10.2: Dihybrid crosses - Mendel

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10.2 Dihybrid crosses - Mendels Second
Experiment

• The Inheritance of Two Traits
• Does the inheritance of one characteristic
  influence the inheritance of another
  characteristic?
• For example Does pea shape influence pea color?

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Mendel performed a Dihybrid Cross

• He crossed two pea plants that differed in two
  traits.
• P generation Pure round yellow (RRYY)
• P generation Pure wrinkled Green (rryy)
• What do you think the results were?

The F1 generation will be heterozygous for both
traits RrYy
Mendel's Experiments
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Moving On to Two Traits at a Time

• Keep T and t for tall and short plants,
  respectively.
• Add R and r for round and wrinkled seeds,
  respectively.
• A double heterozygote male produces four types of
  gametes.

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Cross with a Female Double Heterozygote

• A double heterozygote female produces four types
  of eggs.

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Crossing the Double Heterozygotes

• The male passes on his alleles, two per gamete

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Crossing the Double Heterozygotes

• The female passes on her alleles, two per egg.

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Double Heterozygote Cross Assessing the
Resultant Genotypes

• At least one T yields tall stature.
• At least one R yield round seeds.
• Thus, there are 9 ways (gray) to produce tall,
  round-seeded offspring.

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Double Heterozygote Cross Assessing the
Resultant Genotypes

• Again, at least one T yields tall stature.
• And one R is required for round seeds, so rr must
  produce wrinkled seeds.
• Thus, there are 3 ways (lighter gray) to produce
  tall, wrinkly seeded offspring

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The Third Phenotype in a Double Heterozygote
Cross

• Two t alleles yield short stature.
• At least one R produces round seeds.
• Thus, there are 3 ways (lightest gray) to produce
  short offspring with round seeds.

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The Fourth Phenotype in a Double Heterozygote
Cross

• Two t alleles yield short stature.
• Two r alleles produce wrinkled seeds.
• There is only 1 way to produce short offspring
  with wrinkled seeds.

http//trc.ucdavis.edu/biosci10v/bis10v/media/ch08
/dihybrid_v2.html
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10.2.1 The F1 generation were all round and
yellow

• What happens when you cross F1 with a F1?

The F2 generation 9 round and yellow 3 round and
green 3 wrinkled and yellow 1 wrinkled and
green These results represent a phenotypic ratio
of 9331
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Law of Independent Assortment

• The inheritance of alleles for one trait does not
  affect the inheritance of alleles for another
  trait.
• This means that different pairs of alleles are
  passed to the offspring independently of each
  other.
• A pea plants ability to produce white flowers
  instead of purple ones does not influence the
  same plants ability to produce round peas
  instead of wrinkled peas

• http//www.sumanasinc.com/webcontent/animations/co
  ntent/independentassortment.html

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The Rules of Probablity

• Probablity scale ranges from 0-1
• An event that is certain to occur has a
  probability of 1, while an even that is certain
  NOT to occur has a probability of 0.
• E.g. chances of rolling 3 on a die 1/6
• The probabilities of all possible outcomes for an
  event must add up to 1.

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The Rule of Multiplication

• How do we determine the chance that two or more
  independent events will occur together in some
  specific combination?
• Compute the probability for each independent
  event, then multiply these individual
  probabilities to obtain the overall probability
  of these events occurring together.
• E.g. What is the chance that two coins tossed
  simultaneously will land heads up?
• 1/2 x 1/2 1/4
• If an F1 plant has a genotype Pp, what is the
  probability that a particular F2 plant will be pp?

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• If a parent has a genotype YyRr, what is the
  probability of an F2 plant having the genotype
  YYRR?

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The Rule of Addition

• What is the probability that an F2 plant from a
  monohybrid cross will be heterozygous?
• There are two ways F1 gametes can combine to
  produce a heterozygous result. The dominant
  allele can come from the ovum and the recessive
  allele from the sperm or vice versa.
• By the rule of addition, the probability of an
  event that can occur in two or more different
  ways is the sum of the separate probabilities of
  those ways.
• 1/4 1/4 1/2

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Using rules of probability to solve genetics
problems

• Imagine a trihybrid cross
• P purple flower p white flower
• Y yellow seed y green seed
• R Round seed r wrinkled seed
• PpYyRr x Ppyyrr What fraction of offspring will
  exhibit the recessive phenotype for at least two
  of the three traits?
• Solution List all possible genotypes
• ppyyRr, ppYyrr, Ppyyrr, Ppyyrr, ppyyrr
• Next use rule of multiplication to calculate the
  individual probabilities for each of the
  genotypes
• Use rule of addition to pool the probabilities
  for fulfilling the condition of at least two
  recessive traits.

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Solution PpYyRr x Ppyyrr

• ppyyRr x x
• ppYyrr x x
• Ppyyrr x x
• PPyyrr x x
• ppyyrr x x
• ____________________________________
• Chance of at least 2 recessive traits

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Test Crosses

• A test cross can be used for both monohybrid and
  dihybrid crosses to determine the genotype of an
  unknown individual.
• It involves crossing the unknown genotype with a
  homozygous recessive individual.
• The results will determine the unknown genotype.

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Examples Monohybrids

• In a monohybrid test cross involving height, if
  all offspring are tall, one can deduce that the
  original genotype was TT (homozygous).
• If 50 of the off spring are tall and the other
  50 dwarf, one can deduce that the original
  genotype was Tt (heterozygous)

Examples Dihybrids

• In test cross involving shape and color, if it
  produces plants that show the dominant phenotype
  for both traits that is round and yellow, one can
  conclude that the original genotype was RRYY.
• If the original plant is heterozygous (RrYy), the
  cross will produce a 25 chance for each
  combination.
• 25 Round and Yellow 25 Round and Green
• 25 Wrinkled and Yellow 25 Wrinkled and Green

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10.2.4/5 Define linkage group

• A group of gene whose loci are on the same
  chromosome

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Beyond Mendels Laws

• Incomplete Dominance
• Co-Dominance
• Multiple Alleles

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Incomplete Dominance

• Occurs when neither of the alleles for a certain
  trait is dominant.
• This gives rise to an intermediate expression
  found in individuals that are heterozygous. Ex.
  White flowers and Red flowers are homozygous,
  Pink flowers are heterozygous.

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Co-Dominance

• pairs of alleles that both affect the phenotype
  when present in a heterozygote
• Which of the following offspring would represent
  co-dominance from the mating of a pure black
  rooster and a white hen?
• Black chicken
• White chicken
• Grey chicken
• Black and White
• chicken.

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4.3.3/4 Multiple Alleles

• Occurs when a gene has more than two alleles.
• Ex. Human blood has 3 alleles A, B, O