How Mendelian Inheritance Works: Alleles, Crosses and Ratios

Parents pass traits to their children, but the traits do not blend into an average. A pea plant with purple flowers crossed with a white-flowered plant does not produce medium-colored offspring. Instead, the offspring show one form or the other in predictable proportions. Gregor Mendel worked out these proportions in the 1850s and 1860s by breeding garden peas and counting the results in thousands of plants.

This article explains the vocabulary Mendel's work introduced, the two laws that came from it, and how to predict outcomes with Punnett squares.

Key vocabulary

A gene is a unit of heredity that controls a trait. An allele is one of the alternative versions of a gene, such as the allele for purple flowers or the allele for white flowers. An individual carries two alleles for each gene, one from each parent.

The genotype is the pair of alleles an individual carries, written with letters such as AA, Aa or aa. The phenotype is the observable trait that results. An allele is dominant when one copy is enough to produce its trait in a heterozygote, and recessive when it shows only with two copies.

Using these terms, a plant with genotype Aa and a dominant A allele shows the dominant phenotype, even though it also carries a recessive a allele.

Mendel's first law: segregation

The law of segregation states that the two alleles for each gene separate when gametes form, so each egg or sperm carries only one allele for that gene. At fertilization, the two gametes combine to restore a pair.

This explains why a recessive trait can disappear for a generation and then reappear. The recessive allele is still present in heterozygotes, it is simply masked by the dominant allele.

The monohybrid cross

A monohybrid cross follows a single gene. The classic example is a cross between two heterozygotes, Aa × Aa. Each parent produces two types of gametes, A and a, in equal numbers. A Punnett square lists every possible combination.

	A (from parent 2)	a (from parent 2)
A (from parent 1)	AA	Aa
a (from parent 1)	Aa	aa

The result has four equally likely combinations. These give a genotype ratio of 1 AA : 2 Aa : 1 aa. Because AA and Aa both show the dominant trait, the phenotype ratio is 3 dominant : 1 recessive.

The 3 to 1 ratio is what Mendel observed in the seed and flower traits of his pea plants, and it appears in many laboratory and field crosses where one gene controls a clear trait.

The test cross

Sometimes an organism shows the dominant trait, but its genotype is unknown: it could be AA or Aa. A test cross solves this by crossing it with a homozygous recessive individual, aa.

• If the unknown parent is AA, every offspring is Aa and shows the dominant trait.
• If the unknown parent is Aa, half of the offspring are Aa and half are aa, so 1 dominant : 1 recessive appears.

The test cross is a standard tool in plant and animal breeding because it reveals genotype from the offspring's appearance.

Mendel's second law: independent assortment

The law of independent assortment states that alleles of different genes assort independently when gametes form, provided the genes are on different chromosomes. The inheritance of flower color does not influence the inheritance of seed shape, for example.

This law explains why traits recombine in new combinations. A dihybrid cross follows two genes at once, such as AaBb × AaBb. Each parent makes four gamete types in equal numbers: AB, Ab, aB and ab. Combining these produces 16 equally likely outcomes.

Phenotype	Combinations	Count out of 16
A_ B_ (both dominant)	9	9
A_ bb (first dominant, second recessive)	3	3
aa B_ (first recessive, second dominant)	3	3
aa bb (both recessive)	1	1

The 9 : 3 : 3 : 1 phenotype ratio is one of the most recognized patterns in genetics. The underscore symbol means that either allele at that position produces the dominant phenotype.

When the rules bend

Mendel's rules describe an idealized situation, and real inheritance can differ in several ways.

Linked genes. Genes that sit close together on the same chromosome tend to be inherited together. They violate independent assortment because they travel as a unit, except when crossing over separates them. The closer two genes are, the less often crossing over splits them.

Incomplete dominance. In some cases the heterozygote shows an intermediate phenotype. Snapdragon flowers crossed from red and white parents can produce pink offspring, giving a 1 : 2 : 1 phenotype ratio in the F2 generation.

Codominance. Both alleles are fully expressed in the heterozygote. The ABO blood group system is the standard human example: the I^A and I^B alleles are codominant, so an individual with one of each has type AB blood.

Multiple genes and environment. Height, skin color and many common diseases involve several genes plus environmental influences. Simple ratios rarely describe these traits, which is why they are called polygenic or complex.

Why Mendel's approach mattered

Mendel's experiments were careful and quantitative. He controlled crosses, counted offspring and used the results to test specific predictions. His work was published in 1866 but was largely overlooked until the early 1900s, when other researchers rediscovered it and linked his factors to chromosomes.

The modern concept of the gene grew from that synthesis. Today, Mendelian ratios are taught because they are the cleanest examples of how discrete genes produce predictable patterns, and they remain the starting point for analyzing inherited disease in families.

How to use Punnett squares

To solve a cross, first list the genotypes of both parents. Next, write the gametes each parent can produce, with one allele per gamete. Then fill the square by combining each parental gamete with each gamete from the other parent. Finally, count the boxes for each genotype and each phenotype.

For a dihybrid cross, the method is the same, but the square is larger, with 16 boxes instead of four. A simpler shortcut is to solve each gene separately and multiply the results, which works only when the genes assort independently.

Key takeaways

Mendel showed that heredity works through discrete alleles that segregate into gametes, and that different genes assort independently when they sit on separate chromosomes. These rules produce predictable ratios: 3 to 1 for a monohybrid cross and 9 : 3 : 3 : 1 for a dihybrid cross.

Real inheritance sometimes departs from these ratios through linkage, incomplete dominance, codominance and multiple genes. Those departures do not overturn Mendel's framework. They extend it, and they show how genes interact in actual organisms.