Chapter 8: Laws of Inheritance
In the royal families of nineteenth-century Europe, a strange illness kept appearing. A small cut would not stop bleeding. A knock against a table would swell into a deep bruise that lasted for weeks. The condition was haemophilia, and it ran through the descendants of Queen Victoria of Britain, who lived from 1819 to 1901. Her son Leopold suffered from it. Several of her daughters, who were perfectly healthy themselves, married into the royal houses of Spain, Germany and Russia — and grandsons in those families were born with the same bleeding disorder. The most famous of them was Alexei, the young heir to the Russian throne. Doctors of the time had no explanation. The mothers never showed the disease, yet they clearly carried something that their sons received. It seemed to leap silently across a generation and then reappear, always in boys. Nothing in the medicine of that century could account for it. The answer had, in fact, already been written down — quietly, in a monastery garden in Central Europe, by a monk counting pea plants. Nobody had read it yet. This chapter follows that answer: how characters pass from parents to offspring, why some of them hide, and why a few of them travel differently in sons than in daughters.
Diagram
Fig. 8.1 – An opening illustration showing a simple family tree of a European royal family across three generations, with unaffected carrier mothers and affected sons marked using standard pedigree symbols; label the generations I, II and III.
Each of these questions is answered somewhere in this chapter. Read on, and look out for the answers as they appear.
8.1 Heredity, Genetics and the Work of Mendel
Children resemble their parents, but never exactly. A boy may have his father’s height and his mother’s eye colour, and a feature that neither parent shows. This everyday observation hides a precise biological process: characters are passed from one generation to the next in packets, and those packets follow rules.
The passing on of characters from parents to offspring is called heredity. The branch of biology that studies how this happens is called genetics.
Notice that heredity always comes with variation. Offspring are never exact copies, and explaining both the resemblance and the difference is the central problem of genetics.
The Monk Who Counted Peas
Gregor Johann Mendel (1822–1884) was an Austrian monk who taught science and worked in the garden of his monastery. In 1856 he began a long series of breeding experiments on the garden pea, Pisum sativum. Over about eight years he grew and examined thousands of plants, and — unlike the naturalists before him — he counted the offspring of every cross instead of merely describing them.
That habit of counting is what made his work different. Earlier breeders could see that traits reappeared; Mendel could show in what proportion they reappeared, and numbers can be tested. From his results he proposed a set of principles now called Mendel’s Laws of Inheritance, or Mendelism. Because these principles form the foundation of the entire subject, Mendel is regarded as the Father of Genetics.
Diagram
Fig. 8.2 – Portrait of Gregor Johann Mendel with an inset of the monastery garden plot where the pea experiments were carried out; caption to carry his dates, 1822–1884.
Why the Pea Plant Was the Right Choice
Mendel’s success depended as much on his choice of organism as on his mathematics. A poor choice of plant would have buried the pattern in noise. The pea plant suited the work for the following reasons:
- The pea shows clear, contrasting pairs of traits — tall versus dwarf, round versus wrinkled seed, yellow versus green cotyledons. Each plant falls plainly into one class or the other, with no in-between forms to argue about, so every plant can be scored without doubt.
- It has a short life cycle, so several generations can be raised and compared within a few years.
- Pea plants are naturally self-pollinating. Left alone, a variety breeds true generation after generation, giving Mendel pure lines — dependable starting material of known constitution.
- They can also be cross-pollinated by hand when required, so the experimenter can decide exactly which plant fertilises which.
- The flower structure helps in both respects: the petals enclose the stamens and the carpel tightly, keeping out stray pollen from other plants, yet the flower is large enough to be opened and worked on with a fine brush.
- The plant is easy to grow and maintain, and produces many seeds per cross, giving large numbers to count.
The last point matters more than it looks. Ratios only emerge reliably in large samples; a cross that yields six seeds tells you nothing dependable, while one that yields six hundred tells you a great deal. Mendel’s laws are, in the end, statements about proportions in big numbers.
Diagram
Fig. 8.3 – The seven pairs of contrasting characters Mendel studied in Pisum sativum, drawn side by side: stem height, seed shape, seed (cotyledon) colour, pod shape, pod colour, flower colour and flower position.
| Character studied | Dominant form | Recessive form |
|---|---|---|
| Stem height | Tall | Dwarf |
| Seed shape | Round | Wrinkled |
| Cotyledon colour | Yellow | Green |
| Pod shape | Inflated | Constricted |
| Pod colour | Green | Yellow |
| Flower colour | Violet | White |
| Flower position | Axial | Terminal |
How a Controlled Cross Is Made
To cross two plants deliberately, Mendel first had to prevent the flower from pollinating itself. The unopened flower bud is opened and its immature anthers are removed before they can shed pollen — a step called emasculation. The emasculated flower is then bagged so that no unwanted pollen reaches it. When its stigma is mature, pollen collected from the chosen male parent is dusted on to it by hand, and the flower is bagged again until the pod develops.
Every step here has a purpose, and skipping any one of them ruins the experiment. Miss the emasculation, and the plant fertilises itself, so the “cross” is no cross at all. Miss the bagging, and insect-borne pollen from an unknown plant may reach the stigma, making the parentage of every resulting seed uncertain.
Flowchart
FC 8.1 – Making a controlled cross in pea: select pure-line parents → open flower bud of female parent → remove immature anthers (emasculation) → bag the flower → collect pollen from chosen male parent → dust pollen on mature stigma → re-bag → collect and sow the seeds → score the offspring
Counting large numbers of two contrasting kinds of pea seed is exactly the skill practised in the ISC laboratory when yellow and green pea seeds are scattered and sampled with a quadrat to find the frequency of each type — the same logic of scoring a population that Mendel applied to his garden plots.
8.2 The Monohybrid Cross: Laws of Dominance and Segregation
Mendel did not begin by studying everything at once. He began with a single pair of contrasting traits and followed it patiently through two generations. A cross between two parents that differ in only one pair of contrasting characters is called a monohybrid cross.
For his first experiment he took a pure-breeding tall plant and a pure-breeding dwarf plant. The parents of a cross are together called the parental generation, written \(P\). Their offspring form the first filial generation, written \(F_1\); when the \(F_1\) plants are self-pollinated, their offspring form the second filial generation, or \(F_2\).
What Mendel Actually Saw
Every plant in the \(F_1\) generation was tall. Not one was dwarf, and — just as importantly — not one was of medium height. The dwarf character had vanished completely.
He then allowed these tall \(F_1\) plants to self-pollinate. In the \(F_2\) generation the dwarf plants reappeared, roughly one dwarf for every three tall plants. In his own count of this cross Mendel obtained 787 tall and 277 dwarf plants — a ratio of about \(2.84:1\), which is what a true \(3:1\) ratio looks like in real data.
Diagram
Fig. 8.4 – The monohybrid cross in pea: P generation (pure tall × pure dwarf), all-tall \(F_1\), and the \(F_2\) generation showing three tall plants to one dwarf; label the phenotypic ratio 3 : 1.
The two observations together are the heart of the matter. In the \(F_1\), one character disappeared entirely. In the \(F_2\), it came back unchanged — not diluted, not weakened, but as fully dwarf as the original grandparent. Whatever carries the dwarf character had clearly survived the \(F_1\) generation intact while remaining hidden.
The Law of Dominance
The all-tall \(F_1\) generation tells us that when two contrasting factors are present together, only one of them shows itself. The factor that expresses itself is called dominant; the one that is masked is called recessive.
This also explains why the \(F_1\) plants were tall and not of intermediate height. Dominance is not a blending of the two characters — it is the complete masking of one by the other. The recessive factor is present in the \(F_1\) plant but silent.
The Law of Segregation
Why then does the \(3:1\) ratio appear so reliably in the \(F_2\)? Mendel’s answer was that the two factors controlling a character never fuse or contaminate each other. They stay separate throughout the life of the plant, and when gametes are formed the two factors separate, so that each gamete carries only one of them.
This law is also known as the law of purity of gametes, because a gamete is always pure for a character — it can carry the factor for tallness or the factor for dwarfness, never both, and never a mixture of the two.
Using T for the dominant factor for tallness and t for the recessive factor for dwarfness, the cross can be worked out completely. The pure tall parent is TT and the pure dwarf parent is tt. The TT parent can make only T gametes and the tt parent only t gametes, so every \(F_1\) plant is Tt — tall in appearance, but carrying both factors.
When an \(F_1\) Tt plant forms gametes, segregation gives it two kinds of gamete, T and t, in equal numbers. Self-pollination allows any pollen grain to meet any egg, and the four equally likely combinations are conveniently set out in a chequer board known as a Punnett square.
Diagram
Fig. 8.5 – Punnett square for the cross Tt × Tt: gametes T and t along the top and side, the four boxes filled as TT, Tt, Tt and tt; mark the phenotypes tall, tall, tall, dwarf beneath.
Reading the square gives two different ratios, and students must be careful to keep them apart. Counting what the plants look like, three of the four are tall and one is dwarf — the phenotypic ratio \(3:1\). Counting what factors they carry, one is TT, two are Tt and one is tt — the genotypic ratio \(1:2:1\). The three tall plants are not identical: one of them breeds true, and two of them secretly carry dwarfness.
Flowchart
FC 8.2 – Monohybrid cross: pure tall (TT) × pure dwarf (tt) → gametes T and t → all \(F_1\) tall (Tt) → self-pollination → gametes T and t from each parent → \(F_2\) = 1 TT : 2 Tt : 1 tt → phenotypes 3 tall : 1 dwarf
Telling Two Look-Alikes Apart
Here a practical problem arises. A tall pea plant standing in a field may be TT or Tt — the two look exactly the same. Its appearance cannot settle the question, so the plant must be crossed with a partner chosen so that its offspring reveal the answer. Such a cross of an individual with one of its own parental types is called a back cross, and it has two forms.
In a test cross, the individual is crossed with the homozygous recessive parent type (here, tt). Since the tt parent can contribute only a recessive factor, whatever the offspring show must come from the plant being tested. This is what makes the test cross so useful: the recessive partner acts as a blank sheet on which the unknown genotype writes itself.
If the tested plant is TT, every offspring receives a T from it and all are tall. If the tested plant is Tt, half its gametes carry T and half carry t, so the offspring come out as one tall to one dwarf. The appearance of even a single dwarf offspring proves that the tested plant was heterozygous.
In an out cross, the individual is instead crossed with the homozygous dominant parent type (TT). Every offspring then receives a dominant factor from that parent, so all of them show the dominant character whatever the tested plant carries — a ratio of dominant to recessive of \(1:0\). The out cross therefore cannot be used to test genotype at all, because both possible answers produce the same result. It is worth learning precisely because it is the tempting wrong choice in examination questions.
8.3 The Dihybrid Cross: Law of Independent Assortment
Having settled how one character behaves, Mendel asked a harder question. If two different characters are followed at the same time, do they travel together, or does each one behave as though the other were not there? A cross between two parents differing in two pairs of contrasting characters is called a dihybrid cross.
He chose seed shape and cotyledon colour. One parent was pure-breeding for round seeds with yellow cotyledons — both dominant characters — and the other was pure-breeding for wrinkled seeds with green cotyledons, both recessive. Writing R for round and r for wrinkled, Y for yellow and y for green, the parents are RRYY and rryy.
The \(F_1\) and \(F_2\) Results
The RRYY parent can form only RY gametes and the rryy parent only ry gametes, so every \(F_1\) plant is RrYy. All \(F_1\) seeds were round and yellow, which is exactly what the law of dominance predicts for each character taken separately.
The interesting generation is the next one. When the \(F_1\) plants were self-pollinated, the \(F_2\) seeds fell into four phenotypes, not two:
- round and yellow — 9 parts
- round and green — 3 parts
- wrinkled and yellow — 3 parts
- wrinkled and green — 1 part
This is the classical dihybrid ratio of \(9:3:3:1\).
Two of these four types deserve a second look. Round–green and wrinkled–yellow seeds did not exist in either grandparent. New combinations of characters had appeared, which means the characters had been shuffled and re-dealt rather than handed down as a fixed package.
Why Four Kinds of Gamete Appear
The \(F_1\) plant is RrYy. When it forms gametes, the R and r factors segregate from each other, and the Y and y factors segregate from each other — but the two separations are unconnected. An R may go with either Y or y, and an r may equally go with either Y or y.
The \(F_1\) plant therefore produces four kinds of gamete, in equal numbers: RY, Ry, rY and ry. Since both the male and the female gametes come in these four kinds, there are \(4 \times 4 = 16\) equally likely combinations at fertilisation, which are set out in a sixteen-box Punnett square.
Diagram
Fig. 8.6 – The 16-box Punnett square (chequer board) for the dihybrid cross RrYy × RrYy: gametes RY, Ry, rY and ry along the top and the side, each box filled with its genotype and phenotype; shade the four phenotype classes in the ratio 9 : 3 : 3 : 1.
Working through the square, the sixteen boxes contain nine genotypes but only four phenotypes. Nine boxes carry at least one R and at least one Y and are round and yellow; three carry at least one R with yy and are round and green; three carry rr with at least one Y and are wrinkled and yellow; and the single rryy box is wrinkled and green. The rarest class is the double recessive, which is why it appears just once in sixteen.
Flowchart
FC 8.3 – Dihybrid cross: RRYY (round yellow) × rryy (wrinkled green) → gametes RY and ry → \(F_1\) all RrYy, round and yellow → self-pollination → four gamete types RY, Ry, rY, ry from each parent → 16 combinations → \(F_2\) phenotypes 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green
The Law of Independent Assortment
Mendel drew from this his third principle.
In plain terms, the inheritance of one character does not influence the inheritance of another. Which colour a seed receives has nothing to do with which shape it receives, so all combinations of the two are produced.
Independent assortment has a physical basis that Mendel could not have known. Genes for the two characters lie on different chromosomes. During meiosis, the way one pair of homologous chromosomes lines up at the equator has no bearing on the way another pair lines up, so the maternal and paternal chromosomes are sorted into gametes in every possible combination.
Diagram
Fig. 8.7 – Two pairs of homologous chromosomes at metaphase I shown in their two equally likely orientations, with the resulting four gamete types RY, Ry, rY and ry drawn below each arrangement.
This immediately tells us where the law must fail. If the two genes happen to lie close together on the same chromosome, they cannot be sorted independently and tend to be inherited together — the phenomenon of linkage, which is taken up when gene mapping is discussed. Independent assortment is therefore a law about genes on different chromosomes, and the \(9:3:3:1\) ratio is the signature that this condition has been met.
Solving Dihybrid Problems Without Drawing Sixteen Boxes
Because the two characters are independent, the probabilities for each can simply be multiplied. From a monohybrid cross we already know that \(Rr \times Rr\) gives \(\tfrac{3}{4}\) round and \(\tfrac{1}{4}\) wrinkled, and that \(Yy \times Yy\) gives \(\tfrac{3}{4}\) yellow and \(\tfrac{1}{4}\) green. The chance of a seed being both round and yellow is therefore
\[P(\text{round and yellow}) = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}\]
and in the same way
\[\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}, \qquad \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}, \qquad \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}\]
which reproduces the \(9:3:3:1\) ratio exactly. Here \(P\) stands for probability, a pure number between 0 and 1 with no unit. This multiplication shortcut works only because the two characters assort independently — which is why it is a check on the principle, not merely a trick for saving time.
The Dihybrid Test Cross
The test cross introduced earlier works just as well with two characters. An \(F_1\) RrYy plant crossed with the double recessive rryy gives a very clean result: the rryy parent contributes only ry gametes, so each of the four gamete types of the \(F_1\) plant shows up directly as a phenotype in the offspring. The four classes — round yellow, round green, wrinkled yellow and wrinkled green — appear in a ratio of \(1:1:1:1\).
That ratio is a direct photograph of the gametes produced by the heterozygote, which is why the dihybrid test cross became the standard tool for detecting whether two genes assort independently. Any marked departure from \(1:1:1:1\) is a signal that the two genes are not travelling independently at all.
Taken together, Mendel’s three laws can be summed up in a single sentence: characters are determined by paired factors, some of which are dominant over others; these factors separate cleanly during gamete formation, and pairs controlling different characters are redistributed independently of one another.
8.4 Important Terms Used in Genetics
Genetics has a precise vocabulary, and most mistakes in this subject are vocabulary mistakes rather than reasoning mistakes. The terms below have already been used informally in the crosses worked out so far; this section fixes their exact meaning so that later chapters can use them without hesitation.
Trait, Gene and Allele
A trait, also called a character, is any feature of an organism that can be observed or measured — height of the stem, shape of the seed, colour of a flower, the ability to clot blood normally.
Traits do not appear from nowhere. Each is controlled by a gene, a segment of DNA on a chromosome that carries the information for that character. The fixed position that a particular gene occupies on its chromosome is called its locus.
Chromosomes in a body cell occur in homologous pairs, one member of each pair coming from the mother and one from the father. Both members of a pair carry the same genes at the same loci, but the two copies of a gene need not be identical. The alternative forms of the same gene, sitting at the same locus on the two homologous chromosomes, are called alleles or allelomorphs.
The tall factor T and the dwarf factor t of the earlier crosses are two alleles of a single gene for stem height. They are not two different genes, and this is worth holding on to: a gene is the address, an allele is which version lives there.
Diagram
Fig. 8.8 – A pair of homologous chromosomes drawn side by side, showing three gene loci; at one locus the two homologues carry different alleles (T and t) and at another they carry identical alleles, with labels for gene, locus and allele.
Because the two homologous chromosomes separate during meiosis, the two alleles of a gene always end up in different gametes. A single gamete can therefore never carry both alleles of the same gene — the point already met as the purity of gametes.
Genotype and Phenotype
The genotype of an individual is its genetic make-up, written as the alleles it carries: TT, Tt, tt, RrYy and so on. The phenotype is what the individual actually looks like — tall, dwarf, round, yellow.
The two are not the same thing, and one does not fix the other completely. A TT plant and a Tt plant are both tall: same phenotype, different genotype. This is precisely why a plant’s appearance cannot settle its genetic make-up, and why the test cross had to be invented.
Homozygosity, Heterozygosity and Hemizygosity
An individual that receives identical alleles of a gene from both parents is homozygous for that character — TT (homozygous dominant) or tt (homozygous recessive). Such an individual can produce only one kind of gamete for that gene and therefore breeds true, which is exactly what makes homozygous stocks valuable as pure lines in breeding work.
An individual carrying two different alleles of the same gene is heterozygous, or a hybrid — Tt. It produces two kinds of gamete in equal numbers and does not breed true.
A third condition arises when an individual carries only one copy of a gene instead of the usual two. This is hemizygosity. In human beings, a male has one X chromosome and one Y chromosome. Most of the genes on the X chromosome have no matching partner on the much smaller Y, so for those genes the male has a single allele and nothing to pair it with.
The consequence is important and will be met again. A hemizygous male has no second allele that could mask a recessive one, so any recessive allele he carries on his single X chromosome is expressed straight away. He is neither homozygous nor heterozygous for such a gene; the terms simply do not apply.
Diagram
Fig. 8.9 – Comparison of a homozygous pair (TT), a heterozygous pair (Tt) and the hemizygous condition of a human male (a large X chromosome carrying an allele beside a small Y chromosome with no corresponding locus).
Dominant and Recessive Revisited
Dominance and recessiveness were defined when the monohybrid cross was worked out. One point about them belongs here, because it is a standing source of error. A dominant allele expresses itself both in the homozygous condition (TT) and in the heterozygous condition (Tt); a recessive allele expresses itself only in the homozygous condition (tt), that is, only when no dominant allele is present.
Dominance says nothing whatever about how common an allele is in a population. It describes only how one allele behaves when placed alongside another in the same individual. A dominant allele may be extremely rare and a recessive one may be present in almost everybody — a distinction that examiners test regularly, and one that will be met again when allele frequencies are studied.
8.5 Incomplete Dominance, Co-dominance and Multiple Allelism
The clean \(3:1\) and \(9:3:3:1\) ratios of the previous sections rest on a condition that is easy to overlook: at every gene locus concerned, one allele must be completely dominant over the other. When that condition is not met, Mendel’s laws still operate — the alleles still segregate, and they still assort independently — but the ratios change, because the relationship between the two alleles inside the heterozygote is different.
These situations are usually described as exceptions to Mendel’s laws. It is more accurate to call them exceptions to complete dominance. Segregation is never violated; only the way the heterozygote looks is altered.
Incomplete Dominance
Sometimes the dominant allele does not entirely suppress the recessive one, and the heterozygote shows a phenotype intermediate between the two parents. This is called incomplete dominance, or blending inheritance.
The classic example among plants is the four o’clock plant, Mirabilis jalapa. When a pure red-flowered plant is crossed with a pure white-flowered one, the \(F_1\) plants bear pink flowers — neither parental colour, and neither allele in control.
If these pink \(F_1\) plants are self-pollinated, the parental colours return unchanged in the \(F_2\) along with the intermediate: one red plant to two pink plants to one white plant, a ratio of \(1:2:1\).
Diagram
Fig. 8.10 – Incomplete dominance in Mirabilis jalapa: red-flowered parent (\(R^1R^1\)) × white-flowered parent (\(R^2R^2\)), pink \(F_1\) (\(R^1R^2\)), and the \(F_2\) generation showing 1 red : 2 pink : 1 white with a Punnett square alongside.
That last point deserves emphasis. The pink colour looks like a mixture, and for a long time inheritance was believed to work by the mixing of parental characters. If that were true, the red and white colours could never come back, because a mixture cannot be unmixed. Their clean reappearance in the \(F_2\) is the strongest available proof that the factors of inheritance are particles that stay whole.
Flowchart
FC 8.4 – Incomplete dominance: red (\(R^1R^1\)) × white (\(R^2R^2\)) → gametes \(R^1\) and \(R^2\) → \(F_1\) all pink (\(R^1R^2\)) → self-pollination → \(F_2\) = 1 \(R^1R^1\) red : 2 \(R^1R^2\) pink : 1 \(R^2R^2\) white
Notice what has happened to the ratios. The genotypic ratio is \(1:2:1\), exactly as in an ordinary monohybrid cross — segregation is untouched. But the phenotypic ratio is also \(1:2:1\), because the heterozygote can now be recognised on sight. Wherever the phenotypic and genotypic ratios of a monohybrid cross are the same, dominance is incomplete.
A second example is found in poultry. In Andalusian fowls, a cross between a black bird and a white-feathered bird gives \(F_1\) offspring with blue plumage, and crossing two blue birds restores black, blue and white in the \(F_2\) in the ratio \(1:2:1\). Blue Andalusians can never be made to breed true, because every blue bird is a heterozygote.
Co-dominance
Co-dominance is often confused with incomplete dominance, and the two are genuinely different. In co-dominance, both alleles of the pair are fully and separately expressed in the heterozygote. Nothing is intermediate; both characters appear together.
Coat colour in cattle shows this clearly. A red-coated animal (\(C^RC^R\)) crossed with a white-coated animal (\(C^WC^W\)) gives heterozygous offspring (\(C^RC^W\)) with a roan coat. From a distance the roan looks pinkish, which is why it is mistaken for a blend. Examine the hide closely, however, and it is found to carry red hairs and white hairs side by side. Each individual hair is either red or white; none is intermediate. Both alleles are doing their own work, in full, in different patches of skin.
Crossing two roan animals gives \(F_2\) offspring in the ratio 1 red : 2 roan : 1 white — again \(1:2:1\) for both genotype and phenotype.
Diagram
Fig. 8.11 – Co-dominance in cattle coat colour: red (\(C^RC^R\)) × white (\(C^WC^W\)) giving roan (\(C^RC^W\)), with a magnified inset of roan hide showing separate red and white hairs rather than pink hairs.
In human beings, the AB blood group of the ABO system and the MN blood group system are standard examples of co-dominance. A person of blood group AB carries both the A antigen and the B antigen on the surface of the red blood cells — not a single intermediate antigen, but both, each made by its own allele.
Since both give a \(1:2:1\) ratio, the ratio alone cannot tell them apart. The question to ask is always the same: does the heterozygote show something in between, or does it show both things at once?
Multiple Allelism
So far every gene has been treated as having exactly two alleles. That is a simplification. Work on coat colour in mice in the early 1900s, notably by the French biologist Cuénot, showed that a single gene may exist in more than two alternative forms in a population. When three or more alleles of the same gene are present at one locus in a population, the condition is called multiple allelism, and the alleles concerned are called multiple alleles.
The final clause is the one students forget. However many alleles exist in the population, an individual has only two homologous chromosomes and therefore only two loci to fill. Multiple allelism is a property of a population, not of an individual.
The best-known human example is the ABO blood group system, which is governed by three alleles of one gene: \(I^A\), \(I^B\) and \(i\). The allele \(I^A\) directs the formation of the A antigen and \(I^B\) the B antigen, while \(i\) produces neither. \(I^A\) and \(I^B\) are co-dominant with each other, and both are completely dominant over \(i\). From these relationships the four blood groups follow directly.
| Blood group (phenotype) | Possible genotypes | Antigen on red cells |
|---|---|---|
| A | \(I^AI^A\) or \(I^Ai\) | A |
| B | \(I^BI^B\) or \(I^Bi\) | B |
| AB | \(I^AI^B\) | A and B |
| O | \(ii\) | Neither |
Two features of this table are worth reading carefully. Group AB has only one possible genotype, and it is the one case where both alleles show — the co-dominant heterozygote. Group O also has only one possible genotype, because a single dominant allele of either kind would change the group; O is the homozygous recessive. Groups A and B, by contrast, each have two possible genotypes, so a person of group A may or may not be carrying a hidden \(i\) allele.
Determining a blood group with antisera is the first experiment in the ISC practical course, and it is a direct reading of a genotype from a phenotype: the clumping of red cells with anti-A and anti-B sera reveals which antigens are present and therefore which alleles the person carries.
8.6 Polygenic and Pleiotropic Inheritance
Every character studied so far has fallen into sharp classes. A pea plant is tall or dwarf, a seed is round or wrinkled, a person’s blood group is A, B, AB or O. Variation of this kind, with distinct classes and nothing in between, is called discontinuous variation.
Most of the characters we notice in ourselves are not like this at all. Human height, skin colour, body weight and the yield of a crop vary by small degrees across a whole range, with no natural dividing lines. This is continuous variation, and it needs a different explanation — not a departure from Mendel’s laws, but Mendel’s laws applied to several genes at once.
Polygenic Inheritance
When a single character is controlled by two or more genes, each contributing a small effect that adds to the effects of the others, the pattern is called polygenic or quantitative inheritance. The genes concerned are called polygenes, multiple factors or cumulative genes.
The essential idea is dosage. Each contributing allele adds a small, roughly equal amount to the character, and what an individual shows depends on the total number of such alleles it carries, not on which particular genes they came from.
The Swedish geneticist Nilsson-Ehle demonstrated this early in the twentieth century with grain colour in wheat. Grain colour there is governed by three gene pairs. Each contributing allele deepens the red colour by one step; alleles that contribute nothing leave the grain paler. A plant carrying six contributing alleles has deep red grain, one carrying none has white grain, and every intermediate shade exists between them.
When two plants heterozygous at all three gene pairs are crossed, the \(F_2\) generation falls into seven shades in the ratio
\[1 : 6 : 15 : 20 : 15 : 6 : 1\]
Plotted as a histogram, these numbers form the familiar bell-shaped curve: the extreme types are rare and the intermediate types are common. That is exactly the shape of the height distribution in any large group of people, and it is the fingerprint of polygenic control.
Diagram
Fig. 8.12 – Histogram of the \(F_2\) generation for grain colour in wheat controlled by three gene pairs, showing seven colour classes in the ratio 1 : 6 : 15 : 20 : 15 : 6 : 1, with a smooth bell-shaped curve drawn over the bars.
The reason the middle classes are commonest is simple counting. There is only one way to receive all six contributing alleles and only one way to receive none, but there are many different combinations that add up to three. Rare extremes and common intermediates follow from arithmetic, not from any special biological rule.
For a character controlled by \(n\) gene pairs, the number of phenotypic classes in the \(F_2\) is
\[\text{Number of classes} = 2n + 1\]
and the proportion of the \(F_2\) showing either extreme phenotype is
\[\text{Frequency of an extreme} = \frac{1}{4^{\,n}}\]
where \(n\) is the number of gene pairs involved — a pure number with no unit. With one gene pair these expressions give three classes and a frequency of \(\tfrac{1}{4}\), which is the ordinary \(1:2:1\) result of incomplete dominance. Polygenic inheritance is therefore not a new law; it is the same law repeated over several genes.
Continuous Variation in Human Beings
Human skin colour is a much-quoted example of polygenic inheritance. The depth of colour depends on the amount of the pigment melanin in the skin, and several genes influence how much melanin is made. Early studies in the twentieth century, including those of Davenport, proposed that a small number of gene pairs would account for the range observed; later work has shown that many genes are involved, each with a modest effect, which is why the variation is so finely graded.
Human height behaves in the same way, and both characters illustrate a second feature of polygenic characters: they are strongly influenced by the environment. Nutrition, sunlight and general health all affect the phenotype that a given genotype finally produces. Because of this, polygenic characters can never be predicted from a Punnett square in the way that flower colour in a pea can. They are described statistically, in terms of averages and spread, rather than as ratios of exact classes.
Crop breeders work with polygenic characters almost all the time. Grain yield, plant height, oil content and time to maturity are all quantitative characters, which is why improving a crop is a slow business of selecting the best-performing lines over many generations rather than a single dramatic cross.
Pleiotropic Inheritance
Polygenic inheritance is many genes acting on one character. Pleiotropy is the exact opposite — one gene acting on many characters.
This is far more common than it first appears, and the reason is straightforward. A gene makes a protein; that protein may take part in several different pathways, or may be needed at several different places in the developing body. Change the gene, and every pathway that depends on its product is changed at once.
A familiar example sits inside Mendel’s own material. The gene controlling round versus wrinkled seed shape in pea codes for an enzyme that converts sugar into starch. In a plant homozygous for the recessive allele, the enzyme is defective, so less starch is made, more free sugar accumulates, the developing seed absorbs more water and then shrinks unevenly as it dries — giving the wrinkled shape. One gene, and with it seed shape, starch content and sugar content are all altered together.
In human beings, the allele responsible for sickle cell anaemia is strongly pleiotropic. A single change in the gene for the beta chain of haemoglobin alters the shape of the red blood cells, and from that one change follow anaemia, blockage of small blood vessels, pain in the joints and limbs, enlargement of the spleen and increased resistance to malaria. These effects look unconnected in a patient’s case sheet, yet all trace back to one gene.
Phenylketonuria behaves similarly. The gene concerned controls an enzyme of amino acid metabolism, and a defect in it affects mental development, pigmentation of the skin and hair, and the composition of the urine at the same time.
Diagram
Fig. 8.13 – Pleiotropy illustrated as a branching diagram: a single gene at the top with arrows leading to several distinct phenotypic effects, drawn for the sickle cell allele (altered red cell shape, anaemia, blocked capillaries, enlarged spleen, malaria resistance).
Both patterns are worth keeping clearly apart, because examination questions frequently place them side by side and the wording of the two definitions is nearly a mirror image of each other. The question to ask is which side is single: one character being pulled by many genes, or one gene pushing on many characters.
8.7 Cytoplasmic (Plastidial) Inheritance
All the inheritance discussed so far has been nuclear. The genes concerned lie on chromosomes inside the nucleus, both parents contribute equally to the offspring, and it makes no difference which parent supplies which allele. A cross of tall female × dwarf male gives exactly the same result as dwarf female × tall male.
There is a small but important group of characters for which this is not true. Their genes lie outside the nucleus, and the parent of origin decides everything. This is cytoplasmic or extranuclear inheritance.
Where the Extra Genes Are
Two organelles of the cell carry their own DNA: the mitochondria, present in nearly all eukaryotic cells, and the plastids, including the chloroplasts of green plant cells. In each case the DNA is a small circular molecule, quite separate from the nuclear chromosomes, and it carries genes for some of the proteins that the organelle needs in order to work.
These organelle genes are inherited, but they are not inherited in the Mendelian way, because they are not on chromosomes and they take no part in meiosis. They simply travel in the cytoplasm of whichever cell contains them.
Why It Is Almost Always Maternal
The decisive fact is the enormous difference in size between the two gametes. An egg cell is large and full of cytoplasm, containing hundreds or thousands of mitochondria and, in plants, plastids as well. A sperm or a pollen tube nucleus contributes essentially only a nucleus; whatever little cytoplasm it brings is negligible, and in most species is actively excluded or destroyed after fertilisation.
The zygote therefore receives its nuclear genes from both parents but almost all of its cytoplasmic genes from the mother alone. A cytoplasmically inherited character passes down the female line generation after generation, and a father never transmits it to any of his children, whether sons or daughters.
Diagram
Fig. 8.14 – Reciprocal crosses compared: on the left, a nuclear character giving identical offspring in both directions of the cross; on the right, a cytoplasmic character in which the offspring always resemble the female parent, whichever way the cross is made.
Plastidial Inheritance and Leaf Variegation
The clearest plant example is leaf variegation. Certain garden plants bear leaves patched with green and white, and some plants carry whole branches that are entirely green, others entirely white, and others variegated.
The explanation lies in the plastids. Normal plastids develop into functioning green chloroplasts; defective ones cannot make chlorophyll and remain colourless. A cell may contain a mixture of both kinds. As that cell divides again and again, the plastids are distributed to the daughter cells at random, and by chance some daughter cells end up with only green plastids and others with only colourless ones. This gradual separation of the two kinds of plastid into different cell lines is called sorting out, and it is what produces the sharp green and white patches on a variegated leaf.
Now consider crosses between such branches. If the female parent is a flower borne on a green branch, all the offspring are green, whatever branch supplied the pollen. If the female parent is a flower on a white branch, all the offspring are white — and, having no chlorophyll, these seedlings die once the food stored in the seed is exhausted. If the female parent is on a variegated branch, the offspring are a mixture of green, white and variegated plants, because her egg cells carry mixed populations of plastids.
Flowchart
FC 8.5 – Determining the outcome of a cross for plastid-controlled variegation: identify the branch bearing the female parent flower → green branch → all offspring green; white branch → all offspring white; variegated branch → offspring green, white and variegated in no fixed ratio → in every case ignore the pollen parent
The last point in that sequence is the one to remember: the pollen parent contributes nothing, so no fixed ratio appears in the offspring. There is nothing to segregate in a Mendelian sense, which is why cytoplasmic inheritance produces no \(3:1\), no \(1:2:1\) and no \(9:3:3:1\).
Cytoplasmic Male Sterility and Its Use in Agriculture
Mitochondrial genes can also be inherited cytoplasmically, and one such condition has become extremely valuable to plant breeders. In cytoplasmic male sterility, a mitochondrial gene prevents a plant from producing functional pollen, while leaving its egg cells perfectly normal. The condition passes only through the female line.
This solves a real difficulty. Hybrid seed gives higher yields than either parent, but producing it requires that the female parent must not pollinate itself — which in a large field would mean removing the anthers from every flower by hand, exactly the emasculation step described earlier for a single pea flower. A male-sterile female parent makes its own pollen unusable, so the emasculation happens by itself and hybrid seed can be produced on a commercial scale. Cytoplasmic male sterility has been used in this way in maize, sorghum, rice, sunflower and several vegetable crops.
Mitochondrial Inheritance in Human Beings
Human mitochondria come almost entirely from the egg, so disorders caused by faults in mitochondrial DNA show a very distinctive pattern in a family. An affected woman transmits the condition to all of her children, sons and daughters alike, but an affected man transmits it to none of his. Certain inherited disorders of vision and of muscle function follow this pattern.
Diagram
Fig. 8.15 – A three-generation family tree showing mitochondrial inheritance: every child of an affected mother is affected, while no child of an affected father is affected; contrast this in the same figure with the pattern expected for an autosomal dominant character.
Because the mitochondria in every cell of a person’s body trace back to a single egg, mitochondrial DNA is also widely used to trace maternal ancestry over long stretches of time.
8.8 Pedigree Construction and Standard Symbols
Everything established so far came from controlled crosses. A geneticist chose the parents, arranged the mating, raised hundreds of offspring and counted them. None of this is possible with human beings. Human families are small, a generation takes twenty-five years or more, and — decisively — people cannot be bred to order.
Human genetics therefore works backwards. Instead of designing a cross and waiting for the result, the geneticist takes a family in which a character already appears, records how that character is distributed among the relatives, and reasons from the record to the mode of inheritance. The record itself is called a pedigree.
The Standard Symbols
Pedigrees are read by people all over the world, so the symbols are fixed by convention. Using them correctly is a marked skill in the examination, and a diagram drawn with private symbols cannot be read by anyone else.
| Symbol | Meaning |
|---|---|
| Square | Male |
| Circle | Female |
| Diamond | Individual of unspecified or unknown sex |
| Unshaded symbol | Individual not showing the character |
| Fully shaded symbol | Individual showing the character (affected) |
| Symbol with a central dot, or half shading | Carrier — heterozygous but not showing the character |
| Symbol with a diagonal line through it | Individual who has died |
| Horizontal line joining a square and a circle | A mating or marriage |
| Double horizontal line joining them | A consanguineous marriage, that is, between close relatives |
| Short vertical line dropping from the mating line | Line of descent to the children |
| Horizontal sibship line with vertical lines below | The children of that mating, drawn in birth order from left to right |
| Two lines from a single point | Twins; joined by a horizontal bar at the top if identical |
| Arrow, usually labelled P | The proband — the individual through whom the family first came to notice |
| A number written inside a symbol | That many individuals of the same sex and status, drawn as one symbol to save space |
Diagram
Fig. 8.16 – Chart of the standard pedigree symbols listed above, each drawn accurately and labelled, arranged in groups: individuals, affected status, relationships and special notations.
Generations are numbered with Roman numerals (I, II, III …) written down the left-hand margin, the oldest generation at the top. Within each generation, individuals are numbered with Arabic numerals from left to right. Any person in the family can then be named exactly — II-3 means the third individual from the left in the second generation — which is how family members are referred to in a report or an examination answer.
Reading the Common Patterns
Four questions asked of a completed pedigree will usually settle the mode of inheritance.
Does an affected child ever have two unaffected parents? If so, the character must be recessive, since it lay hidden in both parents. If every affected individual has at least one affected parent, the character is more likely to be dominant.
Does the character appear in every generation? A dominant character cannot skip a generation, because it is expressed whenever it is present. A recessive character skips generations freely, travelling unseen through heterozygous carriers.
Are males and females affected in roughly equal numbers? If yes, the gene is autosomal — it lies on one of the ordinary chromosomes. A marked excess of affected males points to a gene on the X chromosome, taken up in the next section.
Is there a consanguineous marriage in the family? Rare recessive characters appear far more often among the children of closely related parents, because relatives are more likely to carry the same rare allele inherited from a common ancestor.
Diagram
Fig. 8.17 – Two contrasting pedigrees drawn side by side over three generations. (a) An autosomal dominant character: affected individuals in every generation, both sexes affected, every affected child having an affected parent. (b) An autosomal recessive character: the character absent in generation II and reappearing in generation III, with carrier individuals marked by a central dot.
Constructing a pedigree is one of the ISC practical exercises: simple, harmless human traits such as the ability to roll the tongue, free or attached earlobes and the presence of a widow’s peak are recorded across a student’s own family and drawn up using exactly these symbols. Working with such traits, rather than with disorders, gives the skill without raising any of the difficulties described below.
8.9 Sex Chromosome Inheritance: Colour Blindness and Haemophilia
Of the 23 pairs of chromosomes in a human body cell, 22 pairs are alike in both sexes. These are the autosomes. The remaining pair differs between the sexes and determines sex itself; these are the sex chromosomes. A woman’s cells contain two X chromosomes, written 44 + XX, and a man’s contain one X and one Y, written 44 + XY.
Every character considered so far has been carried on an autosome, and autosomal characters are inherited identically by sons and daughters. Characters carried on the sex chromosomes are not, and the reason is a simple matter of size.
Why the X and the Y Behave Unequally
The X chromosome is comparatively large and carries a substantial number of genes, most of which have nothing to do with sex — genes for blood clotting, for colour vision, for muscle proteins and much else. The Y chromosome is much smaller and carries few genes, chiefly those that direct the development of male characteristics.
The two chromosomes pair with each other during meiosis only along short regions at their ends, where they do share the same genes. Along the rest of their length they are non-homologous: for most of the genes on the X chromosome there is simply no corresponding gene on the Y.
Diagram
Fig. 8.18 – The human X and Y chromosomes drawn to relative scale side by side, with the short homologous regions at the ends shaded and the long non-homologous region of the X marked, carrying labelled loci for colour vision and blood clotting.
The consequence was met when hemizygosity was defined. A woman has two copies of every X-linked gene and can therefore be homozygous or heterozygous for it. A man has only one copy, with nothing on the Y to pair with it, so whatever allele he carries on his single X is expressed — dominant or recessive alike. There is no second allele available to mask anything.
Genes lying on the non-homologous part of the X chromosome are said to be X-linked, and characters controlled by them show X-chromosomal inheritance.
The Pattern to Expect
Four features identify an X-linked recessive character in a family, and they follow directly from the physical facts above.
- Far more males are affected than females. A male needs only one copy of the recessive allele; a female needs two.
- A father never transmits the character to his son. A son receives his father’s Y chromosome, not his X, so the allele cannot travel from father to son.
- An affected father transmits the allele to every one of his daughters, since each daughter must receive his only X chromosome. Those daughters are heterozygous carriers — they do not show the character but can pass it on.
- A carrier mother transmits the allele to half her sons on average, and those sons are affected.
Putting points 3 and 4 together gives the pattern known as criss-cross inheritance: the character passes from an affected father, through his unaffected daughter, to appear again in her son — that is, from a man to his grandson through a daughter, skipping the intervening generation entirely.
Flowchart
FC 8.6 – Criss-cross inheritance: affected father (\(X^cY\)) → passes his \(X^c\) to all daughters → daughters are unaffected carriers (\(X^CX^c\)) → each carrier daughter passes \(X^c\) to half her children → half her sons are affected (\(X^cY\)) and half her daughters are carriers
Colour Blindness
The commonest form of colour blindness is red–green colour blindness, in which a person cannot distinguish reliably between red and green shades. It arises from a recessive allele of a gene on the X chromosome that is responsible for one of the light-sensitive pigments in the cone cells of the retina.
Writing \(X^C\) for the normal allele and \(X^c\) for the allele for colour blindness, five genotypes are possible in the population — three in women and two in men.
| Genotype | Sex | Phenotype |
|---|---|---|
| \(X^CX^C\) | Female | Normal vision |
| \(X^CX^c\) | Female | Normal vision, but a carrier |
| \(X^cX^c\) | Female | Colour blind |
| \(X^CY\) | Male | Normal vision |
| \(X^cY\) | Male | Colour blind |
Consider the commonest situation: a carrier woman (\(X^CX^c\)) marries a man with normal vision (\(X^CY\)). She produces two kinds of egg, \(X^C\) and \(X^c\), in equal numbers; he produces \(X^C\) sperm and \(Y\) sperm in equal numbers. The four equally likely combinations give one normal daughter, one carrier daughter, one normal son and one colour-blind son.
Diagram
Fig. 8.19 – Punnett square for the cross \(X^CX^c\) (carrier mother) × \(X^CY\) (normal father), showing the four offspring \(X^CX^C\), \(X^CX^c\), \(X^CY\) and \(X^cY\), with phenotypes labelled beneath each.
So half the sons of a carrier mother are expected to be colour blind, while none of her daughters is affected — though half of them are carriers in their turn. It is worth noticing that a carrier mother’s daughters cannot be told apart by looking at them; here, as so often, only the pedigree reveals the genotype.
Now reverse the situation. A colour-blind man (\(X^cY\)) marries a woman with normal vision who is not a carrier (\(X^CX^C\)). Every daughter receives his \(X^c\) and her \(X^C\), so all the daughters are carriers with normal vision; every son receives his Y and her \(X^C\), so all the sons have normal vision. Not one child shows the character, yet the allele has passed to the next generation through every daughter.
Haemophilia
Haemophilia is an X-linked recessive disorder in which the blood fails to clot normally. The recessive allele results in the absence, or the severe deficiency, of one of the proteins required in the chain of reactions that forms a clot. A small cut therefore bleeds for a very long time, and bleeding into joints and muscles after minor knocks causes swelling, pain and long-term damage. It is sometimes called the bleeder’s disease.
Its inheritance follows exactly the pattern set out above, and the family described at the opening of this chapter is the textbook illustration of it: unaffected carrier women in one generation, affected sons in the next, the condition travelling through the female line while showing itself in males.
Diagram
Fig. 8.20 – A four-generation pedigree of an X-linked recessive disorder, using the standard symbols of the previous section: carrier females marked with a central dot, affected males fully shaded, and arrows tracing the allele from an affected male through his carrier daughters to his affected grandsons.
Affected women are extremely rare, for the reason given in the sidebar above: a girl would need a haemophilic father and a mother who is at least a carrier.
A Note on Y-linked Characters
A few genes lie on the non-homologous portion of the Y chromosome. Characters controlled by them are called Y-linked or holandric characters, and they show the simplest pattern of all: they pass from father to every son and to no daughter, appearing in an unbroken male line. Since the Y chromosome carries very few genes, such characters are correspondingly few, which is why X-chromosomal inheritance is the case that matters in practice.
8.10 Summary
Heredity is the transmission of characters from parents to offspring; genetics is the scientific study of heredity and of the variation that goes with it. Offspring always resemble their parents without being identical to them, and explaining both facts together is the central problem of the subject.
Gregor Johann Mendel (1822–1884), working on the garden pea Pisum sativum from 1856, established the basic laws of inheritance. His decisive innovation was to count the offspring of every cross rather than merely describe them, which is why he is regarded as the Father of Genetics.
His results were presented in 1865 and printed the following year, but went unnoticed for about thirty-five years until de Vries, Correns and von Tschermak independently reached similar conclusions in 1900 and rediscovered his paper.
The pea was a fortunate choice because it shows clear contrasting traits, has a short life cycle, is naturally self-pollinating so pure lines are maintained, can be cross-pollinated by hand, has a flower structure that excludes stray pollen, and yields large numbers of seeds for counting.
A controlled cross requires emasculation of the female parent’s flower bud followed by bagging, then hand pollination and re-bagging. Skipping emasculation allows self-pollination; skipping bagging allows unknown pollen in, and either error destroys the experiment.
A monohybrid cross involves parents differing in one pair of contrasting characters. Pure tall (TT) × pure dwarf (tt) gives an all-tall \(F_1\) (Tt) and an \(F_2\) of 3 tall : 1 dwarf.
The Law of Dominance states that when two contrasting characters are brought together, only one — the dominant — appears in the \(F_1\), while the other — the recessive — remains hidden but unchanged.
The Law of Segregation states that the two alleles of a character do not blend but separate during gamete formation, so that every gamete carries only one of them. It is also called the law of purity of gametes.
The \(F_2\) of a monohybrid cross gives a phenotypic ratio of 3 : 1 but a genotypic ratio of 1 : 2 : 1, because the three tall plants are not alike — one is TT and two are Tt.
A test cross is a cross with the homozygous recessive type and reveals whether an individual showing the dominant character is homozygous (all offspring dominant) or heterozygous (1 : 1). An out cross, with the homozygous dominant type, gives all dominant offspring either way and therefore cannot reveal the genotype.
A dihybrid cross involves two pairs of contrasting characters. RRYY × rryy gives an \(F_1\) of RrYy, and self-pollination gives an \(F_2\) of 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green.
The Law of Independent Assortment states that the alleles of one gene are distributed into the gametes independently of the alleles of another gene. Its physical basis is the independent orientation of different homologous pairs at metaphase I, so it holds only for genes on different chromosomes.
The appearance of round–green and wrinkled–yellow seeds, absent from both grandparents, is the real evidence for independent assortment; the \(9:3:3:1\) ratio can also be obtained by multiplying the separate \(\tfrac{3}{4}\) and \(\tfrac{1}{4}\) probabilities of the two characters.
A dihybrid test cross gives a 1 : 1 : 1 : 1 ratio, which is a direct display of the four gamete types produced by the heterozygote.
A trait is an observable character; a gene is a segment of DNA at a fixed locus that controls it; alleles are the alternative forms of the same gene occupying the same locus on homologous chromosomes.
Genotype is the genetic constitution of an organism and phenotype is its observable expression. The same genotype can give different phenotypes in different environments, and different genotypes (TT and Tt) can give the same phenotype.
An individual is homozygous when it carries two identical alleles, heterozygous when it carries two different alleles, and hemizygous when only one allele is present because the homologous partner is absent — as in a human male for genes on the X chromosome.
Dominance describes how one allele behaves in the presence of another; it says nothing about how common that allele is in a population.
In incomplete dominance neither allele is fully expressed and the heterozygote is intermediate, as in the pink flowers of Mirabilis jalapa and the blue plumage of Andalusian fowls. The \(F_2\) gives 1 : 2 : 1 for both phenotype and genotype, and such an intermediate type can never breed true.
In co-dominance both alleles are fully and separately expressed in the heterozygote, as in the roan coat of cattle, where individual hairs are either red or white, and in the AB and MN blood groups of humans.
Multiple allelism is the existence of three or more alleles of one gene in a population, of which any individual carries only two. The ABO blood group system is governed by three alleles, \(I^A\), \(I^B\) and \(i\); \(I^A\) and \(I^B\) are co-dominant with each other and both are dominant over \(i\).
Polygenic inheritance is the control of one character by several genes with small additive effects, producing continuous variation and a bell-shaped distribution — as in grain colour in wheat, where three gene pairs give seven \(F_2\) classes in the ratio \(1:6:15:20:15:6:1\), and in human height and skin colour.
For \(n\) contributing gene pairs the number of \(F_2\) phenotypic classes is \(2n+1\) and the frequency of either extreme phenotype is \(1/4^{\,n}\). Polygenic characters are also strongly influenced by the environment.
Pleiotropy is the reverse relationship: one gene influencing several apparently unrelated characters, because a single gene product takes part in several pathways. The seed shape gene of pea, the sickle cell allele and the phenylketonuria gene are examples.
Cytoplasmic inheritance involves genes in the DNA of mitochondria and plastids rather than on nuclear chromosomes. Because the egg supplies almost all the cytoplasm of the zygote, such characters are transmitted through the mother alone, in no fixed ratio.
Reciprocal crosses giving unlike results are the standard test for cytoplasmic inheritance, since nuclear genes give identical results in both directions of a cross.
In plastidial inheritance, random distribution of normal and defective plastids during cell division — sorting out — produces green, white and variegated regions, and the offspring of a cross depend entirely on the branch bearing the female parent flower.
Cytoplasmic male sterility, a mitochondrial condition, is used to produce hybrid seed without hand emasculation; over-reliance on a single male-sterile cytoplasm in maize contributed to a major disease epidemic in 1970.
Human mitochondrial disorders pass from an affected mother to all her children and from an affected father to none.
A pedigree is a diagram of the occurrence of a character across the generations of a family, drawn with standard symbols: square for male, circle for female, shaded for affected, dotted for carrier, double line for a consanguineous marriage, Roman numerals for generations and Arabic numerals for individuals.
A pedigree is read by asking whether affected children have unaffected parents (recessive), whether the character appears in every generation (dominant), whether both sexes are equally affected (autosomal), and whether close relatives have married (raising the chance of a rare recessive appearing).
Of the 23 human chromosome pairs, 22 are autosomes and one is the sex chromosome pair — XX in females and XY in males. The X carries many genes unrelated to sex; the small Y carries few, and for most X genes there is no partner on the Y.
X-linked recessive characters are expressed in every male who carries the allele but only in a female who carries it twice. Hence far more males are affected, a father never passes the character to a son, all daughters of an affected father are carriers, and half the sons of a carrier mother are affected — the pattern called criss-cross inheritance.
Red–green colour blindness and haemophilia are the standard examples of X-linked recessive inheritance. Affected females are rare because they require a contribution from both parents.
Y-linked or holandric characters are few, and pass from father to every son and to no daughter.
Flowchart
FC 8.7 – The logic of the whole chapter: parents carry paired alleles → alleles segregate cleanly into gametes (Law of Segregation) → different gene pairs assort independently (Law of Independent Assortment) → random fertilisation combines them → the phenotype depends on the relationship between the alleles present → complete dominance gives 3 : 1 and 9 : 3 : 3 : 1; incomplete dominance and co-dominance give 1 : 2 : 1; many genes acting together give continuous variation; one gene acting widely gives pleiotropy → genes outside the nucleus follow the mother alone → genes on the X chromosome follow the sexes unequally
8.11 Key Terms
Heredity the transmission of characters from parents to their offspring.
Genetics the scientific study of heredity and of the variation that accompanies it.
Pure line a stock that breeds true for a character generation after generation, because it is homozygous for that character.
Emasculation the removal of the immature anthers from a flower before they shed pollen, so that the flower cannot pollinate itself and a controlled cross can be made.
Monohybrid cross a cross between two parents differing in a single pair of contrasting characters.
Filial generation the offspring generation of a cross; the first is written \(F_1\) and the generation obtained from it is written \(F_2\).
Dominant allele an allele that expresses itself both in the homozygous and in the heterozygous condition, masking its recessive partner.
Recessive allele an allele that expresses itself only in the homozygous condition, that is, only when no dominant allele is present.
Law of Dominance when two contrasting characters are brought together, only the dominant one appears in the \(F_1\) generation while the recessive one remains hidden.
Law of Segregation the two alleles of a character do not blend but separate during gamete formation, so that each gamete carries only one of them; also called the law of purity of gametes.
Punnett square a chequer board in which the gametes of the two parents are set along the top and the side, so that every possible combination at fertilisation can be read off.
Phenotypic ratio the proportion in which the different appearances occur among the offspring of a cross, such as 3 : 1 in a monohybrid \(F_2\).
Genotypic ratio the proportion in which the different genetic constitutions occur among the offspring of a cross, such as 1 : 2 : 1 in a monohybrid \(F_2\).
Back cross a cross of an individual with one of its own parental types.
Test cross a cross with the homozygous recessive type, used to find whether an individual showing a dominant character is homozygous or heterozygous.
Out cross a cross with the homozygous dominant type, which gives all dominant offspring and therefore cannot reveal the genotype being tested.
Dihybrid cross a cross between two parents differing in two pairs of contrasting characters.
Law of Independent Assortment the alleles of one gene pair are distributed into the gametes independently of the alleles of another gene pair, provided the two genes lie on different chromosomes.
Trait an observable or measurable characteristic of an organism; also called a character.
Gene the unit of inheritance — a segment of DNA at a definite position on a chromosome, controlling a particular trait.
Locus the fixed position occupied by a particular gene on its chromosome.
Allele one of the alternative forms of the same gene, occupying the same locus on homologous chromosomes.
Genotype the genetic constitution of an organism, written in terms of the alleles it carries.
Phenotype the observable expression of an organism’s genotype, as shaped by the environment in which it develops.
Homozygous carrying two identical alleles of a gene, and therefore breeding true for that character.
Heterozygous carrying two different alleles of a gene, and therefore not breeding true for that character.
Hemizygous carrying only one allele of a gene because the homologous partner locus is absent, as in a human male for genes on the X chromosome.
Incomplete dominance the condition in which neither allele is fully dominant, so that the heterozygote shows a phenotype intermediate between the two parents.
Co-dominance the condition in which both alleles are fully and separately expressed in the heterozygote, so that both parental characters appear together.
Multiple alleles three or more alternative forms of the same gene present at one locus in a population, of which any individual can carry only two.
Discontinuous variation variation in which individuals fall into a few sharply separated classes with no intermediates.
Continuous variation variation that grades smoothly across a range, with no natural dividing lines between individuals.
Polygenic inheritance the control of a single character by two or more genes whose small effects add together, producing continuous variation.
Pleiotropy the condition in which a single gene influences two or more apparently unrelated characters of an organism.
Cytoplasmic inheritance the transmission of characters controlled by genes in the DNA of mitochondria and plastids rather than by nuclear genes, and therefore inherited almost entirely through the mother.
Plastidial inheritance cytoplasmic inheritance in which the genes concerned lie in the DNA of the plastids, as in leaf variegation.
Reciprocal cross a pair of crosses made in both directions, used to detect cytoplasmic inheritance, which alone gives unlike results in the two directions.
Sorting out the random separation of two kinds of plastid into different cell lines during repeated cell division, producing the green and white patches of a variegated leaf.
Cytoplasmic male sterility a maternally inherited mitochondrial condition in which a plant cannot produce functional pollen, used to avoid hand emasculation in hybrid seed production.
Pedigree a diagram showing the occurrence of a character across the successive generations of a family, drawn with standard symbols.
Proband the individual through whom a family first came to notice, marked in a pedigree by an arrow.
Carrier a heterozygous individual who does not show a recessive character but can transmit it to the next generation.
Consanguineous marriage a marriage between close relatives, shown in a pedigree by a double horizontal line, which raises the chance of rare recessive characters appearing.
Autosome any chromosome other than a sex chromosome; human body cells contain 44 autosomes.
Sex chromosomes the chromosome pair that differs between the sexes — XX in a human female and XY in a human male.
X-linked gene a gene carried on the X chromosome, usually with no corresponding gene on the Y.
Criss-cross inheritance the pattern in which an X-linked recessive allele passes from an affected father through all his carrier daughters to reappear in half of their sons.
Colour blindness an X-linked recessive condition in which certain shades of red and green cannot be distinguished, owing to a defective cone pigment.
Haemophilia an X-linked recessive disorder of blood clotting caused by deficiency of a clotting factor — factor VIII in haemophilia A and factor IX in haemophilia B.
Holandric gene a gene carried on the Y chromosome, passing from father to every son and to no daughter.
8.12 Points to Ponder
Mendel’s paper was available in print for about thirty-five years before anyone acted on it. What does this tell you about how scientific ideas gain acceptance? Is being correct enough, or does a discovery also need the surrounding science to be ready for it?
Mendel worked with seven characters in pea, and every one of them turned out to behave independently. Later work showed that pea has only seven pairs of chromosomes. Was Mendel fortunate, or would his laws have emerged anyway from a less convenient set of characters? Consider what he might have concluded if two of his characters had been closely linked.
A pure line is genetically uniform, which is exactly what makes it useful in an experiment. The same uniformity, spread across a whole region’s fields, is what made the maize crop of 1970 so vulnerable. When is genetic uniformity an advantage and when is it a danger?
Dominance is often spoken of as though it meant “stronger” or “better”. Take a recessive allele that is extremely common in a population and a dominant allele that is very rare, and explain to yourself why neither frequency nor usefulness has anything to do with dominance.
The phenotype is described as the expression of the genotype in an environment. If two children with the same genetic potential for height grow up with very different nutrition, how much of the difference in their adult heights should be called genetic? What does this suggest about claims that any human ability is simply “in the genes”?
Blood grouping can prove that a man is not a child’s father but can never prove that he is. Why does a test that excludes carry so much less risk of injustice than a test that appears to confirm? Consider how a result should be worded so that a person without training in genetics does not over-read it.
A pedigree drawn about one patient records information about relatives who were never asked and may not wish to know. Where would you draw the line between a doctor’s duty to warn a relative at risk and a patient’s right to confidentiality?
Mitochondrial replacement can spare a family a severe inherited disorder, but the change is made to the germ line and will be carried by every descendant in the female line. Should a decision whose consequences fall entirely on people not yet born be taken by their parents, by doctors, or by the state?
X-linked recessive disorders fall overwhelmingly on males, while the women who transmit them show nothing at all. What burdens — medical, social and emotional — does this asymmetry place on carrier women, and how should genetic counselling take account of them?
Colour blindness is used to screen candidates out of certain occupations. Is such screening a reasonable safety measure, an unfair exclusion, or something that depends entirely on the job in question? Frame the strongest case on each side before deciding.
Cytoplasmic male sterility saves a breeder the labour of emasculating flowers by hand. Trace the chain from a single mitochondrial gene to the price of hybrid seed in a market, and consider how many steps in that chain a farmer buying the seed would ever see.
Mendel worked out the laws of inheritance without any knowledge of chromosomes, genes or DNA. Nothing discovered since has overturned them. What does that survival say about the difference between a description of a pattern and an explanation of its mechanism, and about which of the two lasts longer?
Continuous variation was once thought to disprove Mendelian inheritance, since it produces no ratios at all. Explain to yourself how a theory built on sharp classes turned out to account for smooth variation as well, and what that episode suggests about apparent exceptions to a scientific law.
If a simple genetic test could tell a couple, before a child was born, that the child would be a carrier of a recessive disorder but would never be affected by it — should they be told? Would your answer change if the test result concerned a condition that appears only in middle age?
8.13 Objective Questions
- Mendel allowed his \(F_1\) tall plants to self-pollinate rather than crossing them with the dwarf parent. The chief advantage of doing so was that it:
- produced a larger number of seeds
- allowed the hidden recessive character to reappear
- removed the need for emasculation
- prevented independent assortment
- Emasculation is carried out on the flower of the female parent in order to:
- remove the stigma before pollination
- prevent self-pollination
- increase the number of ovules
- make the flower attractive to insects
- In Mendel’s monohybrid cross for stem height, the observed \(F_2\) count was 787 tall and 277 dwarf plants. This departure from an exact 3 : 1 ratio is best explained by:
- incomplete dominance of the tall allele
- the chance nature of fertilisation in a finite sample
- linkage between the two alleles
- an error in Mendel’s counting
- A gamete produced by a plant of genotype Tt can carry:
- both T and t
- either T or t, but never both
- a blend of T and t
- neither T nor t
- An \(F_1\) plant of genotype RrYy produces gametes of the types:
- RY and ry only
- Ry and rY only
- RY, Ry, rY and ry
- RR, Rr, Yy and yy
- The fraction of the \(F_2\) generation of a dihybrid cross that is homozygous for both recessive characters is:
- \(\tfrac{9}{16}\)
- \(\tfrac{3}{16}\)
- \(\tfrac{1}{16}\)
- \(\tfrac{1}{4}\)
- A dihybrid test cross gives offspring in the ratio 1 : 1 : 1 : 1. This ratio is a direct indication of:
- the phenotypes of the two parents
- the four kinds of gamete produced by the heterozygote
- incomplete dominance at both loci
- the number of chromosomes in the gamete
- The fixed position occupied by a gene on a chromosome is called its:
- allele
- locus
- genome
- centromere
- A human male is said to be hemizygous for genes on the X chromosome because he:
- carries two identical alleles of each such gene
- carries only one allele of each such gene
- carries the corresponding allele on the Y chromosome
- does not express such genes at all
- Two pea plants look alike but have different genotypes. This is possible when:
- one is homozygous dominant and the other heterozygous
- one is homozygous recessive and the other heterozygous
- both are homozygous recessive
- the character shows incomplete dominance
- In the roan coat of cattle, examination of the hide shows separate red hairs and white hairs rather than pink hairs. This observation establishes that the character shows:
- incomplete dominance
- co-dominance
- complete dominance
- polygenic inheritance
- A blue Andalusian fowl can never be made to breed true because:
- the blue allele is lethal in the homozygous condition
- blue birds are always sterile
- blue is the phenotype of the heterozygote
- blue plumage is controlled by cytoplasmic genes
- A person of blood group O has the genotype:
- \(I^AI^B\)
- \(I^Ai\)
- \(I^Bi\)
- \(ii\)
- Although the ABO blood group system has three alleles, any one person can carry only two of them. The reason is that:
- the third allele is always recessive
- there are only two homologous chromosomes carrying that locus
- one allele is destroyed during gamete formation
- the alleles are co-dominant
- A character controlled by three pairs of polygenes acting cumulatively will show, in the \(F_2\) generation, a total number of phenotypic classes equal to:
- 3
- 4
- 7
- 9
- Which of the following is the best example of pleiotropy?
- Height in human beings
- Grain colour in wheat
- The sickle cell allele affecting red cell shape, spleen size and malaria resistance
- Seed shape and seed colour assorting independently in pea
- Reciprocal crosses give unlike results in the two directions. This is the standard indication of:
- co-dominance
- cytoplasmic inheritance
- polygenic inheritance
- complete dominance
- A flower borne on a wholly white branch of a variegated plant is pollinated by pollen from a wholly green branch. The offspring will be:
- all green
- all white
- all variegated
- green and white in the ratio 3 : 1
- Cytoplasmic male sterility is valued by plant breeders chiefly because it:
- increases the number of seeds per plant
- removes the need for emasculation by hand
- makes the crop resistant to disease
- allows the plant to be propagated by cuttings
- In a pedigree, a double horizontal line joining a square and a circle indicates:
- a mating that produced no children
- a consanguineous marriage
- identical twins
- an affected couple
- In a pedigree, an affected child is born to two unaffected parents. The character concerned must be:
- dominant
- recessive
- Y-linked
- cytoplasmic
- The observation that rules out X linkage most decisively in a pedigree is:
- more affected males than affected females
- transmission from an affected father to his son
- an unaffected carrier mother
- the character skipping a generation
- A colour blind man marries a woman who is homozygous for normal vision. Among their children:
- all the sons will be colour blind
- all the daughters will be colour blind
- all the daughters will be carriers and all the sons normal
- half the sons and half the daughters will be colour blind
- Haemophilia A results from the deficiency of:
- factor VIII
- factor IX
- haemoglobin
- tyrosinase
- A gene carried on the Y chromosome, and therefore passing from father to every son and to no daughter, is described as:
- X-linked
- holandric
- pleiotropic
- hemizygous
Assertion (A): A test cross uses a homozygous recessive partner. Reason (R): A homozygous recessive parent can contribute only recessive alleles, so the offspring reveal the gametes of the parent being tested.
Assertion (A): An out cross cannot be used to determine whether an individual is homozygous or heterozygous. Reason (R): The dominant homozygous partner contributes a dominant allele to every offspring, so all offspring show the dominant character whatever the tested individual carries.
Assertion (A): The law of segregation is also called the law of purity of gametes. Reason (R): A gamete carries only one allele of a gene and never a mixture of the two.
Assertion (A): The law of independent assortment does not hold for every pair of genes. Reason (R): Genes lying close together on the same chromosome cannot be distributed into gametes independently of each other.
Assertion (A): Wherever the phenotypic and genotypic ratios of a monohybrid cross are identical, dominance is not complete. Reason (R): The heterozygote can be told apart from the homozygous dominant by its appearance.
Assertion (A): Incomplete dominance disproves the particulate nature of inheritance. Reason (R): The parental colours reappear unchanged in the \(F_2\) generation of a cross showing incomplete dominance.
Assertion (A): Multiple allelism is a property of a population rather than of an individual. Reason (R): An individual has only two homologous chromosomes and can therefore carry only two alleles of a gene at a time.
Assertion (A): Polygenic characters produce a bell-shaped distribution in which the extreme types are rare. Reason (R): There are many combinations of alleles that give an intermediate value, but only one that gives each extreme.
Assertion (A): Polygenic characters cannot be predicted from a Punnett square in the way that flower colour in pea can. Reason (R): Polygenic characters violate the law of segregation.
Assertion (A): Cytoplasmically inherited characters are transmitted almost entirely through the mother. Reason (R): The egg contributes nearly all the cytoplasm, and hence nearly all the mitochondria and plastids, of the zygote.
Assertion (A): Cytoplasmic inheritance produces no fixed Mendelian ratios in the offspring. Reason (R): Organelle genes do not lie on chromosomes and take no part in meiosis.
Assertion (A): X-linked recessive disorders appear far more often in males than in females. Reason (R): A male has only one X chromosome, so a recessive allele on it has no partner allele to mask it.
Assertion (A): An affected father transmits an X-linked recessive allele to all of his daughters. Reason (R): He has only one X chromosome, and every daughter must receive it.
Assertion (A): A dominant allele is always the commonest allele in a population. Reason (R): Dominance describes the behaviour of an allele in the presence of another allele, not its frequency.
Assertion (A): In a pedigree, an unaffected sibling of a child with an autosomal recessive disorder cannot be identified with certainty as a carrier. Reason (R): Such a sibling has a two in three chance of being heterozygous and a one in three chance of being homozygous normal.
A cross between tall (TT) and dwarf (tt) pea plants produces all tall offspring. What is the reason?
- Blending of traits
- Dominance of the tall allele
- Mutation in genes
- Independent assortment
- During gamete formation, alleles separate from each other. Which law explains this?
- Law of Dominance
- Law of Segregation
- Law of Independent Assortment
- Law of Purity of Gametes
- In a dihybrid cross, which ratio is expected in the \(F_2\) generation?
- 3 : 1
- 1 : 2 : 1
- 9 : 3 : 3 : 1
- 1 : 1
- A heterozygous individual expresses only one of its two traits. This is due to:
- Co-dominance
- Dominance
- Incomplete dominance
- Multiple allelism
- Which of the following best defines genotype?
- Physical appearance
- Genetic constitution
- Environmental effect
- Observable trait
- A plant with genotype Tt is crossed with tt. What will be the phenotypic ratio of the offspring?
- 1 : 1
- 3 : 1
- 9 : 3 : 3 : 1
- All tall
- A dihybrid cross results in four phenotypes. Which principle is being demonstrated?
- Segregation
- Dominance
- Independent assortment
- Co-dominance
- A test cross is used to determine:
- Phenotype
- Dominance
- Genotype
- Number of alleles in a population
- Crossing red and white flowers produces pink flowers. This is an example of:
- Co-dominance
- Incomplete dominance
- Complete dominance
- Multiple allelism
- A phenotypic ratio of 1 : 2 : 1 in the \(F_2\) generation indicates:
- Complete dominance
- Incomplete dominance or co-dominance
- Independent assortment
- Hemizygosity
- In co-dominance, the phenotype of the heterozygote shows:
- Only the dominant trait
- A blended trait
- Both traits equally expressed
- Only the recessive trait
- Which statement best evaluates Mendel’s laws?
- They explain all inheritance patterns
- They apply only to plants
- They explain basic inheritance but have exceptions
- They are incorrect
- Dominant traits are not always the commonest traits in a population because:
- They mutate frequently
- Frequency depends on allele distribution
- They are always advantageous
- They disappear quickly
- Which method is most reliable for determining the genotype of an individual showing a dominant character?
- Self-cross
- Test cross
- Out cross
- Reciprocal cross
Assertion (A): Gregor Johann Mendel is known as the Father of Genetics. Reason (R): He performed experiments on Pisum sativum to study inheritance.
Assertion (A): Heredity refers to the transmission of traits from parents to offspring. Reason (R): Genetics is the scientific study of heredity.
Assertion (A): The \(F_1\) generation of a monohybrid cross shows a uniform phenotype. Reason (R): A dominant allele expresses itself in the heterozygous condition.
Assertion (A): Recessive traits are not expressed in the \(F_1\) generation. Reason (R): Recessive alleles are completely lost during gamete formation.
Assertion (A): Independent assortment produces variation in the offspring. Reason (R): Alleles of different genes assort independently during gamete formation.
Assertion (A): Crossing Tt × Tt results in a 3 : 1 phenotypic ratio. Reason (R): Both alleles express equally in the heterozygous condition.
Assertion (A): A 1 : 2 : 1 phenotypic ratio indicates incomplete dominance. Reason (R): Both alleles influence the phenotype in the heterozygous condition.
Assertion (A): Dominant traits are always more frequent in a population. Reason (R): The frequency of a trait depends on allele distribution in the population.
Assertion (A): A dihybrid cross produces four phenotypes in the \(F_2\) generation. Reason (R): Two pairs of alleles assort independently.
Gregor Mendel is known as the ______ of Genetics.
The study of heredity is called ______.
A cross involving one pair of contrasting traits is called a ______ cross.
The physical appearance of an organism is known as its ______.
The trait that appears in the \(F_1\) generation is called the ______ trait.
During gamete formation, alleles separate according to the law of ______.
In a dihybrid cross, the phenotypic ratio observed in the \(F_2\) generation is ______.
When both alleles express equally in a trait, the phenomenon is called ______.
A cross between Tt and Tt produces a genotypic ratio of ______.
The crossing of \(F_1\) progeny with a homozygous recessive parent is called a ______ cross.
In incomplete dominance, the \(F_2\) phenotypic ratio is ______.
The reappearance of recessive traits in the \(F_2\) generation supports the law of ______.
The independent inheritance of seed shape and seed colour is explained by the law of ______.
The experiments on the ______ plant helped Mendel establish his laws of inheritance.
An allele that expresses itself only in the homozygous condition is called ______.
A cross involving two pairs of contrasting traits is termed a ______ cross.
The formation of pink flowers from red and white parents is an example of ______ dominance.
8.14 Check Your Concepts
Mendel’s decisive innovation was to count his offspring rather than merely describe them. Explain why counting, and not observation alone, was what allowed the laws of inheritance to be discovered.
Six features of the pea plant made it suitable for Mendel’s work. Choose the two that you consider most important, and justify your choice by explaining what would have gone wrong without each of them.
The steps of a controlled cross are given below in the wrong order. Rearrange them correctly and state, for each of the two bagging steps, what would happen if it were omitted.
- Dust pollen from the chosen male parent on the mature stigma
- Bag the flower
- Open the unopened flower bud of the female parent
- Collect and sow the seeds
- Remove the immature anthers
- Re-bag the flower until the pod develops
A student writes that in the \(F_1\) generation of a monohybrid cross “the dwarf allele is destroyed”. Identify the error, and describe the observation from the \(F_2\) generation that disproves the statement.
Why does a monohybrid cross give a phenotypic ratio of 3 : 1 but a genotypic ratio of 1 : 2 : 1? Explain what information is lost when only the phenotypes are counted.
What would happen to the \(F_2\) ratio of a monohybrid cross if only twelve seeds were collected instead of twelve hundred? Explain why this does not weaken Mendel’s law.
A breeder tests a violet-flowered pea plant with an out cross and obtains all violet-flowered offspring. He concludes that his plant is homozygous. Identify the flaw in his reasoning and describe the cross he should have performed instead.
Draw and label a Punnett square for the cross Tt × tt. Mark the phenotypes beneath each box and state the ratio obtained.
Explain why the appearance of round–green and wrinkled–yellow seeds in the \(F_2\) generation of a dihybrid cross is a more important result than the 9 : 3 : 3 : 1 ratio itself.
Using the multiplication of probabilities and not a Punnett square, work out the fraction of the \(F_2\) generation of a dihybrid cross that is round and green. Show your reasoning and state the condition that must be satisfied for this method to be valid.
Describe what happens at metaphase I of meiosis that gives independent assortment its physical basis. Explain how the same event, occurring differently, would produce a different set of gametes.
Under what circumstance does the law of independent assortment fail to hold? Explain why the \(9:3:3:1\) ratio can therefore be regarded as evidence about the position of two genes.
Distinguish between a gene and an allele, using the tall and dwarf characters of pea as your example. Why is it incorrect to describe T and t as “two genes”?
Two seedlings with identical genotypes are grown, one in rich soil and full sunlight and the other in poor soil and shade. They reach different heights. Does this contradict the statement that height is genetically controlled? Explain your answer using the terms genotype and phenotype.
A student states that a human male is “homozygous” for colour vision because he has only one allele. Correct this statement and explain why neither homozygous nor heterozygous is the appropriate term.
Compare incomplete dominance with co-dominance under the following headings: expression in the heterozygote, appearance of the heterozygote, the \(F_2\) phenotypic ratio, and one example of each.
Both incomplete dominance and co-dominance give an \(F_2\) ratio of 1 : 2 : 1. State the single question you would ask about the heterozygote in order to tell the two apart, and apply it to the roan coat of cattle.
Why does a pink-flowered four o’clock plant fail to breed true, however carefully a grower selects pink plants year after year?
Explain why the AB blood group has only one possible genotype while the A blood group has two. What does this imply about the certainty with which each person’s genotype can be read from a blood grouping test?
Match the items in Column I with those in Column II.
| Column I | Column II |
|---|---|
| a. \(I^AI^B\) | i. Cytoplasmic male sterility |
| b. \(X^CX^c\) | ii. Co-dominance in humans |
| c. Mitochondrial gene | iii. Unaffected carrier female |
| d. Wheat grain colour | iv. Criss-cross inheritance |
| e. Affected grandfather to affected grandson | v. Polygenic inheritance |
Distinguish between continuous and discontinuous variation, giving one example of each, and explain why continuous variation once appeared to contradict Mendelian inheritance.
Explain, using the idea of dosage, why the middle classes of a polygenic character are far commoner than the extreme classes.
Polygenic inheritance and pleiotropy are frequently confused. Set out the difference in a single sentence for each, and classify the following: grain yield in rice; a mutation altering both coat colour and fertility in a mouse; skin colour in humans.
Explain how a single change in the gene for the beta chain of haemoglobin can produce effects as different as anaemia, joint pain and resistance to malaria.
A geneticist wishes to establish whether a newly observed character in a plant is controlled by a nuclear gene or a cytoplasmic one. Describe the experiment she should perform and state the result that would point to each conclusion.
Why does cytoplasmic inheritance produce no fixed ratio in the offspring, when nuclear inheritance produces ratios as reliable as 3 : 1?
Explain how the process of sorting out produces the sharp green and white patches on a variegated leaf, rather than a uniformly pale leaf.
A seedling raised from a flower borne on a white branch of a variegated plant germinates but dies shortly afterwards. Explain both observations.
Explain how cytoplasmic male sterility removes the need for hand emasculation in the production of hybrid seed, and describe one risk that arises when a single sterile cytoplasm is used across a very large area.
Draw the standard pedigree symbols for the following, and label each: an affected male, an unaffected female, a carrier female, a consanguineous marriage, a deceased individual, and the proband.
State the four questions you would ask of a completed pedigree in order to identify the mode of inheritance, and explain what each answer tells you.
Explain why rare recessive characters appear more often among the children of closely related parents than among the children of unrelated parents.
In a pedigree, the mother of an affected child is certainly a carrier, but the child’s unaffected sister may or may not be. Explain the difference, and state the probability that the sister is a carrier for an autosomal recessive disorder.
A pedigree shows a character transmitted from an affected father to his son. Which two modes of inheritance can be ruled out at once, and why?
Explain what is meant by criss-cross inheritance, and describe the path an X-linked recessive allele takes from an affected man to an affected great-grandson.
Draw a labelled Punnett square for the cross \(X^CX^c \times X^CY\) and use it to explain why one child in four is expected to be colour blind, while the risk to any particular daughter is zero.
Why are colour blind women so much rarer than colour blind men? State the genotypes of both parents that would be required for a colour blind daughter to be born.
Explain why bleeding into a joint, rather than bleeding from a small cut, is the more serious consequence of haemophilia, and name the protein that is deficient in haemophilia A.
Compare autosomal recessive and X-linked recessive inheritance under the headings: sexes affected, genotype needed in a male, father-to-son transmission, and the status of the daughters of an affected father.
Holandric inheritance is sometimes described as the opposite of criss-cross inheritance. Explain why, and state why holandric genes are of limited importance in human genetics.
Who rediscovered Mendel’s work in 1900?
What is the term for the different forms of the same gene?
Name the organism used by Mendel for his experiments.
What is the unit of inheritance called?
What happens to the two alleles of a gene during gamete formation?
Why do \(F_1\) hybrids appear uniform in a monohybrid cross?
What is meant by genotype?
How can you determine whether a tall pea plant is homozygous or heterozygous?
Predict the phenotypes of the offspring when two heterozygous tall plants are crossed.
What will be the phenotype of the \(F_1\) generation when red and white flowers showing incomplete dominance are crossed?
Why does the recessive trait reappear in the \(F_2\) generation?
How does independent assortment increase variation?
Why is a test cross considered reliable in genetics?
Why do co-dominant traits not show blending?
Draw a cross to demonstrate the law of segregation.
Mention a situation in which co-dominance can be observed in humans.
Riya states that genetics explains inheritance. What term is used for the transmission of traits from parents to offspring?
Aarav observes two identical alleles for a character in a plant. What is this genetic condition called?
Meena reads about a cross involving two traits. What is such a cross known as?
Sohan notices that all \(F_1\) plants are tall when tall and dwarf plants are crossed. Explain why this happens.
Ananya says that genes do not blend in inheritance. Explain this statement with reference to Mendel’s findings.
Kabir observes variation in the \(F_2\) generation of a dihybrid cross. Explain why different combinations appear.
Neha learns about dominant and recessive alleles. Explain how the two differ in expression.
Priya crosses a homozygous round-seeded plant with a wrinkled-seeded plant. What will be the phenotype of the \(F_1\) generation? Explain.
Arjun performs a dihybrid cross and obtains four phenotypes. How can he confirm independent assortment from this result?
Vikram observes pink flowers when red and white flowers are crossed. Identify the genetic phenomenon and justify your answer.
Rohit compares monohybrid and dihybrid crosses. Explain how the number of traits followed affects the phenotypic ratio.
Aditya observes a 1 : 2 : 1 phenotypic ratio. What type of inheritance pattern does this suggest?
Nikhil argues that Mendel’s laws apply universally. Justify or refute this statement in the light of exceptions such as incomplete dominance.
Dev thinks that dominant traits are always more common in a population. Examine whether Dev’s view can be supported.
Isha says that a test cross is better than an out cross for genetic analysis. Explain this statement.
Aditi plans to demonstrate co-dominance using an example that occurs in humans. Suggest an appropriate example and explain how she would present it.
Ishita is preparing a chart on the history of genetics and includes the contributions of early scientists. She wants to mention the scientist who proposed the basic laws of inheritance and the organism he worked on. She also needs to state the year in which his work was rediscovered. Identify these key facts and explain their importance.
Manav is revising key genetic terms before an examination. He comes across the terms allele, homozygous and heterozygous but finds them confusing. Help him by defining these terms with suitable examples.
Tanya is making notes on Mendel’s experiments and wants to list the types of crosses he performed. Differentiate between monohybrid and dihybrid crosses on the basis of the number of traits involved, explaining both clearly.
Bhavya observes that pea plants produce consistent results over generations when self-pollinated. Explain how self-pollination contributes to maintaining pure lines and why this helped Mendel.
Devansh learns that traits are controlled by genes present on chromosomes, but is confused about how genotype and phenotype are related. Explain the relationship with an appropriate example.
Ritika studies Mendel’s law of dominance and notices that one trait masks the other in the \(F_1\) generation. She wonders how this masking occurs at the genetic level. Explain the concept in simple terms.
Harshit reads about independent assortment and observes new trait combinations in the offspring. He is curious why these combinations do not appear in the parents. Explain how this law leads to variation.
Nandini crosses two pea plants, both heterozygous for seed shape and seed colour. She observes four different phenotypes in the offspring. Apply Mendel’s principles to explain how these combinations arise.
Yuvraj suspects that a tall plant may be heterozygous but is unsure how to confirm this experimentally. Explain a suitable cross and the expected results.
Kritika observes that crossing two differently coloured flowers produces an intermediate colour in the next generation. Identify this pattern and explain the ratio expected in the generation after that.
Samar compares the results of monohybrid and dihybrid crosses and notices different phenotypic ratios. He wants to analyse how the number of gene pairs influences inheritance patterns. Explain this difference in detail.
Aarohi studies co-dominance and incomplete dominance and finds that both involve the expression of alleles. Analyse how these two patterns differ in phenotypic expression, with reasoning.
Parth claims that Mendel’s laws can explain all inheritance patterns without exception. However, his teacher mentions cases such as co-dominance and multiple allelism. Examine Parth’s claim with justification.
Raghav suggests that dominant alleles are always advantageous for survival. His classmate disagrees with this assumption. Examine this statement with suitable reasoning.
8.15 Case-Based Questions
- A student is given twelve tall pea plants raised from seed of unknown parentage and asked to identify which of them will breed true. She crosses each plant with a dwarf plant and grows about forty offspring from each cross. Seven of the plants give only tall offspring. Five of them give offspring that are roughly half tall and half dwarf.
- Name the cross the student has performed and state the principle on which it works.
- Give the genotypes of the seven plants and of the five plants.
- Explain why she could not have obtained this information by measuring the plants themselves.
- Suggest what she should conclude about one plant that gave only twelve offspring, all of them tall.
- A nursery sells four o’clock plants in three flower colours: red, pink and white. Customers who buy pink plants and raise seed from them complain that the seedlings do not all come out pink. The nursery owner examines her records and finds that seed from red plants gives only red seedlings, seed from white plants gives only white seedlings, but seed from pink plants gives all three colours.
- Name the type of inheritance shown by flower colour in this plant.
- Give the genotypes of the red, pink and white plants, using suitable symbols.
- State the ratio in which the three colours are expected among the seedlings raised from a pink plant.
- Explain to the nursery owner why she can never produce a pink variety that breeds true, and suggest how she could still supply customers with pink plants reliably.
- In a hospital, four newborn babies are accidentally mixed up in the nursery. Their blood groups are found to be A, B, AB and O. The four sets of parents have the following blood groups: couple 1, both group O; couple 2, group A and group B; couple 3, group AB and group O; couple 4, group A and group O.
- State the genotype of couple 1 and identify with certainty which baby belongs to them.
- Explain why couple 2 could, in principle, be the parents of more than one of the babies.
- Which baby could not possibly belong to couple 3? Justify your answer with genotypes.
- Comment on whether blood grouping alone is sufficient to assign every baby correctly, and state what such a test can and cannot establish.
- A couple attends a genetic counselling clinic. The wife’s brother has haemophilia; her parents and her husband are unaffected. The counsellor draws the family pedigree before advising them.
- State the mode of inheritance of haemophilia and give the genotype of the wife’s mother.
- Calculate the probability that the wife is a carrier, showing your reasoning.
- If the wife is a carrier, state the probability that a son of the couple will be affected and the probability that a daughter will be affected.
- The counsellor’s notes now contain information about the wife’s sister, who has never attended the clinic. Discuss briefly the difficulty this creates.
- A candidate applying for a job as a train driver is screened with Ishihara plates and is found to be red–green colour blind. He is surprised, since neither of his parents nor either of his two sisters has any difficulty with colour. He recalls that his mother’s father had the same difficulty.
- Explain how the candidate can be colour blind when neither of his parents is.
- Give the genotypes of the candidate, his mother and his maternal grandfather.
- State the probability that either of his sisters is a carrier.
- If the candidate has a daughter, state whether she can be colour blind and under what condition.
- A seed company produces hybrid maize on a large scale. Instead of employing labourers to remove the anthers from the flowers of the female parent line, it uses a female line carrying cytoplasmic male sterility. Production costs fall sharply. Some years later, an agricultural scientist advises the company to maintain several different sources of male-sterile cytoplasm rather than the single source it has been using.
- Explain why the male-sterile line must be used as the female parent and not as the pollen parent.
- State how the male sterility is inherited, and explain why it cannot be transmitted through pollen.
- Give the scientific reason behind the adviser’s recommendation.
- Suggest one further precaution the company could take to reduce the risk identified.
- A student performing the ISC practical on pedigree construction records the ability to roll the tongue in her own family. Her father and mother can both roll the tongue. Of their four children, three can roll the tongue and one cannot. Her father’s mother could not roll her tongue.
- Using the standard symbols, draw the pedigree for the three generations described, numbering the generations and the individuals correctly.
- State, with a reason drawn from the pedigree, whether the inability to roll the tongue is dominant or recessive.
- Give the genotypes of the student’s father and mother.
- Explain why a harmless trait of this kind is chosen for a school exercise rather than a disorder.
- A cattle breeder maintains a herd of roan animals. Every year he mates roan bulls with roan cows and is dissatisfied that his calves are never uniformly roan. A visiting veterinarian examines the hide of a roan animal under a hand lens and points out that it carries red hairs and white hairs side by side.
- Name the phenomenon that coat colour in these cattle illustrates, and justify the name using the veterinarian’s observation.
- Give the genotypes of the roan, red and white animals, and state the ratio expected among the calves of a roan × roan mating.
- Suggest a mating that would give the breeder a calf crop in which every animal is roan, and explain why it works.
- Explain why this character is not an example of incomplete dominance, even though the \(F_2\) ratio is the same.
- A gardener buys an ornamental plant whose leaves are patched with green and white. She takes cuttings and also raises seedlings. Seed collected from flowers on a fully green branch gives only green seedlings. Seed collected from flowers on a white branch gives seedlings that germinate but soon die. Seed collected from flowers on a variegated branch gives green, white and variegated seedlings in no fixed proportion.
- Name the type of inheritance shown by this character and state where the genes concerned are located.
- Explain why the pollen parent has no influence on the results.
- Account for the death of the seedlings raised from the white branch.
- Explain why no definite Mendelian ratio appears among the seedlings from the variegated branch.
- A wheat breeder crosses a variety with deep red grain with one having white grain. The \(F_1\) plants all have grain of an intermediate shade. In the \(F_2\) generation the breeder records seven distinguishable shades of grain colour, with the deepest and the palest being much the rarest.
- Name the type of inheritance shown, and calculate the number of gene pairs involved from the number of classes observed.
- State the expected ratio of the seven classes in the \(F_2\) generation.
- Calculate the fraction of the \(F_2\) generation expected to show either extreme phenotype.
- Explain why the breeder cannot select for deep red grain as quickly as a breeder selecting for a character controlled by a single gene.
- A physician notices that in one family, a disorder of muscle function is present in a woman, in all four of her children, and in all three children of her affected daughter. Her affected son, however, has two children, neither of whom is affected. Nobody in the family has been treated for a chromosomal disorder.
- Identify the mode of inheritance and give your reason.
- Explain why the affected son transmits the condition to none of his children.
- Explain why this pattern cannot be autosomal dominant, even though the character appears in every generation.
- Draw the three-generation pedigree described, using the standard symbols.
- A student sets up a dihybrid cross in pea for seed shape and seed colour and grows 320 seeds in the \(F_2\) generation. She records 182 round yellow, 59 round green, 61 wrinkled yellow and 18 wrinkled green. A classmate tells her the experiment has failed because the numbers do not match 9 : 3 : 3 : 1 exactly.
- Calculate the numbers expected in each class for 320 seeds on a 9 : 3 : 3 : 1 ratio.
- Comment on whether the classmate’s objection is justified, giving a reason.
- State which two of the four classes did not occur in either grandparent, and explain how they arose.
- Describe the single cross the student could perform on an \(F_1\) plant to display its four gamete types directly, and state the ratio she would expect.
- Ananya crosses a tall pea plant with a dwarf plant and observes that all \(F_1\) offspring are tall. She is puzzled that the dwarf trait did not appear in the first generation. Later, in the \(F_2\) generation, dwarf plants reappear. She wants to understand the genetic reason behind this pattern and to relate it to Mendel’s experiments.
- Why are all the \(F_1\) plants tall?
- Which law explains the masking of the dwarf trait?
- Why does the dwarf trait reappear in the \(F_2\) generation?
- Rohan studies that alleles occur in pairs and separate during gamete formation. He performs a cross and finds variation in the offspring. He wonders how traits remain distinct and do not blend, and tries to connect this observation with Mendel’s law.
- State the law responsible for the separation of alleles.
- What happens to the alleles during gamete formation?
- How does this law prevent the blending of traits?
- Ishita observes that when two traits are considered together, new combinations appear in the offspring. She crosses pea plants for seed colour and seed shape and finds phenotypes that were not present in the parents. She is curious about the reason for such variation and links her observation to Mendelian inheritance.
- Which law explains the formation of new combinations?
- What is the expected phenotypic ratio in the \(F_2\) generation?
- Why do these new combinations not appear in the parents?
- Kunal reads about dominant and recessive alleles. He notices that some traits mask others in the offspring, and that even though a recessive allele is present it is not expressed. He wants to understand the principle behind this observation and to relate it to Mendel’s findings.
- Define a dominant allele.
- Define a recessive allele.
- Which law explains this masking effect?
- Pooja crosses two heterozygous tall plants (Tt × Tt) and records both tall and dwarf plants in the offspring. She wants to calculate the expected genotypic and phenotypic ratios and to justify the result using Mendelian principles.
- What is the genotypic ratio?
- What is the phenotypic ratio?
- Which law explains this ratio?
- Aditya performs a dihybrid cross involving seed colour and seed shape. He observes four different phenotypes in the \(F_2\) generation and wants to verify whether independent assortment has occurred, and to determine the expected ratio.
- State the expected phenotypic ratio.
- Which law explains this result?
- What does this law state?
- Vivek crosses red and white flowers and obtains pink flowers in the \(F_1\) generation. He notices that neither parental trait is completely expressed. In the \(F_2\) generation he observes three types of phenotypes, and wants to identify this inheritance pattern and compare it with Mendelian dominance.
- Name the type of inheritance observed.
- What is the \(F_2\) phenotypic ratio?
- Why is neither trait completely dominant?
- Sakshi compares the results of monohybrid and dihybrid crosses and observes different phenotypic ratios in each case. She wants to analyse how the number of traits followed affects inheritance patterns and to relate this to Mendel’s laws, preparing a comparison chart for better understanding.
- What is the phenotypic ratio in a monohybrid cross?
- What is the phenotypic ratio in a dihybrid cross?
- Why do these ratios differ?
- Tanvi observes a 1 : 2 : 1 phenotypic ratio in a plant cross. She realises that this does not follow typical Mendelian dominance and wants to analyse which type of inheritance pattern is involved, comparing it carefully with complete dominance.
- Identify the inheritance pattern.
- What is the genotypic ratio in this case?
- How is it different from complete dominance?
- Mehak argues that Mendel’s laws apply to all inheritance patterns. Her teacher gives examples such as co-dominance and incomplete dominance, and she is asked to evaluate whether Mendel’s laws are universally applicable and to justify her answer with reasoning.
- Are Mendel’s laws universally applicable?
- Name one exception.
- Why do such exceptions occur?
- Diya thinks that dominant traits are always more common in a population. Her classmate disagrees with this idea. She is asked to evaluate whether dominance is related to frequency and to justify her answer with logic, considering real genetic examples.
- Are dominant traits always more common?
- Give a reason for your answer.
- Provide one example.
- Harsh compares a test cross and an out cross. He wants to evaluate which method is more reliable for determining genotype, analysing their outcomes and usefulness before deciding which is better for genetic analysis.
- What is a test cross?
- What is an out cross?
- Which method is more reliable, and why?
8.16 Practice With Data
In a monohybrid cross between two heterozygous tall pea plants, 1064 seeds are grown to maturity. Calculate (a) the expected number of dwarf plants, (b) the expected number of tall plants that are heterozygous, and (c) the expected number of tall plants that would breed true.
Mendel recorded 787 tall and 277 dwarf plants in the \(F_2\) generation of his cross for stem height. Calculate the observed ratio to two decimal places, calculate the numbers that would have been expected for a ratio of exactly 3 : 1 from the same total, and comment on the size of the difference.
A dihybrid cross in pea produces 1600 seeds in the \(F_2\) generation. Calculate the expected number of seeds in each of the four phenotypic classes, and then calculate the expected number that are homozygous for both characters.
The table gives the \(F_2\) results of four independent dihybrid crosses, each grown from a different number of seeds.
| Cross | Round yellow | Round green | Wrinkled yellow | Wrinkled green |
|---|---|---|---|---|
| I | 36 | 11 | 13 | 4 |
| II | 315 | 108 | 101 | 32 |
| III | 9 | 4 | 2 | 1 |
| IV | 566 | 190 | 187 | 65 |
Calculate the ratio obtained in each cross, reduced so that the smallest class is 1. State which cross gives the closest agreement with 9 : 3 : 3 : 1 and explain, in terms of sample size, why that is so.
An \(F_1\) plant of genotype RrYy is test crossed and 240 offspring are obtained. Calculate the expected number in each phenotypic class. If the actual counts were 96, 24, 22 and 98 for the four classes in the usual order, state whether the result is consistent with independent assortment and give a reason.
Using the multiplication of probabilities, calculate the fraction of the \(F_2\) generation of a trihybrid cross (AaBbCc × AaBbCc) that would show all three dominant characters, and the fraction that would be homozygous recessive for all three. Show the working for each.
In a school practical, yellow and green pea seeds are scattered on a table top and sampled with a quadrat of 30 cm × 30 cm divided into blocks of 6 cm × 6 cm. The counts obtained in eight blocks are given below.
| Block | Yellow seeds | Green seeds |
|---|---|---|
| 1 | 14 | 5 |
| 2 | 11 | 3 |
| 3 | 17 | 6 |
| 4 | 9 | 4 |
| 5 | 15 | 4 |
| 6 | 12 | 5 |
| 7 | 16 | 5 |
| 8 | 10 | 4 |
Calculate (a) the total number of blocks in the quadrat, (b) the frequency of each seed type over the eight blocks sampled, expressed as a percentage, and (c) the ratio of yellow to green seeds. State which Mendelian ratio this most closely resembles.
A character is controlled by five pairs of polygenes acting cumulatively. Calculate (a) the number of phenotypic classes expected in the \(F_2\) generation of a cross between two individuals heterozygous at all five loci, (b) the fraction of the \(F_2\) expected to show either extreme phenotype, and (c) the number of contributing alleles carried by an individual belonging to the middle class.
In a cross between wheat varieties differing at three gene pairs for grain colour, 1024 \(F_2\) plants are raised. Using the ratio 1 : 6 : 15 : 20 : 15 : 6 : 1, calculate the expected number of plants in each of the seven colour classes, and state how many would be expected to have grain as deeply coloured as the darker grandparent.
A woman of blood group AB marries a man of blood group O. Calculate the probability that (a) their first child will be of blood group A, (b) their first child will be of blood group O, and (c) their first two children will both be of blood group B.
In a survey of 2400 people, the blood groups recorded were: A, 720; B, 792; AB, 168; O, 720. Calculate the percentage of the sample in each group, and state which group must be homozygous in every individual counted. Explain why the number of people carrying the allele \(i\) is certainly greater than the number recorded as group O.
A carrier woman for colour blindness marries a man with normal colour vision. They have six children. Calculate (a) the probability that any one child is colour blind, (b) the probability that any one son is colour blind, and (c) the expected number of carrier daughters if three of the six children are girls.
In a population survey of 5000 men and 5000 women, 402 men and 21 women were found to be red–green colour blind. Calculate the percentage of affected individuals in each sex, calculate how many times commoner the condition is in men than in women, and explain the difference in terms of the number of X chromosomes each sex carries.
Two unaffected parents have an affected child with an autosomal recessive disorder. Calculate (a) the probability that their next child will be affected, (b) the probability that their next child will be an unaffected carrier, (c) the probability that an unaffected child of theirs is a carrier, and (d) the probability that their next two children will both be unaffected.
The histogram below is described by the following counts, obtained for plant height in an \(F_2\) population of 640 plants.
| Height class (cm) | Number of plants |
|---|---|
| 20–29 | 12 |
| 30–39 | 68 |
| 40–49 | 174 |
| 50–59 | 216 |
| 60–69 | 132 |
| 70–79 | 34 |
| 80–89 | 4 |
State the shape of the distribution, name the type of inheritance it indicates, and calculate the percentage of plants falling in the two extreme classes taken together. Explain why the middle classes are so much larger.