypes in dihybrid cross
What are the probabilities of each genotype?
P(AABB) P(AB) ? P(AB) ? 0.25 0.25
0.0625 P(AABb) P(AB) ? P(Ab) ? P(Ab) ?
P(AB) ? 0.250.25 0.250.25 0.125 P(AAbb)
P(Ab) ? P(Ab) ? 0.25 0.25
0.0625 P(AaBb) P(AB) ? P(ab) ? P(ab) ?
P(AB) ? P(Ab) ? P(aB) ? P(aB) ? P(Ab) ?
0.25 (add them all up)
P(AaBB) 0.125 P(Aabb) 0.125 P(aaBB)
0.0625 P(aaBb) 0.125 P(aabb) 0.0625
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Probabilities of phenotypes in dihybrid cross
What are the probabilities of each phenotype?
P(AB) P(AABB) P(AABb) P(AaBB) P(AaBb)
0.0625 0.125 0.125 0.25 0.5625 P(Ab)
P(AAbb) P(Aabb) 0.0625 0.125
0.1875 P(aB) P(aaBB) P(aaBb) 0.0625
0.125 0.1875 P(ab) P(aabb) 0.0625
If you are familiar with it, note that these
probabilities give you the classic 9 3 3
1 ratio
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Exercise
Cross AaBb father with an aaBb mother What are
the probabilities of each genotype and phenotype?
Fathers gametes P(AB) 0.25 P(Ab) 0.25
P(aB) 0.25 P(ab) 0.25 Mothers gametes
P(aB) 0.5 P(ab) 0.5
Genotypic probabilities P(AaBB) P(AB) ?
P(aB) ? 0.25 0.5 0.125 1/8 P(AaBb)
P(AB) ? P(ab) ? P(Ab) ? P(aB) ? 0.25
0.5 0.25 0.5 0.25 1/4 P(Aabb) P(Ab) ?
P(ab) ? 0.25 0.5 0.125 1/8 P(aaBB)
P(aB) ? P(aB) ? 0.25 0.5 0.125
1/8 P(aaBb) P(aB) ? P(ab) ? P(ab) ? P(aB)
? 0.25 0.5 0.25 0.5 0.25 1/4 P(aabb)
P(ab) ? P(ab) ? 0.25 0.5 0.125 1/8
Phenotypic probabilities P(AB) P(AaBB)
P(AaBb) 0.125 0.25 0.375 3/8 P(Ab)
P(Aabb) 0.125 1/8 P(aB) P(aaBB) P(aaBb)
0.125 0.25 0.375 3/8 P(ab) P(aabb)
0.125 1/8
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As a Punnet Square
Mothers gametes Mothers gametes
aB ab
Fathers gametes AB AaBB (AB) AaBb (AB)
Fathers gametes Ab AaBb (AB) Aabb (Ab)
Fathers gametes aB aaBB (aB) aaBb (aB)
Fathers gametes ab aaBb (aB) aabb (ab)
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Multiple offspring
What if we take our parents are breed them so
they produce 100 offspring? Each offspring is
completely independent from the others. The
previous values still describe the probability of
any individual offspring having a specific
genotype or phenotype. But how many of the 100
offspring should have each genotype? Each
phenotype? What is the probability that
heterozygous parents will have 100 brown-eyed
offspring? 99 brown-eyed offspring and 1
blue-eyed offspring? 98 brown-eyed offspring and
2 blue-eyed offspring? (etc.) How do we
calculate this?