Use the rules of inheritance, including dominant and recessive alleles, genotype and phenotype, and Punnett squares, to predict the probability of traits in offspring and apply statistical reasoning to genetic crosses (MA STE HS-LS3-3, using mathematics).

What this topic is asking

The Massachusetts STE framework (HS-LS3-3) asks you to apply probability to explain the variation and distribution of traits in offspring. On the High School Biology MCAS, this is the most mathematical biology topic: you set up a Punnett square, read off a ratio, and convert it to a probability. The crosscutting concept is cause and effect (alleles cause traits), and the science practice is using mathematics and computational thinking.

Alleles, genotype, and phenotype

An organism has two alleles for each gene, one from each parent (delivered by the gametes meiosis makes). The combination of alleles is the genotype, and it can be:

• Homozygous dominant ($TT$): two dominant alleles.
• Heterozygous ($Tt$): one of each. The dominant trait shows.
• Homozygous recessive ($tt$): two recessive alleles. The recessive trait shows.

So $TT$ and $Tt$ both give the tall phenotype, while only $tt$ gives the short phenotype. This is why a recessive trait can skip a generation and reappear.

Using a Punnett square

A Punnett square is a grid that predicts the offspring of a cross. Put one parent's possible gametes along the top and the other parent's down the side, then fill each cell with the combined alleles. For a cross of two heterozygous tall pea plants, $Tt \times Tt$:

The four cells are $TT$, $Tt$, $Tt$, $tt$. Reading the phenotypes: three plants are tall ($TT$, $Tt$, $Tt$) and one is short ($tt$), a $3:1$ ratio. Reading the genotypes: $1\,TT : 2\,Tt : 1\,tt$.

Ratios are probabilities

Here is the statistical idea the MCAS rewards. A Punnett-square ratio is a probability, not a promise. A $3:1$ phenotype ratio means each offspring has a $\frac{3}{4}$ chance of showing the dominant trait and a $\frac{1}{4}$ chance of showing the recessive trait. With a large number of offspring the actual proportions get close to the prediction, but with only a few offspring, chance can push the real numbers away from the ratio, just as flipping a coin eight times rarely gives exactly four heads. When a question gives a small sample that does not match the expected ratio, the explanation is almost always that ratios are probabilities and small samples vary.

Try this

Q1. State the difference between genotype and phenotype. [2]

• Cue. Genotype is the alleles an organism carries (such as $Tt$); phenotype is the observable trait that results (such as tall).

Q2. A cross of two heterozygotes ($Aa \times Aa$) is carried out. State the expected phenotype ratio and the probability of a recessive offspring. [2]

• Cue. Ratio $3:1$ (dominant to recessive); probability of a recessive ($aa$) offspring is $\frac{1}{4}$.