Punnett Squares & Genetics

Predicting what the offspring will look like

Junior level — plain language, no maths

Why do you have the eye colour you have? You inherited instructions - genes - from both parents, one copy from each. For many traits, one version of a gene is dominant (it shows up if you have even one copy) and the other is recessive (it only shows if you have two). A Punnett square is a simple grid that predicts the odds of what a child will inherit - and Gregor Mendel worked all this out in the 1860s by breeding thousands of pea plants.

Say a gene comes in a dominant version "A" and a recessive version "a". Each parent carries two copies and passes one, at random, to the child. The Punnett square lists one parent's two options along the top and the other parent's down the side, then fills in every possible combination. Suddenly you can see all the children that are possible, and how likely each one is.

The classic result: cross two parents who each carry one dominant and one recessive gene (Aa × Aa) and their children come out, on average, 3 showing the dominant trait to 1 showing the recessive - the famous 3:1 ratio. It doesn't tell you exactly what any single child will be (that's luck), but over many children the ratio holds, just like flipping coins.

Alleles, genotype, phenotype and the square

Student level — the core equations

The vocabulary first. A gene can exist as different versions called alleles, and you carry two of each (one per parent). Your genotype is the pair you have (AA, Aa or aa); your phenotype is the trait that actually shows. A dominant allele (A) masks a recessive one (a), so both AA and Aa show the dominant phenotype, while only aa shows the recessive. AA and aa are homozygous; Aa is heterozygous - a carrier.

Meiosis splits the pair, so each parent passes just one allele, chosen at random - Mendel's law of segregation. The Punnett square is simply a table of that randomness: one parent's two alleles as columns, the other's as rows, and each of the four cells an equally likely offspring genotype. Count them up for the predicted ratios.

The signature crosses: Aa × Aa gives a 1:2:1 genotype ratio (AA:Aa:aa) and a 3:1 phenotype ratio (dominant:recessive). A test cross against a recessive (Aa × aa) gives 1:1 - which is how you reveal whether a dominant-looking individual is AA or Aa. Traits on two different genes assort independently (Mendel's second law), giving the famous 9:3:3:1 of a dihybrid cross.

Beyond simple dominance

Scholar level — full mathematical depth

01When one gene isn't the whole story

Incomplete dominance (the heterozygote is a blend, like a pink flower), codominance (both alleles show at once, like AB blood type) and multiple alleles (the ABO gene has three in the population) all break the neat dominant/recessive picture - while still obeying the same segregation of alleles into gametes.

02Linkage and recombination

Genes sitting close together on the same chromosome tend to be inherited together - linked - violating independent assortment, unless crossing over separates them. How often that separation happens measures the distance between the genes, which is exactly how the first genetic maps were drawn.

03Sex linkage and pedigrees

Genes on the X chromosome (colour blindness, haemophilia) show different patterns in males and females, because males have only one X. Pedigree analysis applies the same Punnett logic across a family tree to trace, and predict, inherited conditions.

04From ratios to populations

The Hardy-Weinberg principle scales Mendel up from one cross to an entire population, predicting allele and genotype frequencies through \(p^2 + 2pq + q^2 = 1\). It is the "nothing is changing" baseline against which real evolution - selection, drift, migration - is detected.