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Beyond Mendelian inheritance: exceptions and polygenic traits

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Table of contents
  1. What Mendel’s model gets right
  2. Is Mendel oversimplified? The teaching debate
  3. The exceptions, one by one
  4. Incomplete dominance and codominance
  5. Multiple alleles
  6. Sex linkage
  7. Lethal alleles
  8. Epistasis
  9. Linked genes
  10. Genomic imprinting, mitochondria and epigenetics
  11. Incomplete penetrance and environment
  12. Polygenic traits: why height isn’t a Punnett square
  13. Polygenic inheritance Punnett square
  14. Common questions
  15. Is eye color or height controlled by one gene?
  16. Do the exceptions mean Mendel was wrong?
  17. What ratio does incomplete dominance give?
  18. What does every Mendelian ratio assume?
  19. Practice
  20. Related
  21. Sources

Level: High school to college · You’ll need: monohybrid and dihybrid crosses, plus genotype vs phenotype

Mendelian inheritance is the simple model you meet first: one gene, two alleles, one fully dominant over the other, giving tidy ratios like 3:1 and 9:3:3:1. It’s a great model, and it’s still the right place to start. But most real traits don’t follow it exactly. This page walks through the main exceptions, shows what each one does to a Punnett square, and ends with how a polygenic inheritance Punnett square works.

What Mendel’s model gets right

Two of Mendel’s ideas hold up for almost all nuclear genes in sexually reproducing organisms like us (mitochondrial DNA is one exception, covered below):

  • Segregation. Each parent passes on one of its two copies of a gene, at random.
  • Alleles are units. They don’t blend. A pink flower from red and white parents can still have red and white grandchildren.

A third idea, independent assortment, holds for genes on different chromosomes, but not for genes close together on the same chromosome (see linked genes below).

What the simple model adds on top, and where it often breaks, is the link between genotype and trait. It assumes one gene controls one trait, one allele completely hides the other, and the environment doesn’t matter.

Is Mendel oversimplified? The teaching debate

Some geneticists and educators argue that schools lean on the simple model too heavily. In a 2025 paper titled “Teaching School Genetics in the 2020s: Why ‘Naive’ Mendelian Genetics Has to Go,” Kostas Kampourakis of the University of Geneva argues that school genetics often:

  • presents Mendel’s work in a stereotyped way that misrepresents his findings and their historical context,
  • teaches that alleles directly control traits, which is rarely true, and
  • leaves out development and environment, the processes through which genes actually shape an organism.

He also points out a historical warning: oversimplified “one gene, one trait” thinking was used in the early twentieth century to give eugenics a false scientific basis. Earlier, Michael Dougherty (then at the American Society of Human Genetics) proposed inverting the curriculum, teaching complex traits first and Mendel later.

Others defend starting with Mendel because single-gene crosses make probability and meiosis concrete. CrossCalc’s approach sits in between: use the simple model as a model, state its assumptions every time, and show where it stops. That’s what the rest of this page does.

The exceptions, one by one

PatternWhat’s differentEffect on a Punnett squareClassic example
Incomplete dominanceHeterozygote is in betweenAa × Aa gives 1:2:1 phenotypes, not 3:1Red × white snapdragons → pink
CodominanceBoth alleles show fullyHeterozygote shows both traitsMN blood group; AB blood type
Multiple allelesMore than two alleles exist in the populationSame square, more genotype optionsABO blood type (Iᴬ, Iᴮ, i)
Sex linkageGene on the X chromosomeRatios differ for sons and daughtersFruit fly white eyes; calico cats
Lethal allelesOne genotype doesn’t surviveAa × Aa gives 2:1 among survivorsYellow coat in mice
EpistasisOne gene masks another9:3:3:1 becomes, e.g., 9:3:4Mouse coat color and albinism
Linked genesGenes close on one chromosomeParental combinations too commonFruit fly body color and wing size
Polygenic traitsMany genes each add a littleMany classes, a bell-shaped spreadHeight, skin color, eye color
Genomic imprintingEffect depends on the parent of originReciprocal crosses differSome mouse and human growth genes
Mitochondrial inheritanceDNA in mitochondria, from the eggPassed from mother to all childrenMitochondrial DNA variants
Incomplete penetranceNot everyone with the genotype shows the traitPredicted phenotype doesn’t always appearSome inherited cancer risk variants
Gene–environment interactionEnvironment changes the traitSame genotype, different phenotypeSiamese cat points (heat-sensitive enzyme)

Incomplete dominance and codominance

With incomplete dominance, the heterozygote looks in between. Cross two pink snapdragons (Rr × Rr) and you get ¼ red, ½ pink and ¼ white. The genotype ratio and the phenotype ratio are the same (1:2:1), because every genotype looks different.

With codominance, the heterozygote shows both alleles at full strength. A person with blood type AB makes both A and B antigens. Neither is hidden.

Multiple alleles

A person has only two copies of a gene, but a population can have many alleles. The ABO blood group has three main alleles: Iᴬ and Iᴮ are codominant with each other, and both are dominant to i. That gives six genotypes and four blood types.

Sex linkage

Genes on the X chromosome are inherited differently by sons and daughters, because males (XY) have one X and females (XX) have two. A recessive X-linked allele shows up in a son whenever he inherits it from his mother. Calico and tortoiseshell cats are a colorful example. Try it in the cat coat color calculator.

Lethal alleles

If one genotype doesn’t survive, it disappears from the counts. In mice, the yellow coat allele is dominant for color but lethal when homozygous. Yellow × yellow gives 2 yellow : 1 non-yellow among the pups that are born, instead of 3:1.

Epistasis

In epistasis, one gene affects whether another gene’s effect can be seen. In mice, one gene controls agouti vs solid-colored fur, but a second gene can block pigment altogether (albino). A double heterozygote cross gives 9 agouti : 3 solid color : 4 albino. That’s still 16 boxes; the last two classes of 9:3:3:1 merge because albino hides the color gene.

Linked genes

Genes close together on the same chromosome tend to be inherited together. They only separate when crossing over happens between them during meiosis. A dihybrid test cross of linked genes gives too many offspring with the parents’ combinations and too few recombinants, instead of 1:1:1:1. The dihybrid calculator assumes unlinked genes.

Genomic imprinting, mitochondria and epigenetics

In genomic imprinting, a gene copy is switched on or off depending on whether it came from the mother or the father. Mitochondrial DNA is passed on only through the egg, so it follows the mother’s line. And some epigenetic marks, such as DNA methylation, can affect gene activity without changing the DNA sequence. A 2026 mouse study found about 7% of inherited methylation patterns didn’t follow Mendel. See what that study did and didn’t show. Whether epigenetic changes are passed down over many generations in mammals is still debated.

Incomplete penetrance and environment

Even for a single gene, the genotype doesn’t always fix the trait. Penetrance is the share of individuals with a genotype who actually show the trait. Expressivity is how strongly it shows. And the environment can change the result: in Siamese cats, the enzyme for dark pigment works only in cooler parts of the body, so the ears, face, paws and tail are darker.

Polygenic traits: why height isn’t a Punnett square

A polygenic trait is affected by many genes, each with a small effect, plus the environment. Human height is a good example. A 2022 study of 5.4 million people found about 12,000 common genetic variants associated with height. Eye color is also polygenic: two blue-eyed parents can, uncommonly, have a brown-eyed child.

That’s why you can’t predict a child’s height, eye color or skin color with a single-gene Punnett square. But you can use a Punnett square to see why polygenic traits form a smooth, bell-shaped range.

Polygenic inheritance Punnett square

Here’s the classroom additive model. It’s a simplification, labeled as one.

Assumptions: three unlinked genes (A, B, C); each capital allele adds one unit to the trait; lowercase alleles add nothing; no dominance, no environment.

Cross two triple heterozygotes: AaBbCc × AaBbCc. Each parent makes 8 gametes, so the full square has 8 × 8 = 64 boxes. Instead of tracking 27 genotypes, count how many capital alleles each offspring has (0 to 6):

Capital alleles0123456
Boxes out of 641615201561
Probability1.6%9.4%23.4%31.3%23.4%9.4%1.6%

(Percentages are rounded, so they add to slightly over 100%.) That gives a 1:6:15:20:15:6:1 ratio: seven phenotype classes, most offspring in the middle, few at the extremes. With two genes the pattern is 1:4:6:4:1 (16 boxes); with more genes the classes multiply and the shape gets smoother. Add environmental effects and the steps blur into a continuous curve, like the spread of heights in a population.

Shortcut: each of the 6 alleles an offspring receives is capital with probability ½, so the counts are the binomial coefficients for 6 (row 6 of Pascal’s triangle). You can see the 64 boxes in the trihybrid cross calculator with AaBbCc for both parents. Its phenotype classes use dominance, not the additive model, so group the genotypes by capital-letter count yourself.

Common questions

Is eye color or height controlled by one gene?

No. Both are polygenic. Many classroom single-gene examples for human traits (eye color, tongue rolling, earlobes) are myths, though a few, like ABO blood type, really are single-gene.

Do the exceptions mean Mendel was wrong?

No. Segregation still happens. The exceptions are about how genotypes turn into traits, and about genes that aren’t independent.

What ratio does incomplete dominance give?

1:2:1, not 3:1. If heterozygotes look different from both homozygotes, the phenotype ratio matches the genotype ratio.

What does every Mendelian ratio assume?

Many offspring and no linkage, lethality or environmental effect, unless the problem says otherwise.

Practice

  1. Pink snapdragons (Rr) are crossed. What fraction of offspring are pink?
  2. Using the additive model with two genes, AaBb × AaBb: what’s the chance an offspring has exactly 2 capital alleles?
  3. Yellow mice (Yy) are crossed with each other. Out of 90 pups born, about how many are yellow?
  4. A dihybrid test cross gives 45 : 5 : 5 : 45. What explains this instead of 1:1:1:1?
Answers
  1. ½ (1 red : 2 pink : 1 white).
  2. 6/16 = ⅜ (the 1:4:6:4:1 pattern).
  3. About 60. YY doesn’t survive, so the born pups are 2 yellow : 1 non-yellow.
  4. Linked genes. The two common classes are the parental combinations; the rare ones are recombinants from crossing over (10 out of 100, so about 10% recombination).

Sources

Try it: check any cross instantly with the dihybrid cross calculator, or use the monohybrid and trihybrid versions.