Mendelian Genetics & Punnett Square Calculator

Mendelian Genetics Guide

What do I need to know about Mendel's Laws?

Mendel's First Law (Segregation): each organism carries two alleles for each gene; these separate during gamete formation so each gamete carries only one allele. Mendel's Second Law (Independent Assortment): genes on different chromosomes are inherited independently of each other (dihybrid crosses give 9:3:3:1 phenotype ratio when both parents are AaBb heterozygotes). These laws apply to genes on different chromosomes (unlinked genes) and form the foundation of classical genetics. Linked genes (genes located close together on the same chromosome) are inherited together more often than not, breaking the law of independent assortment — the closer two genes sit on a chromosome, the less likely crossing over is to separate them, which is the basis of genetic linkage mapping.

What's the key thing to understand about The Punnett Square?

A Punnett square systematically shows all possible offspring genotypes. For Aa × Aa: top row A, a (parent 1 gametes); left column A, a (parent 2 gametes). Four cells: AA, Aa, Aa, aa. Genotype ratio: 1AA : 2Aa : 1aa. Phenotype ratio (complete dominance): 3 dominant : 1 recessive. Key cross ratios to memorise: homozygous dominant × homozygous recessive → all Aa (100% dominant phenotype). Aa × Aa → 3:1 phenotype ratio. Aa × aa → 1:1 ratio (test cross — used to determine unknown genotype). Carrier × carrier (Aa × Aa, both unaffected but carrying a recessive allele): 1/4 affected, 1/2 carrier, 1/4 unaffected homozygous dominant — the classic 3:1 phenotype ratio, but with the crucial distinction that two-thirds of the unaffected offspring are themselves carriers, relevant for genetic counselling of recessive conditions like cystic fibrosis.

What should I know about Codominance and Incomplete Dominance?

Codominance: both alleles are fully expressed in the heterozygote. Example: blood group AB (IA and IB alleles both expressed), Ayrshire cattle coat colour (red and white coat both show as roan). Heterozygote shows a different phenotype from both homozygotes. Incomplete dominance: heterozygote shows an intermediate phenotype. Example: red snapdragon × white snapdragon → pink heterozygote (RR red, Rr pink, rr white). Unlike codominance, the individual allele products are not separately visible — the blended appearance arises because both alleles are expressed but neither product alone reaches the concentration needed to produce the full-intensity phenotype — unlike codominance (such as AB blood type, where both A and B antigens are fully and separately visible on red blood cells at once), incomplete dominance produces a genuinely intermediate, merged trait.

What should I know about Genetic Counselling Applications?

Punnett squares are used in genetic counselling to estimate risk of inherited conditions. Autosomal recessive (cystic fibrosis, sickle cell): carrier × carrier → 1/4 risk of affected child, 2/3 of unaffected children are carriers. Autosomal dominant (Huntington's disease): affected (Hh) × unaffected (hh) → 1/2 risk of affected child. X-linked recessive (haemophilia, colour blindness): carrier mother × normal father → sons 1/2 affected, daughters all unaffected (but 1/2 carriers). These are probabilities per pregnancy, not fixed outcomes — each conception is an independent event, so having one affected child doesn't reduce or increase the risk for the next. Genetic counsellors use pedigree analysis alongside these Mendelian ratios to estimate risk and, increasingly, alongside direct genetic testing to confirm carrier or affected status rather than relying on probability alone.

What do I need to know about a Worked Dihybrid Cross?

A dihybrid cross tracks two genes simultaneously, assuming independent assortment. Classic example: pea plants heterozygous for seed shape (Rr, round dominant) and seed colour (Yy, yellow dominant): RrYy x RrYy. Each parent produces four equally likely gamete types: RY, Ry, rY, ry. A full 4x4 Punnett square (16 combinations) gives the classic 9:3:3:1 phenotype ratio: 9/16 round yellow, 3/16 round green, 3/16 wrinkled yellow, 1/16 wrinkled green. This ratio can also be found by multiplying the two independent single-gene ratios: round:wrinkled is 3:1, and yellow:green is 3:1, so combined: (3+1) x (3+1) = 16 total parts, with round-yellow = 3x3=9, round-green = 3x1=3, wrinkled-yellow = 1x3=3, wrinkled-green = 1x1=1, confirming 9:3:3:1 without drawing the full square. This multiplication shortcut (the product rule of probability) extends to trihybrid and higher crosses, where a full Punnett square becomes impractical.

What should I know about Sex-Linked Inheritance?

Genes located on the sex chromosomes follow different inheritance patterns from autosomal genes, because males (XY) have only one X chromosome while females (XX) have two. For an X-linked recessive condition (such as red-green colour blindness or haemophilia), a male needs only one copy of the recessive allele on his single X to be affected, since he has no second X carrying a dominant, masking allele. A female needs two copies to be affected, while a single copy makes her an unaffected carrier. This asymmetry explains why X-linked recessive conditions are far more common in males in a population, and produces a distinctive cross pattern: a carrier mother crossed with an unaffected father gives sons who are 50% affected and 50% unaffected, and daughters who are 50% carriers and 50% unaffected, but no affected daughters from this cross — a pattern geneticists look for when distinguishing X-linked from autosomal inheritance in a pedigree.

What should I know about Pedigree Analysis?

A pedigree chart tracks a trait through a family tree using standard symbols (squares for males, circles for females, filled shapes for affected individuals) and lets geneticists work backward from the pattern of inheritance to the most likely genetic cause. An autosomal recessive condition typically skips generations and can appear in children of two unaffected carrier parents; an autosomal dominant condition usually appears in every generation, with an affected parent having roughly a 50% chance of passing it to each child. X-linked recessive conditions show a distinctive pattern: they affect far more males than females, and are never passed from an affected father to a son (since fathers give sons a Y, not an X, chromosome), while daughters of affected fathers become carriers. Reading these patterns correctly lets genetic counsellors estimate the probability that a specific relative is a carrier, or that a future pregnancy will be affected, turning a family history into a quantitative risk figure that, alongside genetic testing, supports informed reproductive decisions.

What do I need to know about Testing a Cross with Chi-Square Analysis?

Punnett squares predict expected ratios, but real crosses never match those ratios exactly just by chance — the chi-square (χ²) test tells you whether an observed deviation is small enough to be ordinary sampling variation or large enough to suggest something else is going on (linked genes, incomplete penetrance, or a scoring error). χ² = Σ[(Observed − Expected)² ÷ Expected] Worked example: a dihybrid cross expected to follow the classic 9:3:3:1 ratio produces 160 offspring. Expected counts are 90, 30, 30 and 10; observed counts are 85, 32, 33 and 10. (85−90)²/90 = 0.278 (32−30)²/30 = 0.133 (33−30)²/30 = 0.300 (10−10)²/10 = 0.000 χ² = 0.278 + 0.133 + 0.300 + 0.000 = 0.711 With four phenotype classes, degrees of freedom = classes − 1 = 3.

Since 0.711 is far below the critical value of 7.81 for 3 degrees of freedom, the null hypothesis — that the observed data fits a 9:3:3:1 ratio — is not rejected. A χ² value above the critical threshold would instead point toward gene linkage, reduced penetrance, or a classification error worth investigating further. Sample size matters enormously for this test: the same proportional deviation scaled to 1,600 offspring (observed 850:320:330:100 vs expected 900:300:300:100) multiplies χ² by exactly 10, to 7.11 — still (just) below the 7.81 threshold but close enough that a slightly larger sample or a slightly bigger discrepancy would flip the conclusion, a reminder that chi-square results are sensitive to how many offspring were actually counted, not just what fraction fell into each class.

Simple Mendelian vs Polygenic Human Traits

Punnett square predictions work cleanly for traits controlled by a single gene with two clear alleles, but most visible human traits are not actually inherited this simply — a useful distinction when applying Mendelian logic to real family traits.

The classic 'brown eyes are dominant over blue' teaching is a simplification that holds roughly at a population level but fails for many individual families, since several genes contribute to eye colour — a genuine single-gene Mendelian cross like this calculator demonstrates applies cleanly to traits such as blood type, but not to most physical appearance traits people commonly ask about.