Bonus Section 2: Subsequent Generations
Tracking inheritance patterns through F₃, F₄, and F₅ generations
Mendel's Persistence: Beyond F₂
Most scientists would have stopped after discovering the 3:1 ratio in F₂. But Mendel was thorough. He continued his experiments through F₃, F₄, and even F₅ generations to verify his laws.
What he discovered was a beautiful mathematical pattern: as generations progressed, the proportion of pure-breeding plants increased while heterozygotes decreased.
"The constant characters which appear in the several varieties of a group of plants may be obtained in all the associations which are possible according to the laws of combination."
The Mathematical Pattern
F₂ Generation:1:2:1 (genotypic)
F₃ Generation:3:2:3 (genotypic)
F₄ Generation:7:2:7 (genotypic)
Pattern:(2ⁿ⁻¹):2:(2ⁿ⁻¹)
Predict the Pattern
Choose a generation and predict the genotypic ratio. Remember: pure-breeding lines increase while heterozygotes remain constant at 2 per every 2ⁿ plants.
F₃ Generation
Generation 3
Expected pattern: (2ⁿ⁻¹):2:(2ⁿ⁻¹)
where n = 1
F₃ Generation
Generation 4
Expected pattern: (2ⁿ⁻¹):2:(2ⁿ⁻¹)
where n = 2
F₃ Generation
Generation 5
Expected pattern: (2ⁿ⁻¹):2:(2ⁿ⁻¹)
where n = 3
F₃ Generation Prediction
What do you predict the genotypic ratio will be in F₃ generation?