1. Gene mutation
The ultimate source of genetic variation is gene mutation. How, in fact, do genetic variants arise?
A mutation is a heritable change of the genetic material.
Geneticists recognize two different levels at which mutation takes place. In gene mutation, an allele of a gene changes, becoming a different allele. Because such a change takes place within a single gene and maps to one chromosomal locus ("point"), a gene mutation is sometimes called a point mutation.
In chromosome mutations, segments of chromosomes, whole chromosomes, or even entire sets of chromosomes change.
Gene mutation is not necessarily a part of such a process; the effects of chromosome mutation are due more to the new arrangements of chromosomes and of the genes that they contain. Nevertheless, some chromosome mutations, in particular those proceeding from chromosome breaks, are accompanied by gene mutations caused by the disruption at the breakpoint.

2. Basic terminology
To consider change, we must have a fixed reference point, or standard. In genetics, the wild type provides the standard (the wild-type allele may be either the form found in nature or the form found in a standard laboratory stock).
Any change away from the wild-type allele is called forward mutation; any change back to the wild-type allele is called reverse mutation.
The non-wild-type allele of a gene is often called a mutation. To use the same word for the process and the product may seem confusing, but in practice little confusion arises.
Thus, we can speak of a dominant mutation or a recessive mutation. Consider, however, how arbitrary these definitions are; the wild type of today may have been a mutation in the evolutionary past, and vice versa.
Another useful term is mutant. A mutant organism or cell is one whose changed phenotype is attributable to the possession of a mutation. Sometimes the noun is left unstated; in this case, a mutant always means an individual or cell with a phenotype that shows that it bears a mutation.
Two other useful terms are mutation event, which is the actual occurrence of a mutation, and mutation frequency, the proportion of mutations in a population of cells or individual organisms.

3. Somatic mutations
A somatic mutation occurs in a single cell of developing somatic tissue in an individual organism; that cell may become the progenitor of a population of identical mutant cells, all of which have descended from the cell that mutated; this phenomenon is particularly important in cancer.
A population of identical cells derived asexually from one progenitor cell is called a clone. Because the members of a clone tend to stay close to one another during development, an observable outcome of a somatic mutation is often a patch of phenotypically mutant cells called a mutant sector. The earlier in development the mutation event, the larger the mutant sector will be.
Somatic mutation in the red Delicious apple. The mutant allele determining the golden color arose in a flower's ovary wall, which eventually developed into the fleshy part of the apple. The seeds are not mutant and will give rise to red-appled trees. In fact, the golden Delicious apple originally arose as a mutant branch on a red Delicious tree.

4. Germinal mutations Somatic mutations are never passed on to progeny.
On the contrary, mutations that occurs in the germ line, special tissue that is set aside in the course of development to form sex cells, will be passed on to the next generation. These are called germinal mutations.
An individual of perfectly normal phenotype and of normal ancestry can harbor undetected mutant sex cells. These mutations can be detected only if they are included in a zygote.
For example, the X-linked hemophilia mutation in European royal families is thought to have arisen in the germ cells of Queen Victoria or one of her parents.

5. Hemophilia
The original hemophilia mutation in the pedigree of the royal families of Europe arose in the reproductive cells of Queen Victoria's parents or of Queen Victoria herself.

6. Point mutations: base substitutions
Point mutations typically refer to alterations of single base pairs of DNA or of a small number of adjacent base pairs.
At the DNA level, there are two main types of point mutational changes: base substitutions and base additions or deletions.
Base substitutions are those mutations in which one base pair is replaced by another. Base substitutions again can be divided into two subtypes: transitions and transversions.
To describe these subtypes, we consider how a mutation alters the sequence on one DNA strand. A transition is the replacement of a base by the other base of the same chemical category (purine replaced by purine: either A to G or G to A; pyrimidine replaced by pyrimidine: either C to T or T to C). A transversion is the opposite the replacement of a base of one chemical category by a base of the other (pyrimidine replaced by purine: C to A, C to G, T to A, T to G; purine replaced by pyrimidine: A to C, A to T, G to C, G to T). In describing the same changes at the double-stranded level of DNA, we must state both members of a base pair: an example of a transition would be G·C  A·T; that of a transversion would be G·C  T·A.

7. Point mutations: additions/deletions
Addition or deletion mutations are actually of nucleotide pairs; nevertheless, the convention is to call them base-pair additions or deletions. The simplest of these mutations are single-base-pair additions or single-base-pair deletions. There are examples in which mutations arise through simultaneous addition or deletion of multiple base pairs at once.
What are the functional consequences of these different types of point mutations?

8. Functional consequences of point mutations (1)
We first consider what happens when a mutation arises in a polypeptide coding part of a gene. Depending on the consequences, single-base substitutions are classified into:
Silent mutations: the mutation changes one codon for an amino acid into another codon for that same amino acid.
Missense mutations: the codon for one amino acid is replaced by a codon for another amino acid.
Nonsense mutations: the codon for one amino acid is replaced by a translation termination (stop) codon.
The severity of the effect of missense and nonsense mutations on the polypeptide may differ. If a missense mutation causes the substitution of a chemically similar amino acid (synonymous substitution), then it is likely that the alteration will have a less-severe effect on the protein's structure and function. Alternatively, chemically different amino acid substitutions, called nonsynonymous substitutions, are more likely to produce severe changes in protein structure and function.
Nonsense mutations will lead to the premature termination of translation. Thus, they have a considerable effect on protein function. Unless they occur very close to the 3’ end of the open reading frame, so that only a partly functional truncated polypeptide is produced, nonsense mutations will produce inactive protein products.

9. Functional consequences of point mutations (2)
On the other hand, single-base additions or deletions have consequences on polypeptide sequence that extend far beyond the site of the mutation itself, like nonsense mutations.
Because the sequence of mRNA is "read" by the translational apparatus in groups of three base pairs (codons), the addition or deletion of a single base pair of DNA will change the reading frame starting from the location of the addition or deletion and extending through to the carboxy terminal of the protein. Hence, these lesions are called frameshift mutations.
These mutations cause the entire amino acid sequence translationally downstream of the mutant site to bear no relation to the original amino acid sequence.
Thus, frameshift mutations typically exhibit complete loss of normal protein structure and function.

10. Examples of point mutations

11. Mutations in non-coding regions
Now let's turn to those mutations that occur in regulatory and other non-coding sequences. Those parts of a gene that are not protein coding contain a variety of crucial functional sites. At the DNA level, there are sites to which specific transcription-regulating proteins must bind. At the RNA level, there are also important functional sequences such as the ribosome-binding sites of bacterial mRNAs and the self-ligating sites for intron excision in eukaryote mRNAs.
The consequences of mutations in parts of a gene other that the polypeptide-coding segments are difficult to predict. In general, the functional consequences of any point mutation (substitution or addition or deletion) in such a region depend on its location and on whether it disrupts a functional site. Mutations that disrupt these sites have the potential to change the expression pattern of a gene in terms of the amount of product expressed at a certain time or in response to certain environmental cues or in certain tissues.
It is important to realize that such regulatory mutations will affect the amount of the protein product of a gene, but they will not alter the structure of the protein.

12. Do mutations arise spontaneously?
Since the beginning of the past century it was widely known that when a population of bacteria is exposed to a toxic environment, some rare cells may acquire the ability to grow much better than most of the other cells in the population (resistance).
In addition, the resistant phenotype was often stable and so appeared to be the consequence of true genetic mutations.
However, it was not known if these mutants were produced spontaneously or if they were induced by the presence of the toxic agent. For many years, most microbiologists believed that mutations in bacteria were induced by exposure to a particular environment. (Salvador Luria once said that "bacteriology is the last stronghold of Lamarckism".)
The first rigorous evidence that mutations in bacteria followed the Darwinian principle of random variation and selection came from a study by Luria and Delbruck (1943).
They studied mutations that made E. coli resistant to phage T1. Phage T1 interacts with specific receptors on the surface of E. coli, enters the cell, and subsequently kills the cell. Thus, when E. coli is spread on a plate with 1010 phage T1, most of the cells are killed. However, rare T1 resistant (TonR) colonies can arise due to mutations in E. coli that alter the T1 receptor in the cell wall.

13. Spontaneous vs induced mutations
Luria noted that the two theories of mutation (spontaneous vs induced) made different statistical predictions.
If the TonR mutations were induced by exposure to phage T1, then every population of cells would be expected to have an equal probability of developing resistance and hence a nearly equal number of TonR colonies would be produced from different cultures.
For example, if there was a 10-8 probability that exposure to phage T1 would induce a TonR mutant, then approximately 10 colonies would arise on each plate spread with 109 bacteria.
In contrast, if TonR mutations were due to random, spontaneous mutations that occured sometime during the growth of the culture prior to exposure to phage T1, then the number of TonR colonies would vary widely between each different culture.
For example, although there is an equal probability (say 10-8) that a TonR mutant would arise per cell division, the number of resistant bacteria in each culture would depend upon whether the mutation occurred during one of the first cell divisions or one of the last cell divisions.

14. Different predictions
The figure shows a cartoon of the two alternative predictions. TonS cells are indicated in white and TonR cells are indicated in black. The shaded area indicates when the cells were exposed to phage T1.
In either of these two cases, if multiple samples from a single culture of bacteria were plated on phage T1, each of the resulting plates should yield approximately the same number of colonies. However, the two possibilities can be distinguished mathematically by comparing the mean and variance of the number of the number of mutants in each culture.

15. The “fluctuation test”
Luria and Delbruck designed their "fluctuation test" as follows.
They inoculated 20 small cultures (0.2 ml), each with a few cells, and incubated them until there were 108 cells per ml. At the same time, a much larger culture also was inoculated and incubated until there were 108 cells per milliliter. The 20 individual cultures and 10 aliquots of the same size from the large culture were plated in the presence of phage.
If resistance were due to random mutation during the incubation period, each culture tube would produce a different number of resistant cells; the number would vary depending on how early in the cascade of growing cells the mutation occurred. These resistant cells would each produce a separate colony when plated with the T1 phage.
If resistance were due to a physiological adaptation occurring after exposure of the cells on the T1 phage, all cultures would be expected to generate resistant cells at roughly the same rate and little variation from culture to culture would be expected.

16. Results of the fluctuation test
Variation from plate to plate was indeed observed in the individual 0.2-ml cultures but not in the samples from the bulk culture (which represent a kind of control experiment). This situation cannot be explained by physiological change, because all the samples spread had the same approximate number of cells. The simplest explanation is random mutation, occurring early in the incubation of the 0.2-ml cultures (producing a large number of resistant cells and, therefore, a large number of colonies) or late (producing few resistant cells and colonies) or not at all (producing no resistant cells).

17. Measuring the mutation rate
Luria and Delbrück's fluctuation test provides a way of measuring the mutation rate towards acquisition of resistance to phage T1.
The 20 cultures that were tested for phage T1 resistance can be divided among those in which no mutation had occurred (11 of the 20 = 0.55) and those in which a mutation had occurred once or more (we cannot distinguish the cultures in which one mutation only had occurred from the others). This situation is well described by the Poisson distribution, in which the probability of zero occurrences of an event (P0) is given by P0 = e-m, where m is the probability that an event will occur.
We can estimate m from data by letting 0.55 = e-m and solving for m (m = -ln 0.55); this gives m = 0.6 mutations/tube.
We can now estimate the number of cell duplications (n) that occurred in each tube. If n is very large, and if the original number of cells was very small, then a sufficiently accurate estimate of the number of cell divisions is given by n itself.
Thus, since n = 0.2 × 108, we arrive at an estimate of the mutation rate (m) of m = 0.6/ 0.2 × 108 = 3 × 10-8.
Note that m is expressed as number of mutations per gene per DNA replication.