Monohybrid Crosses, Punnett Squares & Test Crosses – Detailed Study Notes

Parents & Independent Probabilities

• Each child / offspring is an independent event.
  • If the probability of a given trait is 0.25 (e.g.
    blue eyes) then:
  • 10 children could all lack the trait ( 0.75^{10} chance )
  • 10 children could all show the trait ( 0.25^{10} chance )
• Analogy: Like consecutive coin tosses— previous outcomes do not affect the next.

Punnett-Square “Calculator” Fundamentals

• Grid that combines all gamete alleles from two parents to predict zygote genotypes.
• Conventions
  • Write dominant allele first (e.g. Pp NOT pP)
  • Circle or highlight each cross systematically (row by row or column by column) to avoid omission.
  • True-breeding / pure-bred = homozygous ( PP or pp )
  • Heterozygous = one dominant + one recessive ( Pp ).
• Probabilities derived directly from cell counts:
  \text{Probability} = \frac{\text{# of desired genotypes}}{\text{total # cells}}

Classic Flower-Colour Example

P (Parental) Generation

• Purple flower: homozygous dominant PP
• White flower: homozygous recessive pp

F₁ Cross ( PP \times pp )

• Gametes: P from purple, p from white
• All four cells: Pp (heterozygous)
  • Genotype ratio: 100\%\;Pp
  • Phenotype: all purple (dominant masks recessive)

F₂ Cross ( Pp \times Pp )

• Grid yields: PP, Pp, Pp, pp
  • Genotype ratio: 1\;PP : 2\;Pp : 1\;pp
  • Phenotype ratio: 3 purple : 1 white
• Demonstrates Mendel’s 3 : 1 phenotypic expectation when both parents are heterozygous under complete dominance.

Step-by-Step Problem-Solving Template (Monohybrid, Autosomal)

1. Determine if trait is autosomal or sex-linked.
2. Build a clear legend.
   • One characteristic ⇒ one letter.
   • Example: H = hornless (dominant); h = horn (recessive).
3. Deduce genotypes of all individuals mentioned.
   • Use offspring information where given.
4. Draw Punnett square, fill systematically, then extract
   • Genotype ratio
   • Phenotype ratio / probabilities

Worked Example 1 – Hornless vs Horned Cattle

Legend: H = hornless, h = horned.

• Given calf is horned ⇒ calf = hh.
• Therefore each parent contributed an h.
• Parents are hornless phenotypically ⇒ must be Hh (carriers).

Punnett ( Hh \times Hh )

• Offspring genotypes: HH, Hh, Hh, hh
• Probability next calf is horned: \frac14 = 25\%
• Genotype ratio: 1\;HH : 2\;Hh : 1\;hh
• Phenotype ratio: 3 hornless : 1 horned

Key reinforcement

• Multiple genotypes can share one phenotype.
• When both parents are heterozygous the phenotypic 3 : 1 re-appears.

Worked Example 2 – Albinism in Corn

Legend: A = normal pigment (dominant), a = albino (recessive).

• Parent 1: albino ⇒ aa
• Parent 2: normal & heterozygous ⇒ Aa

Punnett ( aa \times Aa )

• Cells: Aa, Aa, aa, aa
• Genotype ratio: 2\;Aa : 2\;aa (often reduced to 1:1)
• Phenotype ratio: 2 normal : 2 albino ⇒ 1:1

The TEST CROSS (Diagnostic Mating)

Purpose: Determine whether a dominant-phenotype individual is homozygous dominant or heterozygous.

• ALWAYS mate the unknown with a homozygous recessive tester ( pp, hh, aa …)
• Two possible Punnett outcomes
  1. If unknown is PP (or HH, AA …)
  • Gametes P only → offspring all Pp → all show dominant phenotype.
  1. If unknown is Pp
  • Gametes P or p → offspring Pp and pp in 1:1 ratio → mixture of dominant & recessive phenotypes.
• Observation of any recessive offspring immediately reveals heterozygosity in the parent.

Agricultural Application – White vs Black Sheep

• Trait: white wool (dominant) W, black wool (recessive) w.
• Goal: keep only true-breeding white sheep.
• Procedure
  1. Mate white candidate with known black tester ( ww ).
  2. Evaluate lambs:
  • All white ⇒ parent is WW (keep for breeding).
  • Mix of white & black ⇒ parent is Ww (remove from elite breeding program).
• Reason: white wool easier to dye & stronger; black lambs reduce profit.

Probability & Statistics Reminders

• Each mating = independent trial.
• Long-term frequencies converge on Punnett predictions; short term may vary widely.
• Useful general formula: P(\text{event}) = \frac{\text{favourable}}{\text{total}}.

Common Conventions & Tips

• Underline lowercase letters if they resemble capitals (e.g. p vs P).
• Always state legend first— essential for full marks.
• Do genotype ratio before phenotype ratio.
• Never jump from phenotype directly to unique genotype unless the trait is recessive.
• Keep Punnett squares tidy; mis-ordering alleles leads to counting errors.

Why Follow the Full Sequence?

• Skipping steps invites logical or arithmetic mistakes (analogous to stoichiometry in chemistry).
• Even experienced instructors still follow the checklist to guarantee correct solutions.

Coming Extensions (Preview)

• Other inheritance types (incomplete dominance, codominance, sex-linkage) require modified tools— test cross works only under complete dominance.
• Sex-linked problems add X/Y symbols to genotypes.

Study these steps methodically; with repetition Punnett analysis becomes rapid, reliable, and exam-ready.