How Test Crosses Reveal an Unknown Genotype

A dominant phenotype can hide two genotypes

Under complete dominance, an organism with a dominant phenotype may be homozygous dominant ($AA$) or heterozygous ($Aa$). Phenotype alone cannot distinguish the two because one dominant allele is enough to produce the visible trait.

A test cross pairs that unknown organism with a homozygous recessive organism ($aa$). The recessive parent contributes only $a$, so each offspring's phenotype reveals which allele came from the unknown parent.

The two hypotheses predict different offspring

If the unknown parent is $AA$,

$$AA\times aa\longrightarrow100\%\ Aa,$$

so every offspring is expected to express the dominant phenotype.

If the unknown parent is $Aa$,

$$Aa\times aa\longrightarrow\frac12Aa+\frac12aa,$$

so dominant and recessive phenotypes are expected in a 1:1 ratio.

For example, suppose black fur ($B$) is completely dominant to white fur ($b$). Crossing an unknown black animal with a white $bb$ animal creates a test cross. A white offspring must be $bb$, proving that the black parent supplied $b$ and was therefore $Bb$.

Absence of a recessive offspring is probabilistic evidence

A recessive offspring is decisive evidence for heterozygosity under the model, but an all-dominant sample does not prove homozygosity with certainty. If the unknown parent is actually heterozygous, the probability that $N$ independent offspring all show the dominant phenotype is

$$\left(\frac12\right)^N.$$

Six all-dominant offspring would occur with probability $1/64$ under the heterozygous hypothesis. More offspring make an all-dominant result stronger evidence for $AA$, while never turning a finite sample into logical certainty.

Check whether the Mendelian model applies

The simple 1:1 prediction assumes a single autosomal gene, complete dominance, equal allele segregation, random fertilization, and no genotype-dependent survival. Incomplete dominance, codominance, linked loci, segregation distortion, or viability effects can change the observed pattern.

Test crosses are controlled breeding tools for suitable organisms. Human genotype inference instead relies on family pedigrees, molecular testing, and population evidence rather than experimental mating.