Probability and Punnett Models

Objective: Calculate conditional genotype and phenotype probabilities.

A Punnett square combines possible gametes from two parents under stated assumptions. For Aa × Aa with equal allele segregation, offspring genotype probabilities are 1/4 AA, 1/2 Aa, and 1/4 aa. Under complete dominance for a specified trait, corresponding phenotype probabilities are 3/4 dominant and 1/4 recessive. The square represents expected probabilities, not a guaranteed count for four offspring. For Aa × aa, genotype probabilities are 1/2 Aa and 1/2 aa. These calculations assume the symbols describe the same locus, gametes are equally likely as modeled, and other effects such as viability selection do not change the outcomes.

Objective: Apply probability rules with independence and mutually exclusive outcomes.

For independent events A and B, P(A and B) = P(A)P(B). For mutually exclusive outcomes, P(A or B) is the sum of their probabilities. In Aa × Aa, heterozygosity arises by A from one parent and a from the other, or the reverse: 1/4 + 1/4 = 1/2. For independently assorting AaBb × AaBb, P(aabb) = 1/4 × 1/4 = 1/16. Independence must be justified; linkage or other dependencies change the multiplication step. A conditional probability such as P(Aa | dominant phenotype) excludes aa from the denominator, giving 2/3 under simple complete dominance.

Objective: Compare expected ratios with observations and sample size.

If two loci assort independently and each exhibits complete dominance, an AaBb × AaBb cross predicts a 9:3:3:1 phenotype ratio in the simplified model. This prediction arises from multiplying two 3/4 versus 1/4 phenotype probabilities, not from assigning four fixed outcomes to each group of sixteen offspring. Counts in a finite sample vary randomly; larger samples generally make proportions more stable, but a close ratio alone does not prove the underlying assumptions. To evaluate a mismatch, consider linkage, selection, scoring ambiguity, and random sampling. A model should state what phenotypes are distinguishable and how individuals are sampled.