Mendelian Genetics & Punnett Squares

What is Mendelian Genetics?

Discovered in the 1860s by an Austrian monk named Gregor Mendel (who spent years meticulously counting peas in his garden), Mendelian Genetics describes the fundamental laws of how biological traits are passed down from parents to offspring.

Before Mendel, scientists believed traits simply "blended" like paint (red + white = pink forever). Mendel proved that traits are actually inherited as discrete, distinct packages of information, which we now call genes.

Learning Goals: By the end of this guide, you should be able to:

Distinguish between genotype and phenotype.

Understand dominant versus recessive alleles.

Construct and interpret a Punnett Square for a monohybrid cross.

Calculate predicted probability ratios for offspring.

The Genetic Glossary

Before solving crosses, you absolutely must lock down this vocabulary:

Gene: A section of DNA that codes for a specific trait (e.g., eye colour).
Allele: A specific version of a gene (e.g., the allele for brown eyes vs the allele for blue eyes).
Genotype: The actual genetic makeup of an organism, represented by letters (e.g., $Bb$ ). Every person has two alleles for each gene (one from mom, one from dad).
Phenotype: The physical expression or visible trait resulting from the genotype (e.g., actually having Brown eyes).
Homozygous: Having two identical alleles ( $BB$ or $bb$ ).
Heterozygous: Having two different alleles ( $Bb$ ).

Dominant and Recessive Rules

Mendel noticed that some alleles are "stronger" than others.

A Dominant Allele (always written as a capital letter, like $B$ ) will always mask the effect of a weaker allele. If a dominant allele is present, it wins and dictates the phenotype.
A Recessive Allele (written as a lowercase letter, like $b$ ) is hidden whenever a dominant allele is around. The recessive phenotype only shows up if the organism has two recessive alleles ( $bb$ ).

The Punnett Square: Predicting the Future

A Punnett Square is a simple grid tool used to predict the mathematical probability of an offspring inheriting a particular genotype.

How to Build a Monohybrid Cross (One Trait)

Scenario: We are crossing a heterozygous tall pea plant ( $Tt$ ) with a homozygous short pea plant ( $tt$ ). Let $T$ = Tall (Dominant), $t$ = Short (Recessive).

Step 1: Find the Gametes (Sperm & Egg) According to Mendel's Law of Segregation, during meiosis (making sperm or eggs), the two alleles separate.

Parent 1 ( $Tt$ ) can give either a $T$ sperm or a $t$ sperm.
Parent 2 ( $tt$ ) can ONLY give a $t$ egg.

Step 2: Set up the Grid Write Parent 1's possible gametes across the top. Write Parent 2's possible gametes down the left side.

	$T$	$t$
$t$
$t$

Step 3: Fill in the Boxes Drag the letters down from the top and across from the left to fill each empty box. Always write the capital letter first!

	$T$	$t$
$t$	$Tt$	$tt$
$t$	$Tt$	$tt$

Step 4: Calculate the Ratios Looking at the 4 inner outcome boxes:

Genotypic Ratio: 2 $Tt$ (Heterozygous) : 2 $tt$ (Homozygous Recessive). Simplified to $1:1$ .
Phenotypic Ratio: 2 Tall plants : 2 Short plants. Simplified to $1:1$ (or $50\%$ chance tall, $50\%$ chance short).

Worked Examples

Example 1: The standard Heterozygous Cross

Question: Cross two heterozygous Brown-eyed parents ( $Bb \times Bb$ ). ( $B$ = Brown, $b$ = Blue). What is the chance they have a blue-eyed child?

The Punnett Square:

	$B$	$b$
$B$	$BB$	$Bb$
$b$	$Bb$	$bb$

Analysis:

Genotypes: 1 $BB$ : 2 $Bb$ : 1 $bb$ (The classic $1:2:1$ ratio)
Phenotypes: 3 Brown : 1 Blue (The classic $3:1$ ratio)
Answer: There is a 1 in 4 ( $25\%$ ) probability of having a blue-eyed child.

Example 2: The Test Cross

Question: You have a Black dog (Black is dominant, $B$ ), but you don't know if it is $BB$ or $Bb$ . How do you find out? Answer: Perform a Test Cross. You breed the mystery dog with a dog that is homozygous recessive (Brown, $bb$ ).

If the mystery dog is $BB$ : All puppies ( $100\%$ ) will be $Bb$ (Black).
If the mystery dog is $Bb$ : Half the puppies ( $50\%$ ) will be $bb$ (Brown). If even one puppy is born brown, you instantly know the parent was heterozygous!

Common Mistakes

Mixing up Genotype and Phenotype ratios — If asked for the Phenotypic ratio of a $Bb \times Bb$ cross, the answer is $3:1$ , not $1:2:1$ . Read the question carefully!
Assuming "Dominant" means "More Common" — Dominance only refers to which allele wins out in a heterozygote. It does not mean the allele is more common in the wild. For example, the allele for Huntington's disease (a rare, fatal condition) or having six fingers (Polydactyly) is dominant, while holding five fingers is recessive!
Misinterpreting probability — If a Punnett square shows a $25\%$ chance for a blue-eyed child, and the parents have four children, it does NOT mean exactly one must have blue eyes. Each child is an independent coin flip. They could have four blue-eyed children, or zero.

Exam Tips (A-Level / AP / IB)

Define your alleles immediately! At the very top of your exam paper, write " $A$ = Green, $a$ = Yellow". Do not try to hold this in your head, you will confuse yourself halfway through a complex cross.
Always write Capitol letters first — Write $Aa$ , never $aA$ . It makes spotting matching genotypes much easier and prevents counting errors.
In dihybrid crosses (two traits, $AaBb \times AaBb$ ), remember the sacred phenotypic ratio of a double-heterozygote cross: $9:3:3:1$ .

Frequently Asked Questions

What happens if neither allele is dominant?

That breaks classic Mendelian rules! It relies on Incomplete Dominance (red flower + white flower = pink flower) or Codominance (both alleles fight to be fully seen, e.g., a cow with both brown and white spots, or human AB blood type).

Are traits always controlled by just one gene?

Very rarely! Traits like human height, skin colour, or intelligence are Polygenic, meaning they are controlled by the complex addition of dozens or hundreds of different genes interacting together.

Pedigree Logic — Use family tree charts to work backward and deduce the genotypes of ancestors.
Hardy-Weinberg Principle — Take Punnett Squares and apply them to the statistical evolution of entire populations over time.
Meiosis — The underlying cellular division mechanism that causes Mendel's Law of Segregation.