3.1 Mendelian principle of inheritance and deviations from the laws

Gregor Mendel, an Austrian monk, worked out the basic rules of inheritance between 1856 and 1863 by crossing garden pea plants (Pisum sativum) and counting the offspring. He showed that characteristics are passed on by separate units, now called genes, which do not blend but keep their identity from one generation to the next. His results, published in 1866 and rediscovered in 1900, are summarised as the law of segregation and the law of independent assortment. Many crosses follow these laws exactly, but others show deviations, which led to the discovery of linkage, codominance, multiple alleles and other patterns. Example: a bean breeding plot at an agricultural training centre in Katumani crosses purple-flowered and white-flowered bean lines and counts the flower colours in the second generation to show trainees Mendel's 3 : 1 ratio.

Why Mendel used the garden pea

• Contrasting traits: Peas show clear pairs of characters, such as tall and dwarf stems, round and wrinkled seeds, yellow and green seeds.
• Self-pollination: The flower normally pollinates itself, so pure-breeding (true-breeding) lines are easy to keep.
• Easy cross-pollination: Anthers can be removed and pollen transferred by hand to make controlled crosses.
• Short life cycle: Several generations can be grown in a few years.
• Many offspring: Each cross gives many seeds, so ratios are reliable.

Key terms

• Gene: A section of DNA on a chromosome that codes for a characteristic.
• Allele: One of the alternative forms of a gene, such as T (tall) and t (dwarf).
• Dominant allele: An allele that shows its effect when present in one copy; written with a capital letter.
• Recessive allele: An allele that shows its effect only when two copies are present; written with a small letter.
• Genotype: The alleles an organism carries, such as TT, Tt or tt.
• Phenotype: The observable characteristic, resulting from genotype and environment, such as tall or dwarf.
• Homozygous: Having two identical alleles (TT or tt); heterozygous means having two different alleles (Tt).
• P, F1 and F2 generations: The parents, their offspring (first filial generation) and the offspring of crossing F1 individuals (second filial generation).

Mendel's first law: law of segregation

Each characteristic is controlled by a pair of factors (alleles). The two alleles separate (segregate) during gamete formation so that each gamete receives only one allele of each pair. At fertilisation, the pairs are restored at random. In meiosis this matches the separation of homologous chromosomes at anaphase I.

When Mendel crossed pure tall (TT) with pure dwarf (tt) peas, all the F1 were tall (Tt). Self-pollinating the F1 gave an F2 of 787 tall to 277 dwarf, close to 3 : 1.

Mendel's second law: law of independent assortment

When two or more pairs of characteristics are inherited together, the alleles of each pair separate independently of the alleles of the other pairs during gamete formation. A plant RrYy therefore forms four kinds of gametes, RY, Ry, rY and ry, in equal numbers. In meiosis this matches the random orientation of different pairs of homologous chromosomes at metaphase I. Mendel's dihybrid cross of round yellow with wrinkled green peas gave an F2 of 315 round yellow, 108 round green, 101 wrinkled yellow and 32 wrinkled green, close to 9 : 3 : 3 : 1.

Law of dominance

Mendel also observed that in a heterozygote one allele (dominant) masks the expression of the other (recessive). This is often listed as a principle of inheritance, but it does not hold for every gene.

Deviations from Mendel's laws

Many inheritance patterns give ratios different from 3 : 1 and 9 : 3 : 3 : 1. They do not overturn Mendel's laws but add to them.

• Incomplete dominance: Neither allele is fully dominant, and the heterozygote is intermediate. In snapdragons (Antirrhinum), red × white gives pink F1, and the F2 is 1 red : 2 pink : 1 white.
• Codominance: Both alleles are fully expressed in the heterozygote. In shorthorn cattle, red × white gives roan offspring with mixed red and white hairs; in humans, the IA and IB alleles both show in blood group AB.
• Multiple alleles: A gene has more than two alleles in the population, though each individual carries only two. The ABO blood group gene has three: IA, IB and i.
• Lethal alleles: An allele that kills the homozygote changes the expected ratio. In yellow mice, crossing two yellow (Yy) mice gives 2 yellow : 1 grey, because YY embryos die.
• Linkage: Genes close together on the same chromosome do not assort independently, so a dihybrid cross gives mainly parental combinations instead of 9 : 3 : 3 : 1.
• Sex linkage: Genes on the X chromosome give different ratios in males and females, as in haemophilia and colour blindness.
• Epistasis: One gene masks or changes the effect of another, giving modified ratios such as 9 : 3 : 4 or 9 : 7.
• Polygenic inheritance: Characteristics such as height, skin colour, milk yield and maize cob length are controlled by many genes, each with a small effect, giving continuous variation instead of distinct classes.
• Environmental influence: The phenotype also depends on the environment; a tall variety grown on poor soil may be short.
• Cytoplasmic (maternal) inheritance: Genes in mitochondria and chloroplasts pass mainly through the egg, so offspring resemble the mother, as in leaf variegation in some plants.

Testing results: the chi-squared test

Observed results rarely match expected ratios exactly. The chi-squared (χ²) test checks whether the difference is small enough to be due to chance.

χ² = Σ (O − E)² ÷ E, where O is the observed number and E the expected number.

Example calculation: Mendel's F2 of 787 tall and 277 dwarf (total 1,064). Expected 3 : 1 gives 798 tall and 266 dwarf.

Tall: (787 − 798)² ÷ 798 = 121 ÷ 798 = 0.152

Dwarf: (277 − 266)² ÷ 266 = 121 ÷ 266 = 0.455

χ² = 0.152 + 0.455 = 0.607

With 1 degree of freedom (number of classes − 1), the critical value at p = 0.05 is 3.84. Since 0.607 is less than 3.84, the difference is due to chance and the results fit a 3 : 1 ratio.