Lecture Notes: Multiple Traits, Genotypes, and Phenotypes

Key Concepts

• Mendel's Law of Independent Assortment: Allows each trait to be considered independently in crosses.
• Genotype vs. Phenotype: Genotype is the genetic makeup, while phenotype is the observable trait.

Problem 1: Genotypic Proportions

Objective: Compute the probability of progeny having a specific genotype from a cross of two individuals.

Crosses Involved

1. Trait A:

   • Cross: Big A little a x Big A little a
   • Dihybrid cross results:
     • 1/4 Big A Big A
     • 1/2 Heterozygous (Big A little a)
     • 1/4 Little a Little a

2. Trait B:

   • Cross: Big B little b x Little b Little b
   • Test cross results:
     • 1/2 Big B little b
     • 1/2 Little b Little b

3. Trait C:

   • Cross: Big C little c x Big C little c
   • Dihybrid cross results:
     • 1/4 Big C Big C
     • 1/2 Heterozygous (Big C little c)
     • 1/4 Little c Little c

4. Trait D:

   • Cross: Big D little d x Little d Little d
   • Test cross results:
     • 1/2 Heterozygotes (Big D little d)
     • 1/2 Little d Little d

5. Trait E:

   • Cross: Big E little e x Big E little e
   • Dihybrid cross results:
     • 1/4 Big E Big E
     • 1/2 Heterozygous (Big E little e)
     • 1/4 Little e Little e

Probability Calculation

• Desired Genotype: little a little a, little b little b, Big C Big C, Big D little d, little e little e
• Probability Calculation using product rule:
  • Little a little a: 1/4
  • Little b little b: 1/2
  • Big C Big C: 1/4
  • Big D little d: 1/2
  • Little e little e: 1/4
• Combined Probability: ( \frac{1}{256} )
• Note: Changes in parent genotypes affect probabilities.

Problem 2: Genotypic Combinations

Objective: Determine the number of different genotypic combinations possible in the progeny.

Approach

• Use branching diagrams to calculate combinations.
• Each trait contributes branches based on its genotype variations.

Calculation

• Total number of possible combinations: 108

Problem 3: Phenotypic Proportions

Objective: Determine the fraction of progeny with the dominant phenotype for all traits.

Phenotypic Cross Analysis

1. Trait A:
   • 3/4 Dominant (A dash), 1/4 Recessive (little a little a)
2. Trait B: All Dominant (B dash)
3. Trait C: 3/4 Dominant (C dash), 1/4 Recessive (little c little c)
4. Trait D: 1/2 Dominant (D dash), 1/2 Recessive (little d little d)
5. Trait E: 3/4 Dominant (E dash), 1/4 Recessive (little e little e)

Probability Calculation

• Combine probabilities for dominant phenotypes using product rule:
  • A dash: 3/4
  • B dash: 1
  • C dash: 3/4
  • D dash: 1/2
  • E dash: 3/4
• Total Probability: ( \frac{27}{128} )