SimuVeda

Biology · Simulator 032

Genetic Crosses

Choose the genotypes of two parents for one or two genes. The Punnett square gives the expected offspring ratios, then you breed a random sample of offspring and see how closely real counts follow the prediction.

How the model works

Each parent carries two alleles of each gene and passes one, chosen at random, to each offspring (Mendel's law of segregation). With two genes on different chromosomes, the choices are independent (law of independent assortment).

A Punnett square lists every combination of parental gametes. With uppercase alleles dominant:

  • Aa × Aa gives genotypes 1 AA : 2 Aa : 1 aa, and phenotypes 3 dominant : 1 recessive.
  • AaBb × AaBb gives phenotypes 9 : 3 : 3 : 1.
  • Aa × aa (a test cross) gives 1 : 1.

Real families are small samples, so counts scatter around these ratios. The simulator draws offspring with a seeded random generator and computes a chi-square statistic,

χ² = Σ (observed − expected)² / expected

, to show whether the deviation is larger than chance would usually produce.

Assumes complete dominance, unlinked genes and equal survival of all genotypes. Many real traits involve many genes, incomplete dominance or linkage.

Guided experiments

  1. Mendel's 3 : 1. Aa × Aa, breed 400 offspring. Prediction: close to 300 dominant : 100 recessive, never exactly. χ² usually stays below 3.84 (the 5% threshold for one degree of freedom).
  2. Small family. Same cross, only 4 offspring. Prediction: 3 : 1 often fails. 4 : 0 or 2 : 2 are common; with so few, chance dominates.
  3. Dihybrid 9 : 3 : 3 : 1. AaBb × AaBb. Prediction: 16 boxes in the square and four phenotype classes in the ratio 9 : 3 : 3 : 1.

Challenge

A dog with a dominant black coat is crossed with a recessive brown dog. Of 8 puppies, 4 are black and 4 brown. What was the black parent's genotype, and how sure can you be?

Reveal the explanation

A BB parent could only give black puppies, so any brown puppy proves the black parent is Bb; this is a test cross giving 1 : 1. One brown puppy is enough for certainty, whatever the ratio.

References

  • OpenStax, Biology 2e, §12.2 “Characteristics and Traits” and §12.3 “Laws of Inheritance”.