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)
- Determine if trait is autosomal or sex-linked.
- Build a clear legend.
- One characteristic ⇒ one letter.
- Example: H = hornless (dominant); h = horn (recessive).
- Deduce genotypes of all individuals mentioned.
- Use offspring information where given.
- 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
- If unknown is PP (or HH, AA …)
- Gametes P only → offspring all Pp → all show dominant phenotype.
- 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
- Mate white candidate with known black tester ( ww ).
- 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.