The cases that go beyond Mendel's laws

Mendel's laws describe the simplest case. Most real traits escape them — without contradicting them.

Incomplete dominance

In the four o'clock flower, crossing a red flower with a white one gives pink flowers: neither allele dominates completely.

   R//R  red          R//w  PINK         w//w  white

   F2 :  1 red : 2 pink : 1 white        ratio 1:2:1
         (not 3:1)

The heterozygous phenotype is intermediate. Contrary to 19th-century belief, this is not a permanent "blending" of traits: the F2 brings back pure red and pure white, proving the alleles did not merge.

Codominance: blood groups

Here, both alleles are expressed fully and simultaneously.

   alleles:  A,  B  (codominant with each other)  and  O (recessive)

   genotype        phenotype
   ------------    ---------
   A//A or A//O    group A
   B//B or B//O    group B
   A//B            group AB     <- BOTH are expressed
   O//O            group O

This system also illustrates multiple alleles: the gene exists in three versions in the population, even though each individual carries only two.

A practical consequence: two parents of groups A and B can have children of all four groups, if both are heterozygous.

Sex-linked inheritance

Some genes sit on the X chromosome, of which men have only one copy.

   woman :  X X        two alleles -> a recessive allele can be MASKED
   man   :  X Y        only one    -> any allele on X IS EXPRESSED

Hence a striking asymmetry:

   colour blindness:  about 8 % of men,  0.4 % of women
   haemophilia     :  almost exclusively male

A heterozygous woman is a carrier: she does not have the disease but passes it to half her sons. This mechanism spread haemophilia through European royal families from Queen Victoria onwards.

Polygenic traits

Height, skin colour and weight depend not on one gene but on dozens, each making a small contribution. The result is no longer discrete but continuous:

   MENDELIAN trait             POLYGENIC trait
   two clear categories        a bell-shaped distribution

      ██        ██                     ▁▃▅▇█▇▅▃▁
    purple    white                  short  medium  tall

Here we meet the normal distribution again: a sum of many small independent contributions produces a bell curve. Environment adds to it — nutrition explains a large share of adult height, independently of genes.

What Mendel did not see, and why

incomplete dominance  ->  he studied only traits with clear dominance
codominance           ->  likewise
linked genes          ->  his seven traits happened to be independent
sex linkage           ->  peas have no sex chromosomes
polygeny              ->  he set aside continuous traits as too confusing

These exceptions invalidate nothing: Mendel's laws remain exact within their domain. They describe the transmission of alleles, which always follows meiosis; it is the relations between alleles and phenotype that are richer than he supposed.

Summary

• Incomplete dominance: intermediate heterozygous phenotype, ratio 1:2:1.
• Codominance: both alleles expressed (blood group AB).
• Multiple alleles: more than two versions in the population (A, B, O).
• Sex linkage: a recessive allele on X is always expressed in men (colour blindness, haemophilia).
• Polygenic traits: dozens of genes → continuous, bell-shaped distribution.
• These cases do not invalidate Mendel: allele transmission still follows his laws.