Principles of Inheritance and Variation

Gregor Johann Mendel carried out hybridisation experiments on the garden pea, Pisum sativum, for about seven years between 1856 and 1863. People had crossed plants long before him, but their conclusions were vague because they described offspring loosely instead of counting them. Mendel did two things differently. First, he followed one pair of contrasting characters at a time instead of trying to describe the whole plant. Second, he counted every single plant in each generation and expressed the result as a ratio. That switch from description to arithmetic is what made heredity a science.

The choice of the pea plant was not luck. The pea has several features that make it almost ideal for such work. It has many clearly contrasting characters, and Mendel selected seven pairs of them: stem height (tall or dwarf), flower colour (violet or white), flower position (axial or terminal), pod shape (inflated or constricted), pod colour (green or yellow), seed shape (round or wrinkled) and seed colour (yellow or green). Each character has two sharply different forms with nothing in between, so a plant can be sorted into one bin or the other without any judgement call. He also had access to true-breeding varieties, that is, lines that had been self-pollinated over several generations and produced offspring identical to the parent for that character. Starting from true-breeding stock removes all doubt about what the parents were carrying.

The flower of the pea is bisexual and normally self-pollinates, because the petals enclose the reproductive parts before the flower even opens. This means a line stays pure on its own with no effort from the experimenter. At the same time, the flower is large enough to open by hand, so Mendel could remove the immature anthers of one plant (emasculation) and dust pollen from a chosen second plant on its stigma. So the same plant gives him purity when he wants it and controlled crossing when he wants that instead. Add a short life cycle and a large number of seeds per pod, and a single season gives enough plants for the numbers to mean something.

A few words are worth fixing before the crosses. A gene is the unit of inheritance that controls a character; the different forms of that gene are its alleles. If both alleles in an individual are the same, it is homozygous for that gene; if they differ, it is heterozygous. The pair of alleles an individual carries is its genotype; the character we can actually see is its phenotype. Capital letters are used for the allele that expresses itself in the heterozygote and small letters for the one that stays hidden, so a tall pea may be TT or Tt while a dwarf pea can only be tt. Mendel's work went unnoticed in his lifetime and was rediscovered independently in 1900 by de Vries, Correns and von Tschermak, by which time chromosomes had been seen under the microscope and his abstract factors finally had something physical to sit on.

A cross that follows a single pair of contrasting characters is a monohybrid cross. Mendel crossed a true-breeding tall pea plant with a true-breeding dwarf one. The tall parent is TT and the dwarf parent is tt. Each parent makes only one kind of gamete, T from one and t from the other, so every plant of the first filial generation, the F₁, is Tt. Every F₁ plant was tall. The dwarf character had not been destroyed or diluted, because it came back in the next generation.

When the F₁ plants were self-pollinated, the F₂ generation contained both tall and dwarf plants in a ratio of about 3 tall to 1 dwarf. Work out why. A Tt plant makes two kinds of gametes in equal numbers, T and t. Combining male and female gametes at random gives four equally likely combinations: TT, Tt, Tt and tt. Three of these four are tall and one is dwarf, so the phenotypic ratio is 3 : 1. But the underlying genotypic ratio is 1 TT : 2 Tt : 1 tt. The two ratios answer different questions from the same four boxes, so check whether phenotype or genotype is being asked for. The grid used to lay out these combinations, with the gamete types of one parent along the top and of the other parent down the side, is called a Punnett square after Reginald Punnett.

Two laws come out of this. The Law of Dominance says that characters are controlled by discrete units called factors that occur in pairs, and in a dissimilar pair one member dominates and is expressed while the other stays unexpressed. This law explains why the F₁ looked like only one parent and why the 3 : 1 phenotypic ratio hides a 1 : 2 : 1 genotypic ratio. The Law of Segregation, which has no exceptions, says that the two alleles of a pair separate from each other during gamete formation, so that each gamete receives only one of them. The alleles do not blend; a heterozygote produces the two kinds of gametes in equal proportion, each carrying one allele in its pure form. This is why the law is also called the law of purity of gametes.

The two laws create a practical problem. A tall plant may be TT or Tt, and no amount of looking will tell you which. The solution is the test cross: cross the individual of unknown genotype with the homozygous recessive, here a dwarf tt plant. If the unknown is TT, every offspring gets a T from it and a t from the dwarf, so all offspring are Tt and tall. If the unknown is Tt, half the offspring are Tt (tall) and half are tt (dwarf), giving a 1 tall : 1 dwarf ratio. So a single dwarf offspring is enough to prove the unknown parent was heterozygous. Note the difference from a back cross, which simply means crossing the F₁ with either of its parents; a test cross is the particular back cross made with the recessive parent.

Mendel next followed two pairs of characters in the same cross, which is a dihybrid cross. He took seed shape (round R dominant over wrinkled r) together with seed colour (yellow Y dominant over green y). The parents were a true-breeding round-yellow plant, RRYY, and a true-breeding wrinkled-green plant, rryy. The first parent makes only RY gametes and the second only ry gametes, so the whole F₁ is RrYy and every F₁ seed is round and yellow, as expected from dominance.

The interesting generation is the F₂. An RrYy plant produces four kinds of gametes in equal numbers, RY, Ry, rY and ry, because whether a gamete gets R or r has no bearing on whether it gets Y or y. Four gamete types from each side give sixteen equally likely fusion combinations. Sorting those sixteen by appearance gives 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green. Two of these four classes, round green and wrinkled yellow, are combinations that neither grandparent had. New combinations of parental characters have been assembled, and that is the origin of a large part of the variation we see in any population.

Check the 9 : 3 : 3 : 1 against the monohybrid result rather than memorising it. Look at shape alone in the F₂: round seeds number 9 + 3 = 12 and wrinkled seeds number 3 + 1 = 4, which is 3 : 1. Look at colour alone: yellow is 9 + 3 = 12 and green is 3 + 1 = 4, again 3 : 1. Each character on its own behaves exactly as it did in a monohybrid cross, and the dihybrid ratio is just the product of the two, since three quarters times three quarters is nine sixteenths. If you ever forget the ratio you can rebuild it this way in ten seconds. The genotypic breakdown of the same sixteen boxes is 1 RRYY : 2 RRYy : 1 RRyy : 2 RrYY : 4 RrYy : 2 Rryy : 1 rrYY : 2 rrYy : 1 rryy, that is nine genotypes adding up to sixteen.

The conclusion is the Law of Independent Assortment: when two pairs of characters are considered together, the segregation of one pair is independent of the segregation of the other pair. A dihybrid test cross makes the same point even more directly. Crossing the F₁ RrYy with the double recessive rryy gives four kinds of offspring in equal numbers, 1 round yellow : 1 round green : 1 wrinkled yellow : 1 wrinkled green, because the recessive partner contributes nothing that can mask anything, so the offspring simply display the four gamete types of the heterozygote. Keep in mind that this law holds for genes sitting on different chromosomes; genes carried on the same chromosome behave differently, as the section on linkage shows.

Mendel's ratios assume that one allele completely masks the other. In many real cases it does not, and the F₂ phenotypes then depart from 3 : 1 even though the alleles still segregate perfectly.

Incomplete dominance. In the snapdragon or dog flower, Antirrhinum, a cross between a true-breeding red-flowered plant (RR) and a true-breeding white-flowered plant (rr) gives an F₁ that is pink, not red. Selfing this pink F₁ gives an F₂ of 1 red : 2 pink : 1 white. Here the phenotypic ratio 1 : 2 : 1 is the same as the genotypic ratio, because each genotype now looks different. The r allele has not changed; what changed is our expectation, since a single dose of R makes only enough pigment for pink. Nothing is blended, because red and white reappear unchanged in the F₂.

Co-dominance. Here the heterozygote shows the effect of both alleles at once rather than something in between. Human ABO blood groups are the standard example. The allele IA makes the red blood cell add sugar A to its surface, IB makes it add sugar B, and the allele i makes no sugar at all. A person of genotype IAIB carries both sugars on the cell surface and is blood group AB. Both alleles are expressed fully and independently, which is the test for co-dominance.

Multiple alleles. The same ABO gene illustrates a second point. A single individual carries only two alleles, but the gene exists in the population in three forms, IA, IB and i. When a gene has more than two alleles in the population it is said to show multiple allelism. Both IA and IB are dominant to i, while being co-dominant with each other. So group A arises from IAIA or IAi, group B from IBIB or IBi, group AB only from IAIB, and group O only from ii. Six genotypes produce four phenotypes.

Pleiotropy. Usually we speak of one gene controlling one character, but a single gene can affect several apparently unrelated characters, and this is called pleiotropy. It normally happens because the gene controls one step of metabolism on which many things depend. In phenylketonuria, a defect in one enzyme leads both to effects on brain development and to reduced pigmentation of hair and skin. In the pea, the gene for starch synthesis shows another face of the same idea. Homozygotes BB make large starch grains and homozygotes bb make smaller ones; the heterozygote Bb makes grains of intermediate size, so for starch grain size the alleles show incomplete dominance. Yet Bb seeds are as round as BB seeds, so for seed shape the same allele is completely dominant. Whether an allele looks dominant therefore depends on which character you choose to measure.

Polygenic inheritance. Many human characters such as height and skin colour do not fall into neat classes but vary continuously, because they are governed by three or more genes together and are also pushed about by the environment. In the standard model of human skin colour, three genes A, B and C are involved, and each dominant allele adds a fixed amount of pigment while each recessive allele adds none. The genotype AABBCC has six dominant alleles and gives the darkest skin, aabbcc has none and gives the lightest, and a genotype like AaBbCc with three dominant alleles gives an intermediate shade. What matters is only the number of dominant alleles, not which particular genes they belong to, so several different genotypes give the same appearance and the population shows a smooth gradation rather than sharp classes.

Mendel's factors were an abstraction; nobody had seen one. By 1900 chromosomes had been watched through meiosis, and the parallel was hard to miss. Chromosomes occur in pairs, so do alleles. The two chromosomes of a pair separate at meiosis and go into different gametes, exactly as the two alleles of a pair do. Fertilisation restores the pair in both cases. In 1902 Sutton and Boveri put these observations together into the chromosomal theory of inheritance: the behaviour of chromosomes during meiosis and fertilisation is what produces Mendel's laws, and genes are physically carried on chromosomes. Independent assortment then has a physical picture too. During metaphase of the first meiotic division, each pair of chromosomes lines up on the equatorial plate without reference to how the other pairs are lined up, so which member of one pair goes to a given pole is unrelated to which member of another pair goes there.

Thomas Hunt Morgan took the theory further using the fruit fly, Drosophila melanogaster. The fly suited the work as well as the pea had suited Mendel. It can be grown on simple synthetic medium in the laboratory, completes its life cycle in about two weeks, gives a very large number of progeny from a single mating, males and females are easy to tell apart, and it has many inherited variants that can be seen with a low power microscope.

Morgan carried out dihybrid crosses in Drosophila and got a surprise. He crossed yellow-bodied, white-eyed females with brown-bodied, red-eyed males and then intercrossed their F₁ progeny. The F₂ did not come out anywhere near 9 : 3 : 3 : 1. The two parental combinations were far more common than expected, and the two new combinations were far rarer. Morgan explained this by saying that the two genes were located on the same chromosome, so they tended to be inherited together rather than assorting independently. The physical association of genes on a chromosome is called linkage. The generation of non-parental combinations, which happens when crossing over exchanges segments between the two homologous chromosomes during meiosis, is called recombination.

Morgan then noticed that not all linked pairs behave alike. When he studied the genes for white eye and yellow body, only about 1.3 per cent of the progeny were recombinants; the two genes were very tightly linked. But white eye and miniature wing gave about 37.2 per cent recombinants, a much looser association. He concluded that genes lying close together on a chromosome are separated by crossing over only rarely and show low recombination, while genes lying far apart on the same chromosome are separated often and show high recombination. Alfred Sturtevant, working with Morgan, used exactly this idea in reverse: he took recombination frequency as a measure of the distance between two genes and used it to arrange genes in order along the chromosome. This is how the first genetic maps were made, and the same principle was later used in mapping the human genome.

The genetic basis of sex began to emerge in 1891 when Henking followed sperm formation in some insects and found a nuclear structure that entered only half of the sperms. He called it the X body. It was later understood to be a chromosome, and was renamed the X chromosome.

The XX-XO type. In insects such as grasshoppers, the female has a pair of X chromosomes in addition to the autosomes, while the male has only one X and no partner for it. So all eggs carry an X, but the sperms are of two kinds, half with an X and half with none. An egg fertilised by an X-carrying sperm becomes female, and one fertilised by a sperm without an X becomes male.

The XX-XY type. In humans and in Drosophila the female is XX and the male is XY. In humans there are 22 pairs of autosomes plus this pair, so a woman is 44 + XX and a man is 44 + XY. Every ovum carries 22 autosomes and one X. Half the sperms carry 22 autosomes and an X, and the other half carry 22 autosomes and a Y. The mother can only ever give an X, so it is the sperm that decides the sex of the child; a child who inherits an X-carrying sperm is a girl and one who inherits a Y-carrying sperm is a boy. The female is described as homogametic because she makes only one kind of gamete with respect to sex chromosomes, and the male as heterogametic because he makes two kinds. Since half the sperms are of each kind, either outcome is equally likely at every conception.

The ZZ-ZW type. In birds, the arrangement is reversed. The male has two identical sex chromosomes, written ZZ, while the female has two different ones, ZW. Different letters are used precisely to stop us from confusing the systems. Here the female is the heterogametic sex, so in birds it is the mother whose gamete decides the sex of the chick.

Honeybees. Honeybees do not use sex chromosomes at all; they use the number of chromosome sets, a system called haplodiploidy. A fertilised egg develops into a female, either a queen or a worker, and such a female is diploid with 32 chromosomes. An unfertilised egg develops by parthenogenesis into a male, a drone, which is haploid with 16 chromosomes. This has some odd consequences worth stating clearly. A drone has a mother but no father, and since it has no father it cannot have sons, though it does have a grandfather and can have grandsons. Being already haploid, a drone produces sperms by mitosis and not by meiosis.

Mutation. Mutation is a change in the DNA sequence, and it changes the genotype and often the phenotype of an organism. Along with recombination, it is the source of the variation that inheritance then passes on. Loss, gain or rearrangement of a segment of a chromosome is called a chromosomal aberration, and deletions and duplications of this kind are commonly seen in cancer cells. At a much smaller scale, a change in a single base pair of DNA is a point mutation, and sickle-cell anaemia is the classic example of a disease caused by one. Inserting or deleting one or two bases is more damaging than replacing one, because the reading frame of the whole message shifts from that point onwards; these are called frame-shift mutations. Agents that raise the rate of mutation are mutagens, and ultraviolet radiation is a familiar physical example.

Inherited disorders are sorted into two groups by their cause. A Mendelian disorder results from an alteration or mutation in a single gene, so it is passed down in the ordinary Mendelian way and can be traced through a family. A chromosomal disorder results from the absence, excess or abnormal arrangement of one or more chromosomes, so a whole block of genes is involved and Mendelian ratios do not apply. Haemophilia, colour blindness, sickle-cell anaemia, cystic fibrosis, phenylketonuria and thalassemia are the commonly named Mendelian disorders; Down's, Klinefelter's and Turner's syndromes are the commonly named chromosomal ones.

Mendelian disorders are followed using pedigree analysis, the study of a trait through several generations of a family. The chart used is drawn to a fixed convention: each male is shown as a square and each female as a circle; a filled or shaded symbol means the person shows the trait and an unshaded symbol means the person does not. A horizontal line joining a square to a circle represents a marriage, a short vertical line drops from it, and the children hang from a horizontal sibship line below, arranged left to right in order of birth. Each generation occupies one row and is numbered with Roman numerals, while individuals within a row are numbered left to right. Reading such a chart tells you whether the trait is dominant or recessive, and whether it is autosomal or sex-linked. A trait that appears only in males and passes to them through unaffected mothers points to an X-linked recessive gene.

Haemophilia is a sex-linked recessive disorder. A protein taking part in the cascade of reactions that clots blood is affected, so in an affected person even a simple cut leads to prolonged bleeding that does not stop on its own. The gene is on the X chromosome, so an unaffected carrier female can pass it to some of her sons. A female is affected only if she receives the defective allele from both parents, which requires a carrier mother and an affected father, so affected females are extremely rare. The disorder is famous for running through the royal family of Queen Victoria. Red-green colour blindness is a second X-linked recessive condition, in which the pigment of one type of cone cell in the retina is defective so that red and green cannot be told apart; the same logic applies, since a male has only one X and therefore shows the trait whenever he inherits the defective allele, while a female with one normal allele does not.

Sickle-cell anaemia is an autosomal recessive disorder controlled by a single pair of alleles, HbA and HbS. Three genotypes are possible: HbAHbA is normal, HbAHbS is a carrier who appears healthy, and HbSHbS is affected. So the disease appears in a child only when both parents are carriers. The defect is a single base substitution at the sixth codon of the beta globin gene, changing the codon GAG to GUG, which replaces glutamic acid by valine at the sixth position of the beta globin chain. Under low oxygen tension the mutant haemoglobin molecules stick together into long polymers, and the biconcave disc shaped red cell is pulled into an elongated sickle shape.

Phenylketonuria is also autosomal recessive. The affected individual lacks the enzyme that converts the amino acid phenylalanine into tyrosine, so phenylalanine builds up and is converted into phenylpyruvic acid and related derivatives. Their accumulation affects brain development, and the excess is also excreted in the urine because the kidney reabsorbs it poorly. Thalassemia is an autosomal recessive blood disorder that appears when both parents are carriers. A mutation or deletion reduces the rate at which one of the globin chains is made, so too few normal haemoglobin molecules are formed and anaemia results. In alpha thalassemia the alpha chain is affected; its production is controlled by two closely linked genes, HBA1 and HBA2, on chromosome 16 contributed by each parent, and the defect involves mutation or deletion of one or more of these four genes. In beta thalassemia the beta chain is affected, and it is controlled by a single gene HBB on chromosome 11 from each parent.

Chromosomal disorders arise mainly from aneuploidy, the gain or loss of a single chromosome caused by failure of chromatids to separate during cell division. In Down's syndrome, first described by Langdon Down in 1866, an additional copy of chromosome 21 is present, so the cell has 47 chromosomes in place of 46; this trisomy is associated with short stature, a small round head, a furrowed tongue with a partially open mouth, a broad palm with a characteristic crease, and delayed physical and mental development. Klinefelter's syndrome is caused by an additional X chromosome, giving 47 chromosomes with the sex chromosome constitution XXY. The individual has an overall masculine build together with some feminine features such as development of breast tissue, and is sterile. Turner's syndrome is caused by the loss of an X chromosome, giving 45 chromosomes with a single X. The individual is a sterile female with rudimentary ovaries and poorly developed secondary sexual characters. Aneuploidy should not be confused with polyploidy, in which an entire extra set of chromosomes is present because cytokinesis failed after telophase; polyploidy is common in flowering plants and is not the cause of the human syndromes above.