Sexual inheritance depends on halving, then restoring, chromosome number

A gamete is a reproductive cell that carries one set of chromosomes and can fuse with another gamete during fertilization. In animals, sperm and eggs are gametes. In flowering plants, male gametes are carried in pollen, while female gametes are in ovules within the ovary.

A haploid cell has one chromosome of each homologous type. A diploid cell has two chromosomes of each homologous type. In a sexual life cycle, meiosis produces haploid gametes, then fertilization fuses two haploid nuclei to form a diploid zygote, which is a cell produced by fusion of gametes that can develop into a new organism.

Eukaryotes with a sexual life cycle commonly follow this pattern. Mosses, mammals and flowering plants differ in the details, but the logic stays the same: meiosis halves chromosome number, and fertilization restores it. In humans, for example, body cells are diploid and gametes are haploid.

For autosomal genes, a diploid cell has two copies because it has two homologous autosomes: one inherited from each parent. An autosomal gene is a gene located on a non-sex chromosome. Those two copies may be identical versions of the gene, or they may be different versions; that distinction matters once we start using alleles.

Carrying out a controlled cross

A genetic cross is a planned mating between organisms selected for particular traits, either to study inheritance patterns or to breed useful trait combinations. Flowering plants work especially well for this because an investigator can control where the pollen goes.

In a flowering plant, pollen is a structure containing the male gametes. Female gametes are found inside ovules in the ovary. To carry out a cross, pollen from the chosen male parent is placed on the stigma of the chosen female parent. The pollen germinates, a pollen tube grows down the style, and the male gametes reach the ovary, where fertilization can occur.

A controlled cross depends on keeping out unwanted pollen. In practice, the immature anthers are removed from the flower being used as the female parent before they release pollen. The flower is then covered with a bag, so insects or wind cannot bring in pollen from elsewhere. After that, a small brush or anther can be used to apply the chosen pollen to the stigma.

Generations and Punnett grids

The P generation is the parental generation used at the start of a genetic cross. The F1 generation is the first generation of offspring from the P generation. The F2 generation is produced when F1 individuals reproduce with each other or self-fertilize.

A Punnett grid is a table used to predict possible offspring genotypes by combining the gametes from each parent. It isn’t a magic square. It’s just a neat way to keep track of which gametes can meet.

Plants such as peas produce both male and female gametes on the same plant, so they can self-pollinate and therefore self-fertilize. This helps when producing true-breeding lines or F2 offspring. Controlled genetic crosses are not just classroom history: they are widely used to develop crop varieties and ornamental plants with desirable traits, such as flower colour, disease resistance or growth form.

Genes, alleles and genotype

A gene is a length of DNA whose base sequence contributes to a functional product, usually a polypeptide or RNA. An allele is one version of a gene, different from another version at the same locus. Don’t treat the terms as interchangeable: the gene is the DNA region; alleles are the alternative versions of that region.

A genotype is the combination of alleles an organism inherits for one or more genes. For a gene with alleles $D$ and $d$, a diploid individual could have genotype $DD$, $Dd$ or $dd$. Each parent contributed one allele through their gametes.

A homozygous organism is an organism that has two identical alleles of a gene, such as $DD$ or $dd$. A heterozygous organism is an organism that has two different alleles of a gene, such as $Dd$. Since gametes are haploid, a homozygous parent makes gametes carrying only one allele type for that gene, while a heterozygous parent makes gametes carrying one allele or the other.

Allele symbols are shorthand, not the trait itself. By convention, a capital letter often represents a dominant allele and a lower-case letter represents the corresponding recessive allele. Biologically, what matters is the DNA sequence and how it affects the product of the gene.

Phenotype is what can be detected

A phenotype is the observable or measurable traits of an organism, produced by its genotype together with environmental influences. “Observable” doesn’t have to mean something you can see directly. Blood group, enzyme activity and ability to distinguish colours are phenotypes because tests can detect them.

Some human traits come mainly from genotype. ABO blood group is a clear example: your ABO phenotype is determined by alleles at one gene, and it doesn’t change because you practise or because the weather changes.

Other traits come from environment only. A scar from an injury, a tattoo, or the particular language a person learns as a child is not inherited as a DNA sequence. These traits can matter a lot, but they are not passed on through gametes.

Many traits involve genotype interacting with environment. Human height is influenced by many genes, as well as nutrition and health during growth. Human skin pigmentation has a genetic basis, but exposure to sunlight can increase melanin production. Plenty of real biological traits work this way, so avoid the lazy answer “it is genetic” unless the evidence really supports that.

Human trait examples grouped by how genotype and environment contribute to phenotype.

Why heterozygotes can resemble homozygous dominants

A dominant allele is an allele that determines the phenotype in a heterozygote. A recessive allele is an allele whose phenotypic effect is masked in a heterozygote by a dominant allele of the same gene.

In a simple dominant-recessive pattern, the homozygous dominant genotype and the heterozygous genotype give the same phenotype. For example, if T is dominant to t, both $TT$ and $Tt$ show the dominant phenotype. $tt$ shows the recessive phenotype.

The molecular explanation often comes down to the gene product. Many genes code for polypeptides. If a mutation creates a recessive allele that makes a non-functional enzyme, the heterozygote may still produce enough functional enzyme from the dominant allele to show the normal phenotype. So $TT$ and $Tt$ look the same: one working copy is sufficient. The recessive phenotype appears only when both alleles fail to provide enough functional product.

This explanation is common, but it isn’t a universal law. Some alleles are dominant because they make a harmful active product, or because half the normal amount of product is not enough. In many school-level examples, though, “one functional copy makes enough product” explains why carriers do not show the recessive phenotype.

A monohybrid cross is a genetic cross that follows one gene. In a typical cross between two heterozygotes, each parent produces two gamete types. A Punnett grid then predicts a $1:2:1$ genotypic ratio and a $3:1$ phenotypic ratio when one allele is completely dominant.

Same genotype, different expressed traits

Phenotypic plasticity is the ability of an organism with a given genotype to develop different traits in response to its environment, by changing patterns of gene expression. The genotype stays the same. What changes is whether genes are switched on, switched off or expressed at different levels.

Tanning is a useful human example. Greater sunlight exposure can increase expression of genes involved in melanin production in skin cells. If sunlight exposure later drops, melanin production can fall again, so the phenotype may reverse. That reversibility helps show why plasticity is not the same as mutation.

Phenotypic plasticity helps in variable environments because an organism can adjust its phenotype to the conditions it actually experiences. In plants, seedlings grown in darkness often develop differently from seedlings grown in light, even with the same genotype. Some plastic changes can reverse during life; others, especially changes made during development, may be difficult or impossible to reverse.

PKU and recessive inheritance

A genetic disease is a disease caused by one or more alleles that alter normal biological function. Phenylketonuria is a recessive genetic condition caused by mutation in an autosomal gene coding for the enzyme needed to convert phenylalanine to tyrosine.

That enzyme is phenylalanine hydroxylase. Someone with one normal allele and one PKU allele usually still makes enough working enzyme. They are a carrier: a heterozygous individual that can pass on a recessive disease allele without showing the disease phenotype.

With two recessive PKU alleles, a person cannot make enough functional phenylalanine hydroxylase. Phenylalanine builds up, and tyrosine production falls. If untreated, high phenylalanine concentrations can impair brain development. Newborn screening and a diet low in phenylalanine therefore matter: the genotype cannot be changed, but the environment can be managed to reduce the harmful phenotype.

The PKU gene is autosomal, so boys and girls show the same inheritance pattern. If both parents are carriers, each child has a 1 in 4 probability of inheriting both recessive alleles, a 1 in 2 probability of being a carrier, and a 1 in 4 probability of inheriting no PKU allele for that gene.

Gene pools contain more alleles than any one individual can carry

A gene pool is the complete set of alleles found in all individuals of an interbreeding population. A diploid individual can inherit only two alleles of an autosomal gene, but the population as a whole may contain many more than two versions.

A single-nucleotide polymorphism is a position in DNA where individuals in a population differ by one nucleotide base. The abbreviation is SNP, pronounced “snip”. One person might have A at a particular position in a gene, while another has G at that same position. In a long gene, several SNPs can occur, so many allele versions can build up in the gene pool.

Multiple alleles are three or more alleles of the same gene present in a population. This doesn’t mean that one individual has many alleles of the gene. It means the population’s gene pool contains many possible versions, and each diploid individual inherits at most two of them.

That is one reason inheritance is more varied than the simple T and t examples suggest. Those examples are useful for learning the logic, but real gene pools often contain many sequence variants.

Three alleles, four phenotypes

The ABO blood group system is a classic human example of multiple alleles. Use the allele symbols $I^{A}$, $I^{B}$ and $i$. Only one gene is involved, but the population has three common alleles.

A person still inherits just two alleles. The possible genotypes are $I^{A}I^{A}$, $I^{A}i$, $I^{B}I^{B}$, $I^{B}i$, $I^{A}I^{B}$ and $ii$. These give four phenotypes: blood group A, B, AB or O.

ABO blood groups produced by the three alleles Iᴬ, Iᴮ and i.

The $I^{A}$ allele produces the A antigen on red blood cells. The $I^{B}$ allele produces the B antigen. The $i$ allele produces neither A nor B antigen. So $I^{A}$ is dominant over $i$, and $I^{B}$ is dominant over $i$. A person with the genotype $I^{A}I^{B}$ has blood group AB, because both A and B antigens are present.

This system has medical significance because incompatible transfusions can make red blood cells clump when antibodies bind to unfamiliar antigens. For this topic, keep your attention on the inheritance pattern and allele notation; transfusion compatibility fits more naturally with immunity and blood physiology.

Two ways heterozygotes can differ from both homozygotes

Codominance is an inheritance pattern where both alleles in a heterozygote are expressed, producing a dual phenotype. The required example is AB blood type: genotype $I^A I^B$ produces both A and B antigens, so the phenotype is not “halfway” between A and B; it is both.

Incomplete dominance is an inheritance pattern where the heterozygote shows an intermediate phenotype between the two homozygotes. In four o’clock flower, also called marvel of Peru, Mirabilis jalapa, red-flowered and white-flowered homozygotes can produce pink-flowered heterozygotes.

At the phenotypic level, the distinction is straightforward. For codominance, look for a dual phenotype: both effects are seen. For incomplete dominance, look for an intermediate phenotype: the heterozygote sits between the homozygotes. When naming the plant example, either the common name or Mirabilis jalapa is acceptable.

X and Y chromosomes determine typical human sex development

A sex chromosome is a chromosome involved in determining sex and carrying genes with sex-linked inheritance patterns. An autosome is any chromosome that is not a sex chromosome.

Most human females have two X chromosomes. Most human males have one X chromosome and one Y chromosome. Eggs normally carry an X chromosome, while sperm carry either an X or a Y chromosome, so the sperm determines whether the zygote is typically XX or XY.

The Y chromosome carries a gene that starts testis development in the embryo. The testes then secrete hormones, which lead to the development of many male-typical physical characteristics. Without a Y chromosome, development usually follows a female-typical pathway.

The X chromosome is much larger than the Y chromosome and carries far more genes. That is why X-linked inheritance is much more common than Y-linked inheritance. Many X-linked genes are not directly involved in sex development; they’re simply located on the X chromosome.

A sex-linked gene is a gene located on a sex chromosome. In many school genetics examples, that means a gene on the X chromosome. Because males usually have only one X chromosome, a recessive allele on that X can be expressed in males, even when females would need two copies to show the same recessive phenotype.

X-linked recessive inheritance

Haemophilia is a sex-linked genetic disorder where blood clotting is impaired because a clotting factor is absent or defective. Write the alleles as superscript letters on an uppercase X, such as $X^{H}$ for an X chromosome carrying the normal clotting allele and $X^{h}$ for an X chromosome carrying the haemophilia allele. The Y chromosome is written as Y, since it does not carry that allele.

A male with genotype $X^{h}Y$ has haemophilia, as his only X chromosome carries the recessive allele. A female with genotype $X^{H}X^{h}$ is usually a carrier; the normal allele on one X chromosome is enough for normal clotting. A female with genotype $X^{h}X^{h}$ would be affected, but this is much rarer because she has to inherit the haemophilia allele from both parents.

That gives the usual pedigree pattern: more affected males than females, no father-to-son transmission for an X-linked allele, and carrier mothers who can have affected sons. Keep the allele symbols attached to X, not floating by themselves, because the key idea is that the allele is carried on the sex chromosome.

Reading family patterns instead of doing human crosses

A pedigree chart is a family-tree diagram showing how a trait appears across generations. Human geneticists use it because controlled genetic crosses in people would not be ethical.

The standard symbols have to be read carefully. Squares represent males, circles represent females, shaded symbols represent affected individuals, horizontal lines link parents, vertical lines lead to offspring, Roman numerals label generations, and Arabic numerals identify individuals within a generation.

To work out an inheritance pattern, start by looking for contradictions. Two unaffected parents with an affected child strongly suggest a recessive allele. An affected father with all affected daughters but no affected sons may point to an X-linked dominant pattern. If the trait appears mostly in males, and affected fathers do not pass it to sons, X-linked recessive inheritance is a possibility. When males and females are affected in similar numbers, autosomal inheritance is more likely.

A close relative is someone who shares a recent common ancestor, such as a sibling or first cousin. Many societies prohibit marriage between close relatives partly because it raises the probability that both parents carry the same rare recessive allele from a shared ancestor. The child is then more likely to inherit two copies and show the genetic disorder.

Inductive and deductive reasoning

Inductive reasoning means forming a general conclusion from observations of some cases. In a pedigree, several affected children born to unaffected parents may lead you to the general hypothesis that the condition is recessive.

Deductive reasoning means applying a general rule or hypothesis to predict or explain a specific case. Once you hypothesize “this disorder is autosomal recessive”, you can deduce that unaffected parents of an affected child must both be carriers.

A typical workflow is: observe part of the pedigree, induce a likely inheritance pattern, then use that pattern deductively to assign possible genotypes to individuals.

Continuous and discrete variation

Continuous variation is variation in which phenotypes form a range with many possible intermediate values. The required example is human skin colour. Discrete variation is variation in which phenotypes fall into separate categories with no intermediate values, such as ABO blood group.

Compares continuous and discrete variation in inheritance examples.

Several genes affect melanin production and distribution, so they influence skin colour. Environmental exposure to sunlight also affects it. Polygenic inheritance is inheritance of a trait influenced by two or more genes. When multiple genes each add small effects, the phenotypes usually spread across a continuous distribution rather than falling into tidy categories.

ABO blood group works differently. It is a discrete variable: a person is A, B, AB or O. You do not measure someone as 37% blood group A. Skin pigmentation, height and mass, by contrast, can vary along a scale and can be measured with units or ordered continuously.

Measures of central tendency

A measure of central tendency is a statistic that represents the centre or typical value of a data set. The mean is the sum of all values divided by the number of values. The median is the middle value after values are placed in order. The mode is the most frequent value.

The mean works well for many continuous data sets that are roughly symmetrical. The median is often a better choice when the data are skewed or include outliers. For categorical data such as ABO blood group, the mode is useful, because “average blood group” is meaningless.

For a data set, the mean is calculated as $\bar{x} = \sum x / n$, where $\bar{x}$ is the mean value of the variable (same unit as the measured variable), $\sum x$ is the sum of all measured values (same unit as the measured variable), and $n$ is the number of values (dimensionless).

What a box-and-whisker plot shows

A box-and-whisker plot is a graph showing the spread and centre of a continuous data set using the median, quartiles, minimum, maximum and outliers. For variables such as student height, it’s useful because the spread and skew are quick to compare.

A good box-and-whisker plot needs six features: outliers, minimum, first quartile, median, third quartile and maximum. The box goes from the first quartile to the third quartile, with the median marked by a line inside it. The whiskers stretch to the minimum and maximum values that are not outliers.

The interquartile range measures the spread of the middle 50% of the data. $IQR = Q_3 - Q_1$, where $IQR$ is the interquartile range (same unit as the measured variable), $Q_3$ is the third quartile (same unit as the measured variable), and $Q_1$ is the first quartile (same unit as the measured variable).

A data point counts as an outlier if it is more than $1.5 \times IQR$ above the third quartile or more than $1.5 \times IQR$ below the first quartile. So the upper outlier boundary is $Q_3 + 1.5 \times IQR$, and the lower outlier boundary is $Q_1 - 1.5 \times IQR$.

When constructing a box-and-whisker plot, order the data first. Then find the median, first quartile and third quartile before deciding on the whiskers. This sequence prevents most errors.

Segregation: alleles separate into gametes

Segregation means the two alleles of a gene separate into different gametes during meiosis. A diploid cell carries two alleles of most autosomal genes, but a haploid gamete gets only one. That’s why a heterozygote can make two gamete types for a gene.

Independent assortment: unlinked genes separate independently

Independent assortment means alleles of different genes separate into gametes independently of one another. It applies to unlinked genes: genes on different chromosomes, or genes far enough apart on the same chromosome that crossing over makes their inheritance effectively independent.

Chromosome movement explains it. In metaphase I of meiosis, homologous chromosome pairs line up at the equator, and each pair has a random orientation. In anaphase I, homologous chromosomes move to opposite poles. Since each pair orients independently, the allele inherited for one gene does not determine the allele inherited for another unlinked gene.

This connects directly to dihybrid crosses. A double heterozygote for two unlinked genes, such as AaBb, can produce AB, Ab, aB and ab gametes in equal proportions. That equal production gives the familiar dihybrid ratios in the next section.

The wider “doubling and halving” pattern appears across biology. Meiosis halves chromosome number to make gametes, and fertilization restores the diploid number. DNA replication in S phase doubles DNA before division. Glycolysis also splits a six-carbon glucose molecule into two three-carbon molecules, so halving can happen at the molecular level as well as at the chromosome level.

Dihybrid crosses and the 9:3:3:1 ratio

A dihybrid cross follows the inheritance of two genes at the same time. With two unlinked autosomal genes showing complete dominance, crossing two double heterozygotes, $AaBb \times AaBb$, produces four possible gamete types from each parent: AB, Ab, aB and ab.

A $4\times4$ Punnett grid then combines those gametes. You get the 9:3:3:1 phenotypic ratio when both genes show complete dominance and both parents are heterozygous for both genes. The breakdown is 9 with both dominant phenotypes, 3 with the first dominant and second recessive phenotype, 3 with the first recessive and second dominant phenotype, and 1 with both recessive phenotypes.

Test crosses and the 1:1:1:1 ratio

Crossing a double heterozygote with a double homozygous recessive, $AaBb \times aabb$, gives a dihybrid test cross. The recessive parent can only make ab gametes, so the offspring phenotypes show the gametes produced by the double heterozygote directly. If the genes are unlinked, AB, Ab, aB and ab gametes occur with equal probability, giving a 1:1:1:1 phenotypic ratio.

Mendel’s second law has conditions

The 9:3:3:1 and 1:1:1:1 ratios come from what is often called Mendel’s second law: alleles of one gene assort into gametes independently of alleles of another gene. Be careful with the word “law” here. In biology, a law is a reliable prediction under specified conditions, not an exception-proof commandment.

The law applies when genes are on different chromosomes, or far enough apart on the same chromosome that recombination reaches about 50%. Linked genes, selection, small sample sizes, epistasis and other factors can all make observed ratios move away from the simple prediction.

Genes have positions and products

A locus is the exact position of a gene on a chromosome. Human protein-coding genes are found on autosomes $1$–$22$ and on the sex chromosomes $X$ and $Y$. A gene’s base sequence sets the amino acid sequence of its polypeptide product, though alleles can differ slightly in sequence.

A polypeptide product is the amino acid chain made when a coding gene is expressed and translated. For example, a database entry for a human gene usually lists the chromosome, locus, gene name, transcript information and protein product.

Using databases properly

When working with databases, you should be able to locate genes on different chromosomes and spot genes that sit close together on the same chromosome. Ensembl, NCBI Gene and OMIM are examples of databases used for this purpose.

A sensible workflow is:

1. Search the gene name or disease-associated variant.
2. Record the chromosome and locus.
3. Identify the polypeptide product.
4. Compare two genes on different chromosomes with two genes near each other on the same chromosome.

Genes on different chromosomes are unlinked. Genes close together on the same chromosome may be linked and may fail to assort independently. That’s why database skills connect directly to inheritance patterns: the physical location of genes helps explain the ratios seen in crosses.

Linked genes travel together more often than expected

Gene linkage is the tendency of genes located close together on the same chromosome to be inherited together. Autosomal gene linkage is gene linkage involving genes on autosomes rather than sex chromosomes.

Linked genes may not assort independently because they sit on the same physical DNA molecule. In meiosis, a chromosome that carries one allele of the first gene will often carry the nearby allele of the second gene into the same gamete. Crossing over can split them up, but when the genes are close together, that is relatively rare.

In crosses involving linkage, write allele symbols beside vertical lines that represent homologous chromosomes. This isn’t just a neat way to draw it; it shows which allele combinations lie on the same chromosome. For example, AB on one vertical chromosome line and ab on the homologous line is a different arrangement from Ab and aB.

Linked genes are suspected when offspring ratios differ significantly from the ratios expected for independent assortment. Parent-like combinations usually appear more often, while recombinant combinations appear less often. A chi-squared test is used later to decide whether the difference is large enough to count as statistically significant, rather than just ordinary sampling variation.

What counts as recombinant?

A recombinant is a gamete, genotype or phenotype that carries a new combination of alleles compared with the parental combinations. You can use the word at three levels, so say exactly which level you mean: recombinant gametes, recombinant offspring genotypes, or recombinant offspring phenotypes.

For unlinked genes, recombinants appear because homologous chromosome pairs line up randomly during meiosis I. A double heterozygote can produce all four gamete combinations in equal proportions. In a test cross with a double homozygous recessive, the offspring phenotypes directly show those gametes, so you expect a 1:1:1:1 ratio.

For linked genes, crossing over between the two loci produces recombinants. If the parental arrangement is AB/ab, then AB and ab are parental gametes, while Ab and aB are recombinant gametes. In a test cross AB/ab × ab/ab, offspring with genotypes AaBb and aabb are parental types, while Aabb and aaBb are recombinants.

Start by identifying the allele combinations in the original parents. Only after that can you decide which offspring combinations are new. Students often try to spot recombinants from dominance alone, but recombination depends on allele combinations compared with the parents, not on whether a phenotype is dominant or recessive.

Why chi-squared is used

A chi-squared test compares observed frequencies with expected frequencies to judge goodness of fit. In genetics, it’s used to decide whether the offspring numbers you counted fit an expected ratio such as $9:3:3:1$ or $1:1:1:1$.

The null hypothesis is a testable statement that there is no significant difference between observed and expected results. The alternative hypothesis is a testable statement that there is a significant difference between observed and expected results.

For a dihybrid cross, a typical null hypothesis might be: “The observed phenotypic frequencies fit a $9:3:3:1$ ratio.” The alternative would be: “The observed phenotypic frequencies do not fit a $9:3:3:1$ ratio.”

Observed, expected and significance

Observed results are the actual counts collected. Expected results are the counts predicted by the genetic model. To find expected numbers, multiply the total offspring by the expected fraction for each phenotype.

The chi-squared statistic is calculated as $\chi^2 = \sum\left(\frac{(O - E)^2}{E}\right)$, where $\chi^2$ is the chi-squared test statistic (dimensionless), $\sum$ means sum over all categories (dimensionless), $O$ is the observed frequency in a category (individuals), and $E$ is the expected frequency in that category (individuals).

The degrees of freedom for a goodness-of-fit test is usually the number of phenotypic categories minus one. For four dihybrid phenotype classes, degrees of freedom = $3$.

A p-value is the probability of obtaining results at least as different from expected as the observed results, assuming the null hypothesis is true. At the $p = 0.05$ level, where $p$ is the probability value (dimensionless), results are treated as statistically significant if there is less than a 5% probability that the deviation is due to chance sampling alone.

Worked chi-squared goodness-of-fit test for a dihybrid 9:3:3:1 ratio.

If calculated $\chi^2$ is greater than the critical value for the correct degrees of freedom at $p = 0.05$, reject the null hypothesis. If calculated $\chi^2$ is equal to or less than the critical value, do not reject the null hypothesis. Say “do not reject” rather than “prove”, because statistics does not prove the model true; it only tells you whether the data give enough evidence against it.

Samples, populations and effective sampling

Statistical tests usually use a sample to represent a population. In a genetics cross, the $F_2$ generation is the sample; in many experiments, repeated measurements or replicates are the sample. For sampling to work well, the sample must be representative, selected without bias, and large enough to reduce random error. Random sampling means every member of the population has an equal chance of selection, as when quadrat positions are chosen randomly in ecology. The same idea appears in mark-release-recapture methods such as the Lincoln index: the sampled individuals must represent the wider population.

That links genetics and ecology statistics. A p-value is only meaningful if the data come from a sampling method that justifies treating the sample as a model of the population.