Gregor Mendel, a renowned geneticist, is best known for developing the basic premise of genetics and outlining his two Laws of Heredity. These were:

1. Organisms carry two copies, or alleles, of any gene. They transmit a single, randomly selected allele to each offspring.
2. Alleles of different genes are generally¹inherited independently of each other.

These rules mean that each offspring gets one allele for a gene from each parent, and that this happens entirely at random. Every individual's set of alleles is known as their genotype, but the visible effect those alleles have is known as a phenotype.

Alleles usually show one of two basic patterns of Mendelian Inheritance - dominance or recessiveness - depending upon whether the allele itself is dominant or recessive. The most important cases where inheritance is looked at are genetic diseases, so those will be used as examples for most of this entry. Due to the laws of inheritance, certain rules apply to each basic form of inheritance. These laws are often broken, and will be the subject of the second part of this entry.

Punnet Squares

The concept of basic inheritance is difficult to understand without an introduction to Punnet squares and pedigrees. A Punnet square is a table used to predict the potential offspring of parents according to their genotypes. When looking at a single gene being inherited, the following layout can be used:

Each of the 'possible offspring' boxes combines an allele from the mother with one from the father, showing all the possible offspring genotypes that could be produced. As each of a parent's alleles have an equal chance of being passed on, this makes all the possible offspring equally likely to occur. There is therefore a one-in-four chance of the offspring inheriting a particular genotype, something which becomes very important when looking at the chances of a couple producing a child affected by a certain disease.

Pedigrees

A pedigree is basically a family tree, but with symbols to depict whether each family member is male or female and whether they show the phenotype of interest. In the medical world, pedigrees are usually used to track the inheritance of a genetic disease, allowing the investigator to determine which pattern of inheritance, and therefore what sort of allele, is involved. The symbols used are:

These symbols form the basis of all pedigrees, but there are many further symbols:

• Half-shaded symbols are used to depict carriers of the disease.
• A diagonal line is struck through any deceased individuals.
• Twins share the same 'stalk' from branch of siblings and a horizontal line is drawn between identical twins.
• Consanguineous marriages² are indicated by drawing a double line between the couple.
• Time and space is often saved by writing the number of normal children of a certain sex inside a single symbol instead of drawing many of the same symbol.
• In clinical scenarios, the patient of interest is shown by an arrow and is known as the proband.

Dominant Inheritance

In dominant inheritance all the individuals who have the dominant allele show the disease, so any child receiving the allele from one parent will have the disease regardless of which allele the other parent supplies. This is shown in the following Punnet square, where the dominant allele is represented by a capital 'H' and the recessive allele by a lower case 'h'. The dominant allele in this case is that for Huntington's disease, a disease which only appears in later life.

The two Hh individuals have a dominant allele and are therefore affected by the disease, whereas the other two individuals have two recessive alleles and are not affected. This demonstrates that 50% of the children of an affected individual will inherit the disease. It also proves the pattern that every affected individual has an affected parent. Meanwhile, if two affected people have children, the following pattern of 75% affected and 25% unaffected children is also shown:

A pedigree of such a disease might look like this. Since dominant diseases affect every individual with a copy of the allele they are very rare. Only the diseases that do not prevent reproduction³ will persevere, because otherwise they would not be passed on to the next generation.

Recessive Inheritance

Best shown by Mendel's peas, recessive inheritance leads to an entirely different pattern than that of dominant inheritance. Only individuals who have two recessive alleles⁴ will show signs of the disease, although of course those with just one recessive allele (carriers) will be capable of passing it on to their children. The inheritance of a recessive characteristic is shown in the following Punnet square, where the dominant allele is represented by a capital 'C' and the recessive allele by a lower case 'c'. The recessive allele in this case is for cystic fibrosis. Those with the genotype Cc are carriers: they do not show the disease but can pass on their c allele to their children.

Only one of the four offspring has two recessive alleles (cc) and hence the disease, while the other offspring have at least one dominant allele that overrides the effects of the recessive allele. This means that two carriers have a 25% chance of producing an affected child. The other three potential offspring will appear normal, though two out of three will be carriers, so the unaffected child of two carriers has a 67% chance of being a carrier. Meanwhile, if only one parent is a carrier, there will be no affected children, but half of them will inherit the recessive allele and be carriers:

A pedigree of such a disease might look like this.

Complications

Now that we have laid the groundwork it's time to destroy it again by mentioning all the misfits and exceptions. These exceptions tend to affect the normal ratios of offspring, and must be understood lest they mislead those studying pedigrees into mistaking a disease for something it is not.

Lethal Alleles

In some cases of dominant inheritance the dominant allele is so powerful that all offspring with two dominant alleles will die before birth. This alters the pattern of inheritance seen when two affected parents have children:

Only offspring with one or more recessive alleles will develop, so now only 67% of the children will be affected instead of the 75% expected when two Hh individuals have children.

Incomplete Dominance

This is where a dominant allele has only a partial effect on its own and requires a second dominant allele to show its full effects. However, it is also possible for an allele not to be powerful enough to have its full effect without another dominant allele present, leading to confusing 'halfway' versions of the disease.

Co-dominance and Silent Alleles

Best shown by the ABO blood group system, co-dominance exists where two different alleles can both show their effects in the same person and each of them has the ability to override a third recessive allele. A Punnet square for ABO inheritance where the mother has group A blood and the father has group B blood might look like this (Note that while most recessive alleles are shown in lower case, this rule does not apply to the ABO blood group system and so the 'O' allele is written in upper case):

The potential offspring would therefore show the following phenotypes:

The table shows that it is possible for parents with blood groups A and B to have children who have blood group O. The recessive allele for group O is known as a silent allele since it can be hidden for whole generations by the A and B alleles.

Carrier Survival Advantage

In Sickle Cell Anaemia, there is a defect in the gene coding for haemoglobin, causing the individual's red blood cells to take on a sickle shape in certain circumstances. The allele for the disease is co-dominant with the normal allele, so carriers exhibit a milder form of the disease. Interestingly, the malaria parasite Plasmodium cannot multiply inside the red blood cells of those with the disease, giving carriers a degree of protection against malaria. This means that carriers have an advantage over those without any sickle cell alleles, and leads to a higher than expected prevalence of the disease allele in countries where malaria is common.

Epistasis

Epistasis occurs when the action of one gene hides the action of another, thus changing the expected phenotype of an individual. An example is the Bombay phenotype allele⁶, in which inheriting two of the recessive alleles for one gene leads to an inability to express the A, B or AB phenotype from the ABO gene. All offspring with two Bombay phenotype alleles are blood group O regardless of their genotype for the ABO gene, which can lead to the following inheritance of blood groups, where both parents are blood group AB and carriers of the Bombay phenotype allele:

Although it is quite possible for the couple to produce children with blood groups A, B or AB, every child must inherit either the A or B allele from the father and so they cannot inherit the OO genotype. In 99% of cases this means that the couple cannot have a child with blood group O, but it transpires that one couple in a hundred are both carriers for the Bombay allele, giving that couple a 25% chance of having a child with group O blood without the need for a case of false paternity⁷.

Genetic Heterogeneity and Summation

There is often more than one gene involved in a disease, making it possible for alleles of different genes to have the same effects. Often these genes can be completely unrelated except that they are both involved in the same process, meaning that an allele for the disease in either one will cause the disease. Some diseases caused by a pair of recessive alleles for one gene may also be seen in individuals who have one recessive allele for that gene and a recessive allele for another gene associated with the disease. This effect is known as summation of the alleles, and is seen in spinal defects such as spina bifida, where the frequency of any one recessive allele in the population is very low, but a combination of two or more recessive alleles for different genes can trigger the disease.

Pleiotropy, Variable Expressivity and Incomplete Penetrance

Some alleles may have varying effects in different individuals, making it difficult to trace a disease back through a family. This is due to the way the genotype acts within varying individuals, and is known as pleiotropy. A good example of pleiotropy is the case of Tourette's syndrome, where a range of stigmatising behavioural problems and tics can occur. Other diseases may show the same effects in all affected individuals, but the degree to which the disease shows will vary greatly in each case. This is known as variable expressivity and can be seen in such conditions as polydactyly, which causes an extra digit to grow on the hands or feet. The expression of the disease can range from a slight thickening of a thumb to a whole extra thumb next to it.

The most important case in which the phenotypes vary between individuals with the same alleles is that of incomplete penetrance. Basically an extreme case of variable expressivity, this is when an individual appears completely normal despite having the alleles for the disease. The penetrance of a particular disease is measured by looking at how many individuals with the correct allele(s) for the disease also show the disease. This can vary greatly: penetrance of 100% indicates that all individuals with the allele(s) will develop the disease.

Anticipation

A special case of variation in the expression of a disease is that of anticipation, where the disease becomes worse with each passing generation. This happens in the case of mutations that are initially caused by a small defect which then multiplies itself within the DNA, aggravating its effects. The full-blown disease is usually preceded by a pre-mutant individual, someone whose defect is too mild to detect, followed by a mildly affected child and then by a severely affected grandchild.

Germline Mutations

All genetic diseases have to come from somewhere, and this somewhere is a mutation in the DNA of a cell. Only mutations in cells which will pass the mutant allele on to the sex cells (sperm in male humans and egg in female humans) will be passed on to an individual's children, so a new mutation must originally occur in a suitable cell before it can be passed down through the generations. The series of cells which eventually give rise to sex cells are known as the germline. A new mutation in these will affect the offspring but not the parent.

As if it wasn't confusing enough to have an allele for a disease appear out of nowhere, this is not the only problem with new mutations. Mutations usually only affect a proportion of the sex cells, meaning that the proportion of sex cells containing the allele for the disease will not be the 50% seen in random assortment of a parent's alleles. This completely disrupts the nice, simple patterns seen in basic inheritance, so it is normal for parents with one child who has inherited a new mutation to have only a 5% chance of having another affected child.

Phenocopies

While we have so far assumed that all examples of a genetic disease are caused by the individual's genes, this is not always the case. In humans, when the drug thalidomide is given to a pregnant mother, it can cause the shortening of the foetus' limbs, a condition known as phocomelia. Phocomelia can also be a rare genetic disease, but the inheritance of the disease is difficult to trace because of the results of thalidomide on offspring born in the 1960s. Such environmentally-caused versions of a genetic disease are known as phenocopies.

Incomplete Ascertainment

Another problem in determining the true frequency of inheritance of a disease becomes evident when looking at the inheritance of the disease in many families. 75% of the children of parents who are both carriers of a recessive allele will not show the disease, so many families will go completely unnoticed when studies of the disease are carried out. These studies will only examine the families in which an affected child is born, thus producing a higher rate of inheritance than is truly the case. Incomplete ascertainment only tends to be a problem if the disease is very rare or there is no other way of estimating its frequency.

Mitochondrial Inheritance

Mitochondrial inheritance breaks Mendel's laws completely, because only one allele is inherited and it always comes from the mother. Mitochondria are small structures which exist in most cells and have their own DNA which is separate to the human chromosomes. It is present in both the male sperm and the female egg, but the egg destroys all the male mitochondria, meaning that only the mother's mitochondria and its DNA are present in the cells of the offspring. If a mutation that causes a disease occurs in one of the few genes of the mitochondrial DNA, then it will be passed on only by affected females; all of their children will be affected by the disease. Affected males cannot pass on the disease, so a typical pedigree looks like this.

X-linked Inheritance

This is another example of inheritance blatantly breaking Mendel's rules. In X-linked inheritance, the gene involved exists on a part of the X chromosome and not on the Y chromosome. This means that females will frequently have two alleles – a disease allele and a good allele that can substitute for it – men will have only one copy, and display the disease. This means that only females can carry a recessive allele. This is illustrated by the following Punnet square for the inheritance of colour blindness, where Xc represents the X chromosome carrying the allele that causes the disorder:

Each offspring receives one of the two X chromosomes from the mother and either an X (female) or a Y (male) from the father. There is therefore a 50% chance that the child of a female carrier will receive the allele for the disease, but only half of these will be males and affected by the disease. Affected females are less common as they require a female with the allele to have children with a male with the allele (ie an affected male). If an affected male has children with a normal female, all his daughters will receive this Xc chromosome, but all his sons will receive his Y chromosome. For this reason, affected males can only pass on their disease to females and no 'male to male' inheritance is seen. A pedigree of X-linked inheritance might look like this.

Uniparental Disomy

Though it was earlier stated that in ordinary inheritance one allele comes from each parent, this is not always the case. Although a rare occurrence, it is possible for both copies of a chromosome to stick together during sex cell division, leading to two copies of the same chromosome in one cell and no copies in the other. While this can mean the child inherits three copies of a chromosome (eg Down's Syndrome (trisomy 21), where a child inherits three copies of chromosome 21), or only one copy (eg, Turner's syndrome, where a female child inherits only one X chromosome), it is also possible that they will receive two from one parent and none from the other. In this case, the child will have two copies of the same allele for a particular gene on that chromosome, making it possible for a carrier to pass on a recessive allele twice to the same child, thus giving them the recessive disease.

Monosomy and Trisomy

As mentioned above, it is possible for a individual to inherit the wrong number of a certain chromosome, leading to them having one copy (monosomy) or three copies (trisomy) of the same chromosome. Monosomy is fatal before birth except for when it produces an XO female, leading to Turner's syndrome. Trisomy is only compatible with life when it involves chromosome 13, 18 or 21, the offspring having Edward's, Patau or Down's syndrome respectively. These syndromes all lead to a reduced IQ along with various other symptoms. It is also possible to inherit too many sex chromosomes, leading to various combinations including XXY (Klinefelter's), XYY (Jacob's) and XXX, with each combination having a different effect on the IQ, development and fertility of the individual.

Linkage and Recombination

Although genes are generally inherited independently of one another, some genes lie close to one another on the same chromosome and will therefore show linked inheritance. To prevent every gene on the same chromosome from being inherited together, during the production of sex cells, each pair of matching chromosomes get together and swap matching sections to mix the genes up further. This is known as recombination and it means that only genes that are very close together are likely to show continued linked inheritance through the generations.

A rather bizarre problem that can occur due to recombination is the swapping of important parts of the X and Y sex chromosomes in males. Normally the presence of a Y chromosome leads to the development of a male child, but if the two chromosomes get together and swap the parts of them that determine gender, the end products are an X chromosome that confers maleness and a Y chromosome that confers femaleness. This can lead to the confusing results of XY females and XX males.

Mosaicism and Chimerism

The terms mosaic and chimera describe animals whose cells consist of two or more populations of genetically different cells. In a mosaic these cells all come from the same embryo, while in a chimera they come from separate sources. Early in the embryonic development of females, one of the two X chromosomes in each cell is inactivated at random so that each cell has only one active X chromosome. The two X chromosomes can easily have differing alleles, so every female is in fact a mosaic consisting of two sets of cells with slightly different genotypes⁸. This is important in X-linked diseases, because it means that an X-linked recessive allele will appear in half the cells of the body making it is possible for an unlucky carrier to develop symptoms of the disease. Meanwhile, individuals with Turner's syndrome (XO) usually only survive if they are lucky enough to have a mosaic of both faulty XO cells and normal XX cells.

Chimerism is much rarer in humans since it involves a combination of genes from two genetically different individuals before birth. One way for this to occur is for non-identical twins to share a blood supply from the placenta, because this allows cells from one individual to 'seed' themselves in the body of the other. If the twin providing the cells is of a different gender then the twin receiving the cells will end up infertile due to hormone imbalances. However, it is possible for a twin of the same gender to provide some of the precursors of the other twin's sex cells, leading to the bizarre occurrence of an individual producing sex cells containing their twin's genes. Although extremely rare, such events could lead to all sorts of confusion, even leading to cases of supposed false maternity.

And It Gets Worse

All the above complications are well-known exceptions to the two rules above and are demonstrable in various diseases and scenarios. However, they all rely on the fact that they are simply exceptions to the rule, and otherwise the rule remains intact. The problem with this approach is that the Human Genome Project has discovered that human genes have a habit of copying themselves so that there are two sections containing the same gene (and four alleles in total). This behaviour is seen in all DNA, even the bits which don't code for anything, and is actually important in terms of evolution. It means that the gene for a protein can replicate itself within the chromosome, after which it is possible for the gene to mutate to produce a novel protein while leaving behind the old version on itself. An example of this is seen in human antibodies, where genes for several different structures of antibody have evolved from one original gene.