5.1.1 The genome

DNA, genes and chromosomes

1. DNA stores genetic information in its base sequence, the order of its bases.
2. In a plant or animal cell, most DNA is packaged with proteins into chromosomes in the nucleus.
3. A chromosome contains many genes, each occupying a particular position along its DNA.
4. The base sequence of a protein-coding gene determines the order of amino acids in a protein.
5. Proteins include enzymes, structural components and some hormones, so their activities help produce an organism's characteristics.
6. The genome includes both coding DNA and non-coding DNA, rather than only the genes that code for proteins.
7. Mitochondria also contain a small amount of DNA, and plant chloroplasts have DNA, so an organism's genetic material is not confined to its nuclear chromosomes.
8. Most nucleated body cells of an individual contain the same genetic information, although different cell types use different genes.

Alleles and characteristics

1. Individuals of the same species usually have the same types of genes but may carry different alleles of those genes.
2. For a gene on an ordinary chromosome pair, an individual inherits one allele from each parent.
3. A genotype describes the alleles present, whereas a phenotype describes the resulting observable or measurable characteristics.
4. A phenotype can include a physical feature, such as flower colour, or a biochemical characteristic, such as a blood group.
5. An organism's environment can also influence its phenotype, so knowing its genotype does not always predict its exact appearance or size.

Describing allele combinations

1. For a simple gene with a dominant and a recessive allele, use the same letter in upper and lower case, such as $A$ and $a$.
2. The genotypes $AA$ and $aa$ are homozygous because each contains two copies of the same allele.
3. The genotype $Aa$ is heterozygous because it contains two different alleles.
4. With complete dominance, both $AA$ and $Aa$ produce the dominant phenotype, whereas $aa$ produces the recessive phenotype.
5. A recessive allele is still present in a heterozygote and can be inherited even though it does not determine that individual's phenotype.

Gametes carry inherited information

1. Animal gametes are sperm cells and egg cells, which carry genetic information from parents to offspring.
2. The nucleus of each gamete carries one allele of each gene on an ordinary chromosome pair.
3. When gamete nuclei fuse at fertilisation, their genetic information combines in the first cell of the offspring.
4. This explains why an offspring inherits alleles from both parents while retaining its own combination of genetic information.

5.1.2 Environment and phenotype

Genes and environment shape phenotype

1. An organism's phenotype develops through the interaction of its genome with its environment.
2. Genetic differences arise because individuals inherit different alleles, while environmental differences arise from different conditions or experiences.
3. Blood group is an example of a characteristic largely determined by inherited alleles.
4. A scar is an acquired feature resulting from an injury and healing, rather than a new allele inherited from a parent.
5. Height depends on inherited factors and on conditions during growth, including nutrition and illness.
6. Body mass is influenced by inherited factors together with food intake, physical activity and other environmental conditions.
7. Plant growth depends on inherited characteristics together with the supply of light, water and mineral ions.

Comparing environmental effects

1. Identical twins have almost identical genomes but may develop different body masses or other characteristics when their experiences differ.
2. Clones are useful for investigating environmental effects because their inherited genetic differences are greatly reduced.
3. If genetically similar organisms develop different phenotypes under different conditions, this supports an environmental influence.
4. A fair comparison changes the environmental factor of interest while keeping other relevant conditions the same.
5. Simply finding a correlation between a condition and a characteristic does not prove that the condition caused the difference.

Continuous and discontinuous variation

1. Continuous variation produces a range of measurements with intermediate values, such as height, body mass or leaf length.
2. Recording height to the nearest centimetre does not make height discontinuous, because the gaps arise from measurement precision.
3. Discontinuous variation produces distinct categories, such as the blood groups $\mathrm{A}$, $\mathrm{B}$, $\mathrm{AB}$ and $\mathrm{O}$.
4. Eye colour can be recorded in categories for a survey, although real iris colour contains finer variation within those categories.
5. The pattern of variation and the cause of variation are different questions, so continuous does not mean environmental and discontinuous does not mean unaffected by the environment.

Displaying variation

1. For continuous measurements, group values into equal-width intervals and draw a histogram with touching bars.
2. Many large samples show values clustered near the middle with fewer at the extremes, but continuous data do not have to form a perfectly symmetrical bell shape.
3. For categorical data, draw a bar chart with a separate bar for each category and gaps between bars.
4. Label the horizontal axis with the measured characteristic and units or the category names, and label the vertical axis with frequency.

Calculating a mean

1. Calculate a mean by dividing the sum of the measurements by the number of measurements: $mean=\frac{sum\; of\; measurements}{number\; of\; measurements}$.
2. Retain the original measurement unit and inspect the spread as well as the mean when comparing samples.

5.1.3 Variants and mutations

Mutations produce variants

1. A mutation changes the sequence of bases in DNA and can create a genetic variant.
2. A variant within a gene may form a different allele of that gene.
3. All genetic variants originate through mutations, although an individual may inherit a variant that first arose many generations earlier.
4. Mutations can arise spontaneously, for example when DNA is copied, rather than occurring because an organism needs a useful characteristic.
5. Some environmental agents, including ionising radiation and certain chemicals, increase the frequency of mutations.
6. A substitution replaces a base, an insertion adds a base, and a deletion removes a base from a DNA sequence.

Variants have different effects

1. Most variants produce no detectable change in phenotype, so a DNA difference does not necessarily produce a visible difference.
2. Some variants influence a characteristic without deciding it completely, because other genetic and environmental factors also contribute.
3. Very few variants have an effect large enough to determine a particular characteristic.
4. A variant may be harmful, beneficial or neutral, depending on its effect and the environment in which the organism lives.
5. A harmful effect can reduce survival or reproduction, whereas a beneficial effect can increase survival or reproduction in particular conditions.

Passing a variant to offspring

1. If a cell carrying a variant divides, its DNA can be copied into its descendant cells.
2. In sexual reproduction, a variant can be inherited when it is present in a gamete that contributes to fertilisation.
3. A mutation confined to an ordinary body cell is not normally passed to offspring through sexual reproduction.
4. Sexual reproduction brings existing alleles into new combinations, while mutation is the original source of new variants.

Interpreting evidence

1. When DNA sequences are supplied, compare corresponding positions to identify the changed base or an added or missing base.
2. Use the reported characteristic to decide whether the variant has no detected effect, influences the phenotype or determines the feature being considered.
3. A sequence difference alone is insufficient evidence that the organism will be harmed.

5.1.4 How genetic variants influence phenotype

Coding variants affect proteins

1. A gene's base sequence determines the amino acid sequence of the protein it codes for.
2. A variant in coding DNA may change the base sequence copied into messenger RNA, written $\mathrm{mRNA}$.
3. When the message is translated at a ribosome, the changed sequence may cause a different amino acid to be added to the protein.
4. The amino acid sequence affects how the chain folds into its specific three-dimensional shape.
5. A change in folding can alter the protein's structure and therefore its activity.
6. The resulting effect on a cell's processes may change the organism's phenotype.

Changes to an enzyme's active site

1. An enzyme binds its substrate at an active site with a complementary shape.
2. If a coding variant changes an amino acid important to folding, the enzyme's active site may change shape.
3. The substrate may then bind less effectively or fail to bind, so fewer enzyme-substrate complexes form.
4. The enzyme-controlled reaction may slow down or stop, changing the amount of product made.
5. If that product is a pigment, a reduced supply can change the colour of a tissue.

Protein changes can alter cells

1. The same reasoning applies to proteins other than enzymes, including transport proteins and structural proteins.
2. A variant affecting haemoglobin can alter how haemoglobin molecules behave and can cause red blood cells to become sickle-shaped under low-oxygen conditions.
3. The example links a DNA difference to a protein difference and then to a change in cell properties.

Non-coding variants affect expression

1. Some non-coding DNA regulates whether a gene is used and how much of its product is made.
2. A variant in a regulatory region can prevent the gene from being transcribed.
3. If transcription is prevented, no $\mathrm{mRNA}$ copy of that gene is produced.
4. Without the $\mathrm{mRNA}$ message, ribosomes cannot make that protein from the affected copy of the gene.
5. Other regulatory changes may increase or decrease transcription, altering the amount of protein produced.
6. A non-coding variant can therefore change phenotype even when the protein-coding sequence itself has not changed.

Distinguishing the two mechanisms

1. A coding variant can change what the protein is like and how effectively it works.
2. A non-coding regulatory variant can change whether, when or how much of a protein is made.
3. Both routes can affect the same characteristic, but the explanation must identify the route supported by the information given.
4. A variant outside an important coding or regulatory sequence may have no detectable phenotypic effect.

5.1.5 Asexual and sexual reproduction

Two ways to reproduce

1. Sexual reproduction combines genetic information when male and female gamete nuclei fuse.
2. The gametes usually come from two parents, although self-fertilisation can occur in some organisms.
3. The first cell formed is a zygote, which divides and develops into an offspring.
4. In animals, the gametes are sperm and eggs; in flowering plants, pollen delivers male gametes to an ovule containing an egg cell.
5. Asexual reproduction involves one parent and no fusion of gametes, usually producing offspring genetically identical to that parent.
6. In plants and animals, asexual reproduction involves mitosis, whereas bacteria reproduce by binary fission rather than mitosis.

Asexual reproduction can be rapid

1. One parent can reproduce without finding a mate, allowing an isolated organism to establish a population.
2. Less time and energy are required for mate attraction and mating, so offspring can often be produced rapidly in favourable conditions.
3. Repeated asexual reproduction can produce many offspring in a short period, allowing rapid use of available food or space.
4. Successful combinations of alleles are retained in clones, which is useful when the environment remains suitable.
5. Bacteria copy their DNA before binary fission, then divide to form two cells that can each reproduce again.
6. Strawberry plants produce runners that root and grow into new plants, while potato tubers can develop into new plants from their buds.
7. Yeast can reproduce asexually by budding, in which a small outgrowth receives a copied nucleus and separates from the parent cell.
8. A Hydra can form a bud that grows and separates into a new animal.

Clones share vulnerabilities

1. Asexual offspring usually have little genetic variation, apart from differences introduced by mutations.
2. If a disease can infect the parent, many genetically similar offspring may also be susceptible.
3. A change in temperature, food availability or other conditions may affect most members of a clone population in a similar way.
4. Rapid production of offspring is therefore less helpful if few can survive the changed conditions.
5. Clones can still develop different phenotypes when they experience different environments.

Sexual reproduction increases variation

1. Sexual reproduction usually produces offspring with different combinations of alleles.
2. This genetic variation makes it more likely that at least some offspring can survive a new disease or an environmental change.
3. Variation does not guarantee survival and does not mean that all sexually produced offspring are better suited to their surroundings.
4. Finding a mate, producing gametes and transferring them can require time and energy.
5. Fertilisation may fail, particularly when gametes are released into the environment or pollen does not reach a suitable flower.
6. Reproduction may therefore be slower or less reliable when population density is low.

Offspring number and survival

1. The number produced per reproductive event varies greatly among organisms and cannot be predicted from reproductive mode alone.
2. Many mammals produce relatively few young and invest substantial resources in pregnancy and parental care.
3. Many fish release large numbers of gametes, but only a fraction produce offspring that survive to adulthood.
4. Many flowering plants produce numerous seeds sexually, while runners may produce fewer new plants per event but establish them rapidly.
5. To compare reproductive success, consider offspring per event, frequency of reproduction, time to maturity and survival to reproductive age.
6. An organism that produces fewer young per event can still produce more surviving offspring over time if it reproduces frequently or its young survive well.

5.1.6 Haploid and diploid

One set or two sets

1. A set of chromosomes contains one of each chromosome type for that species.
2. A haploid nucleus contains one set, represented by $n$, while a diploid nucleus contains two sets, represented by $2n$.
3. The symbols $n$ and $2n$ describe the number of chromosome sets rather than the size of a cell.
4. Human gametes, sperm and eggs, are haploid and normally contain $23$ chromosomes.
5. Most human nucleated body cells are diploid and normally contain $46$ chromosomes.
6. The human diploid total can be organised as $23$ pairs, with one chromosome of each pair inherited from each parent.

Chromosome pairs

1. The chromosomes in an ordinary homologous pair have the same genes at the same positions.
2. They need not have identical DNA sequences because they can carry different alleles of those genes.
3. A haploid gamete has one member from each ordinary homologous pair and therefore one copy of each of those genes.
4. The matching pair in a diploid nucleus contains two gene copies, even when their alleles differ.

Fertilisation combines two sets

1. At fertilisation, the nuclei of two haploid gametes fuse and combine their chromosome sets.
2. The resulting zygote has two sets of chromosomes and is therefore diploid.
3. The relationship is $n+n\to 2n$.
4. In humans, this is $23+23\to 46$, with $23$ chromosomes contributed by each parent.
5. Subsequent normal mitotic divisions copy and distribute the chromosomes so that the developing organism's daughter cells retain the diploid number.

Applying chromosome numbers

1. Different species have different chromosome numbers, so use the number supplied rather than automatically using the human total.
2. If the diploid number is known, calculate the haploid number using $n=\frac{diploid\; chromosome\; number}{2}$.
3. If the haploid number is known, double it to find the diploid number: $2n=2\times haploid\; chromosome\; number$.
4. Count sets rather than assuming that any even chromosome number must be diploid, since a haploid number can also be even.

Reading chromosome diagrams

1. Identify matching chromosome types using their length, shape and gene positions when these are shown.
2. Two copies of each ordinary chromosome type indicate two sets, whereas one copy of each type indicates one set.
3. The two joined arms of an X-shaped replicated chromosome are sister chromatids, not a homologous pair.
4. Copying DNA does not by itself change a diploid nucleus into a nucleus with four chromosome sets.
5. Mature human red blood cells have no nucleus, so the usual diploid body-cell chromosome count does not apply to them.

5.1.7 Meiotic cell division

Meiosis and gametes

1. Meiosis is the form of cell division that produces gametes, and in humans it takes place only in the testes and the ovaries.
2. In flowering plants the same division occurs in the anthers, which make pollen, and in the ovules, which make egg cells.
3. One diploid parent cell that enters meiosis gives rise to four haploid daughter cells.
4. A diploid human body cell holds $46$ chromosomes arranged as $23$ homologous pairs, one chromosome of each pair having come from each parent.
5. Each gamete formed from that cell holds $23$ chromosomes, exactly one taken from every pair.
6. The change is written $2n\to n$, where $n$ stands for one complete set of chromosomes.
7. In humans $n=23$, so a body cell is $2n=46$ and a sperm cell or egg cell is $n=23$.
8. Meiosis is the only division in the body that changes the chromosome number, which is why it is confined to the reproductive organs.

Why the number is halved

1. Fertilisation is the fusion of a male gamete nucleus with a female gamete nucleus.
2. Two haploid nuclei fuse, so the zygote that forms carries $23+23=46$ chromosomes.
3. The diploid number is restored exactly, and the zygote then divides repeatedly by mitosis to build the whole organism.
4. Every body cell of the new individual therefore carries the same $46$ chromosomes as the body cells of its parents.
5. Because one full set arrives from each parent, every homologous pair holds one maternal chromosome and one paternal chromosome.
6. If gametes were diploid, the chromosome number would double at every fertilisation, running $46\to 92\to 184$ in three generations.
7. A cell with the wrong chromosome number carries the wrong number of copies of every gene on the extra chromosomes, so it cannot develop normally.
8. Meiosis is described as a reduction division because it is the step that takes one chromosome away from every pair.

The two divisions of meiosis

1. Before meiosis starts, every chromosome is copied during interphase, so it becomes two identical sister chromatids joined at a centromere.
2. Meiosis I separates the homologous pairs, and it is this division that halves the chromosome number.
   1. Prophase I: the chromosomes condense and each one pairs up alongside its homologous partner.
   2. Metaphase I: the pairs line up along the equator of the cell, each pair positioned independently of the others.
   3. Anaphase I: spindle fibres pull one whole chromosome of each pair to each pole, so the sister chromatids stay joined together.
   4. Telophase I: two nuclei form and the cell divides, producing two cells that are already haploid.
3. Meiosis II separates the sister chromatids and runs in the same way as mitosis.
   1. Prophase II: the chromosomes condense again inside each of the two new cells.
   2. Metaphase II: the chromosomes line up singly along the equator.
   3. Anaphase II: each centromere divides and the sister chromatids are pulled to opposite poles.
   4. Telophase II: four nuclei form and both cells divide, giving four haploid cells in total.
4. The overall result is one diploid cell becoming four haploid cells, each carrying one chromosome from every original pair.

How meiosis creates variation

1. Crossing over happens in prophase I, when the chromatids of a homologous pair lie against each other and swap matching sections of DNA.
2. The point at which they join and exchange material is called a chiasma, and every chromatid that leaves it carries a new combination of alleles.
3. Independent assortment happens at metaphase I, because the way one pair lines up at the equator has no effect on the way any other pair lines up.
4. Either chromosome of a pair can end up facing either pole, so each pair contributes one of two possible outcomes to the gamete.
5. For $n$ homologous pairs the number of possible chromosome combinations in a gamete is $2^n$.
6. With $n=23$ in humans this gives $2^{23}=8388608$ combinations from independent assortment alone, before crossing over is counted.
7. Random fertilisation adds a further step, because any one of those sperm cells can fuse with any one of those egg cells.
8. The four gametes produced by one meiosis are therefore genetically different from one another, and offspring differ from their parents and from each other.

Meiosis compared with mitosis

1. Mitosis produces two daughter cells, whereas meiosis produces four.
2. Mitosis keeps the chromosome number at $2n$, whereas meiosis reduces it to $n$.
3. Mitosis involves a single division, whereas meiosis involves two divisions one straight after the other.
4. The cells made by mitosis are genetically identical to the parent cell, whereas the cells made by meiosis are all genetically different.
5. Mitosis occurs throughout the body for growth, repair and asexual reproduction, whereas meiosis occurs only in the reproductive organs.
6. Neither crossing over nor independent assortment occurs in mitosis, which is why mitosis produces no genetic variation.

5.1.8 Single gene inheritance

Genes and alleles

1. A gene is a section of DNA carrying the instructions for one protein, and it sits at a fixed position on a chromosome called its locus.
2. Because chromosomes come in homologous pairs, a body cell carries two copies of every gene, one on each chromosome of the pair.
3. The two copies may be the same version or two different versions, and each version is called an allele.
4. New alleles arise when a mutation changes the base sequence of a gene, which changes the instruction and often changes the protein made from it.
5. A gene may have many alleles across a whole population, but any one diploid individual carries only two of them.
6. Alleles are written as letters, and both alleles of the same gene are written with the same letter, for example $T$ and $t$.

Dominant and recessive alleles

1. A dominant allele determines the phenotype whenever it is present, so one copy is enough for its effect to show.
2. A recessive allele determines the phenotype only when no dominant allele of that gene is present, so two copies are needed.
3. Dominant alleles are written as capital letters and recessive alleles as the matching lower case letter, so $T$ and $t$ are two alleles of one gene.
4. Writing $T$ alongside $s$ would suggest two separate genes rather than two versions of the same gene, so the letters must always match.
5. When a dominant and a recessive allele are present together, the protein coded by the dominant allele is enough to produce the dominant characteristic.
6. A recessive characteristic can therefore disappear for a generation and reappear later, whenever two recessive alleles meet in the same individual.

Genotype and phenotype

1. The genotype is the pair of alleles an individual carries for a gene, written as two letters such as $TT$, $Tt$ or $tt$.
2. The phenotype is the characteristic that can be seen or measured, such as a tall stem or a short stem.
3. The genotype decides which proteins the cell can make, and those proteins, together with the conditions the organism grows in, produce the phenotype.
4. Two individuals with different genotypes can share one phenotype, because $TT$ and $Tt$ both give a tall stem.
5. The recessive phenotype has only one possible genotype, because a short stem can only come from $tt$.

Homozygous and heterozygous

1. An individual is homozygous for a gene when its two alleles are identical, written $TT$ for homozygous dominant and $tt$ for homozygous recessive.
2. An individual is heterozygous when its two alleles are different, written $Tt$.
3. A homozygous individual can pass on only one kind of allele, so it is described as pure-breeding for that characteristic.
4. A heterozygous individual can pass on either of its two alleles, so its offspring are not all alike.
5. A heterozygous individual that shows the dominant characteristic while carrying a recessive allele is a carrier of that allele.
6. A carrier passes the recessive allele on unseen, which is how a recessive characteristic can appear in offspring whose parents do not show it.

How alleles pass to offspring

1. Meiosis separates the two alleles of a gene, because the homologous chromosomes carrying them are pulled into different gametes.
2. Every gamete therefore carries one allele of the gene and never both.
3. A homozygous $TT$ parent makes only $T$ gametes, and a homozygous $tt$ parent makes only $t$ gametes.
4. A heterozygous $Tt$ parent makes $T$ gametes and $t$ gametes in equal numbers.
5. At fertilisation one allele carried by the male gamete joins one allele carried by the female gamete, which rebuilds the pair in the zygote.
6. A cross that follows one gene through this route is a monohybrid cross, and it is set out as a genetic diagram.
7. A genetic diagram is written in a fixed order, and every line of it earns credit.
   1. Line 1: the phenotypes of the two parents, described in words.
   2. Line 2: the genotypes of the two parents, written as pairs of allele letters.
   3. Line 3: the gametes each parent can make, written as single alleles.
   4. Line 4: the offspring genotypes produced by combining those gametes.
   5. Line 5: the offspring phenotypes that follow from those genotypes.

Crosses between the genotypes

1. A cross between two homozygous parents, $TT\times tt$, gives every offspring the genotype $Tt$, so all of them show the dominant characteristic.
2. A cross between two heterozygous parents, $Tt\times Tt$, gives offspring of genotype $TT$, $Tt$, $Tt$ and $tt$.
3. Three of those four offspring carry at least one $T$ and show the dominant characteristic, while the fourth is $tt$ and shows the recessive characteristic.
4. A cross between a heterozygote and a homozygous recessive parent, $Tt\times tt$, gives offspring of genotype $Tt$, $Tt$, $tt$ and $tt$.
5. Half of those offspring show the dominant characteristic and half show the recessive characteristic.
6. Any cross involving a homozygous dominant parent, such as $TT\times Tt$, gives no recessive offspring at all, because every offspring receives at least one $T$.
7. The recessive characteristic appears only in an offspring that receives a recessive allele from both parents at once.

5.1.9 Predicting single gene crosses

Building a Punnett square

1. A Punnett square is a grid that combines the gametes of two parents so that every possible offspring genotype appears in the table.
2. The grid is built in the same six steps every time.
   1. Write the genotype of each parent, for example $Bb$ for the father and $Bb$ for the mother.
   2. Work out the gametes each parent can make, writing single alleles only, so a $Bb$ parent makes $B$ and $b$.
   3. Draw a $2\times 2$ grid, place one parent's gametes above the two columns and the other parent's gametes beside the two rows.
   4. Fill each box by combining the allele at the head of its column with the allele at the start of its row.
   5. Write the dominant allele first inside each box, so a box holding $b$ and $B$ is written $Bb$.
   6. Read off the phenotype of each box, remembering that one dominant allele is enough to give the dominant characteristic.
3. Two gamete types from each parent give $2\times 2=4$ boxes, and each box is one equally likely outcome of fertilisation.
4. A parent that is homozygous makes only one kind of gamete, so its allele is simply repeated along its side of the grid.

Reading ratios from the grid

1. The genotype ratio counts the boxes by genotype, so $Bb\times Bb$ gives $1BB:2Bb:1bb$.
2. The phenotype ratio counts the boxes by appearance, so the same cross gives $3:1$ dominant to recessive.
3. The cross $Bb\times bb$ gives $Bb$, $Bb$, $bb$ and $bb$, which is $1:1$ by genotype and $1:1$ by phenotype.
4. The cross $BB\times bb$ fills all four boxes with $Bb$, so every offspring shows the dominant characteristic.
5. The cross $BB\times Bb$ gives $BB$, $BB$, $Bb$ and $Bb$, which is $1:1$ by genotype but gives no recessive offspring at all.
6. A ratio is converted to a fraction using $fraction=\frac{parts\; of\; interest}{total\; parts}$.
7. A ratio of $3:1$ therefore means $3$ parts out of $4$, which is $\frac{3}{4}$, and $\frac{3}{4}\times 100=75\%$.
8. A ratio of $1:1$ means $1$ part out of $2$, which is $\frac{1}{2}$ and therefore $50\%$.
9. A ratio is simplified by dividing both parts by their highest common factor, so $27:9$ becomes $3:1$.

Probability for one offspring

1. Each box of a completed grid is one equally likely outcome, so a single box carries a probability of $\frac{1}{4}$.
2. The probability of any genotype is the number of boxes showing it divided by the total number of boxes.
3. From $Bb\times Bb$ the probability of $bb$ is $\frac{1}{4}$, of $Bb$ is $\frac{2}{4}=\frac{1}{2}$ and of $BB$ is $\frac{1}{4}$.
4. The probability of the dominant phenotype from that cross is $\frac{3}{4}$, which is $0.75$ as a decimal and $75\%$ as a percentage.
5. Every probability lies between $0$ and $1$, and the probabilities of all possible outcomes of a cross add up to $1$.
6. Each fertilisation is an independent event, so the outcome of one offspring has no effect on the next.
7. Parents who already have three children showing the dominant characteristic still face a probability of $\frac{1}{4}$ that the fourth shows the recessive one.

Expected and observed numbers

1. The expected number of offspring of one type is found from $expected\; number=probability\times total\; number\; of\; offspring$.
2. From $Bb\times Bb$ with $40$ offspring, the expected number showing the recessive characteristic is $\frac{1}{4}\times 40=10$.
3. The expected number showing the dominant characteristic is $\frac{3}{4}\times 40=30$.
4. Observed numbers rarely match expected numbers exactly, because which gamete fuses with which is a matter of chance.
5. The more offspring are counted, the closer the observed proportions usually come to the expected ones.
6. Observed results close to the expected ratio support the genotypes proposed for the parents.
7. Observed results a long way from the expected ratio suggest that one of the parent genotypes was wrong, or that too few offspring were counted.

5.1.10 Sex determination

The sex chromosomes

1. A human body cell holds $23$ pairs of chromosomes, and $22$ of those pairs are autosomes, which look the same in both sexes.
2. The twenty third pair is the pair of sex chromosomes, and this pair decides whether an individual develops as female or male.
3. A female has two X chromosomes, written $XX$, so this pair is fully matched like any other pair.
4. A male has one X chromosome and one Y chromosome, written $XY$, and the Y is much shorter than the X.
5. The Y chromosome carries a gene that switches on the development of testes in the early embryo.
6. An embryo with no Y chromosome has no copy of that gene, so it develops ovaries instead.
7. The X chromosome also carries many genes with nothing to do with sex, so every individual needs at least one copy of it.

Gametes and a child's sex

1. Meiosis separates the two sex chromosomes, so every gamete receives exactly one of them.
2. A female is $XX$, so every egg cell she makes carries an X chromosome.
3. A male is $XY$, so half the sperm cells he makes carry an X chromosome and half carry a Y chromosome.
4. The egg cell always supplies an X, so the sex of the child depends entirely on which kind of sperm reaches it first.
5. An X sperm fusing with the egg gives a zygote of genotype $XX$, which develops as a female.
6. A Y sperm fusing with the egg gives a zygote of genotype $XY$, which develops as a male.
7. Equal numbers of X sperm and Y sperm are made, which is why the two outcomes are equally likely.

The genetic cross for sex

1. Sex determination is set out as a genetic cross in exactly the same way as any other single gene cross.
   1. Parent genotypes: the mother is $XX$ and the father is $XY$.
   2. Gametes: the mother produces $X$ and $X$, while the father produces $X$ and $Y$.
   3. Grid: the mother's gametes go along the top of a $2\times 2$ Punnett square and the father's gametes go down the side.
   4. Offspring genotypes: the four boxes give $XX$, $XX$, $XY$ and $XY$.
   5. Offspring phenotypes: two female and two male.
2. The phenotype ratio is therefore $1:1$ female to male.
3. The probability that any one child is male is $\frac{2}{4}=\frac{1}{2}$, which is $50\%$.
4. That prediction applies afresh to every pregnancy, because each fertilisation is an independent event.
5. Birth records show slightly more boys than girls born each year, which is close to but not exactly the predicted $1:1$.

5.1.11 Multiple gene inheritance

Most features involve many genes

1. Single gene inheritance, with two clear alleles and a predictable ratio, is the exception among characteristics rather than the rule.
2. Polygenic inheritance means that one characteristic is controlled by several genes, which are often carried on different chromosomes.
3. Each of those genes has its own alleles, and each one contributes a small part of the finished characteristic.
4. The small contributions add together, so an individual carrying more of the alleles that increase the characteristic ends up further along the range.
5. Human height, body mass, skin colour and eye colour are all controlled in this way.
6. Skin colour depends on several genes that between them control how much melanin the skin cells produce.
7. Eye colour was once taught as a single gene with brown dominant over blue, but several genes are now known to contribute to it.
8. The link runs the other way as well, because one gene can affect more than one characteristic at the same time.

Why the range is continuous

1. A characteristic controlled by one gene with two alleles has only a few possible outcomes, so individuals fall into separate groups with nothing in between.
2. That pattern is discontinuous variation, and the data are displayed as a bar chart with a gap between each bar.
3. A characteristic controlled by many genes has a very large number of possible allele combinations.
4. For $n$ genes each having two alleles, the number of possible genotypes is $3^n$, so even five genes give $3^5=243$ different genotypes.
5. Those many combinations produce values that overlap and run smoothly from one extreme to the other with no gaps.
6. That pattern is continuous variation, and the data are displayed as a histogram whose bars touch.
7. The histogram of a polygenic characteristic usually forms a bell shaped curve, with most individuals near the middle and few at either extreme.
8. The environment widens the range still further, because factors such as diet and sunlight change the value an individual actually reaches.
9. Human height shows both effects at once, since many genes set the potential height and nutrition during childhood decides how much of it is reached.

Working with polygenic features

1. A Punnett square cannot be drawn for a polygenic characteristic, because each parent produces far more gamete types than a $2\times 2$ grid can hold.
2. Polygenic characteristics are therefore studied by measuring and plotting distributions rather than by predicting ratios.
3. Data are collected by measuring a large sample, grouping the values into equal classes and plotting the frequency of each class.
4. A large sample matters, because a small one leaves gaps that make continuous variation look discontinuous.
5. Offspring of a polygenic characteristic tend to fall somewhere between their two parents rather than matching either one exactly.
6. Two tall parents usually have tall children, but no genetic diagram can predict the exact height of any one child.
7. A characteristic that clearly runs in families yet never gives clean $3:1$ or $1:1$ ratios is a strong sign that several genes are involved.

5.1.12 Development of our understanding of genetics

Mendel and his pea plants

1. Gregor Mendel was a monk who studied inheritance in the garden of his monastery at Brno during the $1850$s and $1860$s.
2. He chose the garden pea because it grows quickly, produces large numbers of offspring and shows characteristics that fall into two clear forms.
3. He followed seven characteristics, among them stem height, flower colour, seed shape and pod colour.
4. He began with pure-breeding lines, checking over several generations that each line always produced offspring like itself.
5. He controlled pollination by hand, and the method mattered as much as the counting.
   1. The anthers were cut out of a flower before its own pollen ripened, so the plant could not pollinate itself.
   2. Pollen from a chosen plant was then brushed onto the stigma of that flower with a fine brush.
   3. The treated flower was covered with a small bag so that no stray pollen from other plants could reach it.
6. Every cross therefore had a known male parent and a known female parent, which is what made the results interpretable.
7. He counted every offspring rather than judging by eye, working with thousands of plants so that chance had little effect on the proportions he found.

What the crosses showed

1. Crossing a pure-breeding tall plant with a pure-breeding short plant gave a first generation in which every plant was tall.
2. The short form had not been lost, because crossing those tall offspring with one another brought short plants back in the following generation.
3. In that second generation the plants appeared in a ratio close to three tall to one short.
4. One of his crosses gave $787$ tall plants and $277$ short plants, which is a ratio of $2.84:1$.
5. The same pattern of one form vanishing and then returning at about $3:1$ appeared in all seven characteristics he followed.
6. From these counts Mendel drew three conclusions, none of which needed any knowledge of what was inside the cell.
   1. Each characteristic is controlled by a pair of separate units of inheritance, one received from each parent.
   2. One unit of a pair can mask the other, which explains why the short form disappeared in the first generation.
   3. The two units of a pair separate when gametes are formed, so each gamete carries only one of them.
7. Those three conclusions are recognised today as alleles, dominance, and the separation of alleles during meiosis.

Why his work was ignored

1. Mendel published his results in $1866$ in the journal of a local natural history society, which few biologists elsewhere read.
2. His argument rested on ratios and counting, an approach unfamiliar to naturalists who described organisms rather than measured them.
3. Most biologists of the time accepted blending inheritance, in which the characteristics of the two parents mixed to give an intermediate offspring.
4. Mendel's units stayed separate and could reappear unchanged in a later generation, which contradicted blending directly.
5. Nothing was known of chromosomes, genes or DNA, so there was no structure inside the cell that his units could be matched to.
6. Mendel became abbot of his monastery in $1868$, and the administrative work that followed left him little time for breeding experiments.
7. He died in $1884$ without his explanation having been taken up by other biologists.

From units to genes

1. During the $1880$s better microscopes and new stains allowed biologists to watch chromosomes move during cell division.
2. Chromosomes were seen to occur in pairs, to separate during the division that forms gametes, and to be restored to pairs at fertilisation.
3. That behaviour matched Mendel's units of inheritance point for point, which is why his paper was rediscovered and confirmed around $1900$.
4. By $1915$ genes had been shown to lie in a fixed order along chromosomes, which gave Mendel's units a physical position in the cell.
5. In $1953$ the double helix structure of DNA was described, showing how a gene can be copied exactly and how it stores a coded instruction.
6. Mendel's units of inheritance are now called genes, and the alternative forms he described as masking one another are now called alleles.
7. The development therefore runs in a clear order: Mendel's counted ratios, then the observed behaviour of chromosomes, then genes, then the structure of DNA.