Each parent is heterozygous (Aa) for one gene. Both make two kinds of gamete, A and a, so the 2×2 square gives a 1:2:1 genotype ratio and, because A is dominant, a 3:1 phenotype ratio.
Cross a pure-breeding round-seeded pea with a pure-breeding wrinkled-seeded one and the whole first generation is round — the wrinkled trait seems to vanish. Let those round offspring breed with each other and wrinkled seeds reappear, in about one of every four plants. That reliable reappearance is the puzzle Gregor Mendel solved in the 1860s: traits are carried by discrete “factors” (we now call them genes) that come in versions called alleles, and they do not blend — they hide and resurface.
Seed shape is one gene with two alleles: $R$ (round, dominant) and $r$ (wrinkled, recessive). Each plant carries two alleles — its genotype is $RR$, $Rr$, or $rr$ — but shows only one phenotype, round unless it is $rr$. By the law of segregation, the two alleles separate when gametes form, so an $Rr$ plant makes two kinds of gamete, half $R$ and half $r$. Those gamete probabilities are exactly what the Punnett square lists along its edges.
Each box of the square is one equally likely fertilization, so the offspring odds are just the fraction of boxes of each kind. For $Rr \times Rr$ the four boxes give genotypes $1\,RR : 2\,Rr : 1\,rr$, and since $R$ is dominant the phenotype ratio is $3:1$ — in probability terms, $P(\text{round}) = \tfrac{3}{4}$. Add a second, independent gene (seed color, $Y$ yellow dominant, $y$ green) and the law of independent assortment lets each gene run its own $3:1$. Multiply them: $\tfrac{3}{4}\times\tfrac{3}{4}=\tfrac{9}{16}$ show both dominants, and the full dihybrid ratio is $9:3:3:1$.
Start on 1 gene with the Aa × Aa preset and confirm the $3:1$ phenotype, $1:2:1$ genotype split. Switch Parent 2 to $aa$ for a test cross and watch it become $1:1$ — that is how you expose a hidden recessive. Set one parent to $AA$ and see every box turn dominant. Finally press 2 genes (dihybrid) with both parents $RrYy$: the square grows to $16$ boxes and the bar chart snaps to the $9:3:3:1$ pattern. Toggle Label boxes with phenotype to see how four genotype groups collapse into the colored classes.
| Step | What happens |
|---|---|
| 1. Genotypes | Each parent has two alleles per gene, e.g. $Rr$. You set these with the dropdowns. |
| 2. Segregation | The two alleles separate into gametes. $Rr$ makes $\tfrac12 R$ and $\tfrac12 r$; $RR$ makes only $R$. These become the row and column headers. |
| 3. Assortment | For two genes, each gamete gets one allele of each gene independently, so $RrYy$ makes four gamete types: $RY,\,Ry,\,rY,\,ry$. |
| 4. Fertilization | Every box unites one gamete from each parent into an offspring genotype, sorted dominant-first ($Rr$, not $rR$). |
| 5. Counting | Each box is equally likely, so the fraction of boxes of each genotype is its probability; grouping by dominance gives the phenotype ratio. |
A monohybrid cross follows a single gene. The signature result is the $Rr \times Rr$ cross: a $2\times2$ square of four boxes holding $RR$, $Rr$, $Rr$, $rr$. The genotype ratio is $1:2:1$, but because the dominant allele masks the recessive one in three of the four boxes, the phenotype ratio is $3:1$. Change the parents and the pattern changes predictably: $RR \times rr$ gives all $Rr$ (all dominant); $Rr \times rr$ — the test cross — gives $1:1$, the tell-tale sign that the dominant parent was carrying a hidden recessive allele.
A dihybrid cross tracks two genes that assort independently. With both parents $RrYy$, each makes four equally likely gametes, so the square is $4\times4 = 16$ boxes. Counting phenotypes gives $9$ round-yellow, $3$ round-green, $3$ wrinkled-yellow, and $1$ wrinkled-green — the famous $9:3:3:1$. It is simply two independent $3:1$ ratios multiplied together, which is why the product rule of probability ($P(A \text{ and } B) = P(A)\times P(B)$) is the fastest way to predict any single class without drawing the whole grid.
Mendel chose pea traits that happen to be controlled by single genes with clean dominance, which is why his ratios are so crisp. The same logic predicts single-gene human traits and genetic conditions such as cystic fibrosis (recessive) or Huntington’s disease (dominant). But many traits add complications — incomplete dominance (a blended heterozygote, so the phenotype ratio equals the $1:2:1$ genotype ratio), codominance (both alleles show, as in human AB blood), polygenic traits like height, sex linkage, and environmental effects. Mendel’s laws are the foundation everything else builds on.
A Punnett square is a grid that predicts the possible genotypes of offspring from a cross. You write one parent’s gametes (each carrying one allele per gene) across the top and the other parent’s gametes down the side, then fill each inner box by combining the allele from its column with the one from its row. Because every box is equally likely, counting the boxes of each genotype or phenotype gives the expected ratio. A heterozygous cross, Aa × Aa, yields one AA, two Aa, and one aa — a 1:2:1 genotype ratio and a 3:1 phenotype ratio. It is named after Reginald Punnett.
Key takeaway: list each parent’s gametes on the two sides, fill every box with the combined alleles, and count the boxes to get the probability of each genotype and phenotype.The genotype is the set of alleles an organism carries, written as AA, Aa, or aa. The phenotype is the observable trait, such as round seeds or purple flowers. They differ because of dominance: a dominant allele masks a recessive one, so AA and Aa look identical and only aa shows the recessive trait. That is exactly why a heterozygous cross gives a 1:2:1 genotype ratio but a 3:1 phenotype ratio — the genotype is the instruction, the phenotype is the result after dominance acts.
Key takeaway: genotype is the allele combination; phenotype is the visible trait, and because dominance hides recessives two genotypes can share one phenotype.It states that each organism carries two alleles per gene, one from each parent, and that these two alleles separate during gamete formation so each gamete gets only one. At fertilization two gametes fuse and the offspring again has two alleles. This is why an Aa parent makes two equally common gametes, A and a, and why alleles line up one at a time along the edges of a Punnett square. Mendel deduced it from pea crosses in the 1860s; we now know it reflects the separation of homologous chromosomes during meiosis.
Key takeaway: the two alleles of a gene separate during gamete formation so each gamete carries just one, which is why heterozygotes make two equally common gametes.Independent assortment says the alleles of different genes go into gametes independently, so which allele a gamete gets for one gene does not affect what it gets for another (true for genes on different chromosomes). A doubly heterozygous RrYy parent therefore makes four equally likely gametes — RY, Ry, rY, ry — and crossing two of them fills a 16-box square. Counting phenotypes gives nine both-dominant, three and three for the mixed classes, and one both-recessive: 9:3:3:1. It is just two separate 3:1 ratios multiplied, since ¾ × ¾ = 9/16.
Key takeaway: different genes are inherited independently, so a dihybrid cross combines two 3:1 ratios into 9:3:3:1.A test cross finds the unknown genotype of an individual showing a dominant trait, which could be homozygous (AA) or heterozygous (Aa). You cross it with a homozygous recessive (aa) partner, whose genotype is certain. If the unknown is AA, every offspring inherits a dominant allele and all look dominant. If it is Aa, about half the offspring are aa and show the recessive trait, giving a 1:1 ratio. So any recessive offspring reveals a hidden recessive allele in the unknown parent.
Key takeaway: crossing a dominant-looking individual with a homozygous recessive partner tells you, from whether recessive offspring appear, if it was homozygous or heterozygous.Count the boxes and remember dominance. Each Aa parent makes A and a gametes equally, so the 2×2 square holds AA, Aa, Aa, aa — a 1:2:1 genotype ratio. But A is dominant, so AA and both Aa boxes (three of four) all show the dominant phenotype, and only the single aa box shows the recessive one: 3:1. A 1:1 ratio comes from a different cross, the test cross Aa × aa, where half the offspring are Aa and half aa.
Key takeaway: the 1:2:1 genotypes collapse into 3:1 phenotypes because the dominant allele masks the recessive in three of the four boxes.The ratios are probabilities, not guarantees — expected proportions over many offspring, like a coin landing heads half the time. A small family can stray from 3:1 by chance; the ratio shows up clearly only with large numbers. Many traits also break simple dominance: incomplete dominance gives an intermediate heterozygote (pink from red and white) and a 1:2:1 phenotype ratio; codominance shows both alleles (AB blood); polygenic traits like height involve many genes; and the environment, sex linkage, and gene interactions add further layers. Mendel’s laws are the foundation, not the whole story.
Key takeaway: Punnett ratios are expected probabilities seen clearly only with many offspring, and real inheritance often adds incomplete dominance, codominance, polygenic effects, and environment.