Solve monohybrid crosses with Punnett squares

Core Concepts (the 20% that explains 80%)

HOW to build a Punnett square — derivation from first principles

We rely on Mendel's Law of Segregation: the two alleles of a gene separate during gamete formation, so each gamete gets exactly one.

Step-by-step method:

Write each parent's genotype.
List the possible gametes (split the pair) for each parent.
Draw a grid: one parent's gametes label the columns, the other's the rows.
Fill each cell by combining the column allele + row allele.
Count genotype ratios, then convert to phenotype ratios using dominance.

Formula Why the ratios come out as they do

For a cross $Aa \times Aa$ , each parent gives $A$ with probability $\tfrac12$ and $a$ with probability $\tfrac12$ . By the product rule (independent events) and sum rule: $P(AA)=\tfrac12\cdot\tfrac12=\tfrac14,\quad P(aa)=\tfrac14$ $P(Aa)=\underbrace{\tfrac12\cdot\tfrac12}_{A\,\text{from dad},\,a\,\text{mom}}+\underbrace{\tfrac12\cdot\tfrac12}_{a\,\text{dad},\,A\,\text{mom}}=\tfrac12$ Genotype ratio $= 1\,AA : 2\,Aa : 1\,aa$ . Since $A$ is dominant, $AA$ and $Aa$ look alike: $\text{Phenotype ratio}=3\ \text{dominant} : 1\ \text{recessive}$ The Punnett square is this probability calculation drawn as a 2×2 grid (4 equally likely cells).

Figure — Solve monohybrid crosses with Punnett squares

Worked Examples

Worked example Example 1 — Heterozygous × Heterozygous (

$Yy \times Yy$ ) Trait: pea seed color. $Y$ = yellow (dominant), $y$ = green (recessive).

	Y	y
Y	$YY$	$Yy$
y	$Yy$	$yy$

Why split into $Y$ and $y$ ? Segregation: each $Yy$ parent makes half $Y$ gametes, half $y$ .
Why fill cells by combining? Each cell = one fertilization event (one sperm × one egg).
Genotype: $1\,YY : 2\,Yy : 1\,yy$ .
Phenotype: $3$ yellow $: 1$ green. Why? $YY$ and $Yy$ both show yellow.

Worked example Example 3 — Homozygous dominant × homozygous recessive (

$YY \times yy$ , the $F_1$ )

	Y	Y
y	$Yy$	$Yy$
y	$Yy$	$Yy$

Why are all offspring $Yy$ ? One parent can only give $Y$ , the other only $y$ .
Phenotype: $100\%$ yellow. This is the uniform $F_1$ generation. Crossing two of these $F_1$ gives back the $3{:}1$ of Example 1.

Forecast-then-Verify

Recall Predict before you compute

A pure-breeding tall plant ( $TT$ ) is crossed with a short plant ( $tt$ ). The $F_1$ is self-crossed. Forecast: What phenotype ratio in $F_2$ ? Verify: $F_1 = Tt$ . $Tt \times Tt \Rightarrow 1\,TT:2\,Tt:1\,tt \Rightarrow$ 3 tall : 1 short. ✓

Common Mistakes (Steel-manned)

Flashcards

What does a monohybrid cross study?

Inheritance of a single gene/trait across generations.

State Mendel's Law of Segregation.

The two alleles of a gene separate during gamete formation; each gamete receives exactly one allele.

Genotype ratio of

Aa \times Aa

1\,AA : 2\,Aa : 1\,aa

Phenotype ratio of

Aa \times Aa

(complete dominance)?

3 dominant : 1 recessive.

Why is

Aa

phenotype identical to

AA

One dominant allele produces enough functional product to show the dominant trait.

What is a test cross and why use

aa

Crossing an unknown dominant with homozygous recessive (

aa

); offspring phenotypes directly reveal the unknown's gametes.

Phenotype ratio of test cross

Aa \times aa

1 dominant : 1 recessive.

Result of

AA \times aa

All offspring

Aa

→ 100% dominant phenotype (

F_1

uniform).

Each cell in a 2×2 Punnett square represents what probability?

\tfrac14

(equally likely fertilization outcome).

Difference between genotype and phenotype?

Genotype = allele pair (e.g.,

Yy

); phenotype = observable trait (e.g., yellow).

How many gamete types does a homozygote produce?

One.

How many gamete types does a heterozygote produce?

Two (each ~50%).

Recall Feynman: explain to a 12-year-old

Imagine each parent has two "trait cards" but can only hand ONE card to a baby. Dad shuffles his two cards and gives one; Mom does the same. The Punnett square is a tiny table listing every way Dad's card can meet Mom's card. Some cards are "loud" (dominant) — if a baby gets even one loud card, that's what you see. A "quiet" (recessive) trait only appears when the baby gets two quiet cards. Count the boxes, and you can predict how the babies will probably look!

Connections

Mendel's Law of Segregation — the biological basis of why we split alleles.
Law of Independent Assortment — extends this to dihybrid (two-gene) crosses.
Probability rules in genetics — product & sum rules behind the square.
Incomplete dominance and codominance — when $3{:}1$ becomes $1{:}2{:}1$ in phenotype.
Test cross — practical use of monohybrid logic.
Genotype vs Phenotype — core distinction underlying ratio interpretation.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, monohybrid cross ka matlab hai hum sirf ek hi trait (jaise pea ka seed color) ko track kar rahe hain. Har parent ke paas us gene ke do allele hote hain, lekin Law of Segregation ke according har parent apne baby ko sirf ek allele deta hai. Punnett square bas ek chhoti si table hai jisme hum dad ke possible gametes ko upar (columns) aur mom ke gametes ko side me (rows) likhte hain, aur har box me combine karke baby ka genotype nikalte hain.

Sabse important baat: dominant allele (capital letter, jaise $Y$ ) sirf ek copy se hi apna effect dikha deta hai, kyunki wo ek working protein banata hai. Recessive trait ( $yy$ ) tabhi dikhta hai jab dono copies recessive ho. Isiliye $Yy$ bhi yellow dikhta hai, $YY$ ki tarah — ye "paint mixing" jaisa nahi hota, blend nahi hota (complete dominance me).

Classic result yaad rakho: $Yy \times Yy$ karne par genotype ratio aata hai $1\,YY:2\,Yy:1\,yy$ , aur phenotype ratio aata hai 3 yellow : 1 green. Test cross ( $Yy \times yy$ ) me ratio $1:1$ aata hai — ye trick se hum pata kar sakte hain ki koi yellow plant $YY$ hai ya $Yy$ . Exam me dhyan rakho: genotype ratio aur phenotype ratio alag-alag cheez hain, jo question pooche wahi do!

Har box ka probability $\tfrac14$ hota hai. Do boxes me $Yy$ aaya, isliye $Yy$ ka chance $\tfrac24=\tfrac12$ ho gaya. Bas yahi product rule aur sum rule chhupa hua hai Punnett square ke peeche. Samajh gaye toh genetics ke aadhe numericals yahin se ban jayenge!

Test yourself — Mendelian Genetics

Connections