Coefficient of coincidence
Encyclopedia
In genetics, the coefficient of coincidence (c.o.c.) is a measure of interference in the formation of chromosomal crossover
Chromosomal crossover
Chromosomal crossover is an exchange of genetic material between homologous chromosomes. It is one of the final phases of genetic recombination, which occurs during prophase I of meiosis in a process called synapsis. Synapsis begins before the synaptonemal complex develops, and is not completed...

s during meiosis
Meiosis
Meiosis is a special type of cell division necessary for sexual reproduction. The cells produced by meiosis are gametes or spores. The animals' gametes are called sperm and egg cells....

. It is generally the case that, if there is a crossover at one spot on a chromosome, this decreases the likelihood of a crossover in a nearby spot. This is called interference.

The coefficient of coincidence is typically calculated from recombination rates between three genes. If there are three genes in the order A B C, then we can determine how closely linked
Genetic linkage
Genetic linkage is the tendency of certain loci or alleles to be inherited together. Genetic loci that are physically close to one another on the same chromosome tend to stay together during meiosis, and are thus genetically linked.-Background:...

 they are by frequency of recombination. Knowing the recombination rate between A and B and the recombination rate between B and C, we would naively expect the double recombination rate to be the product
Product (mathematics)
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication...

 of these two rates.

The coefficient of coincidence is calculated by dividing the actual frequency of double recombinants by this expected frequency:
c.o.c. = actual double recombinant frequency / expected double recombinant frequency


Interference is then defined as follows:
interference = 1 - c.o.c.


This figure tells us how strongly a crossover in one of the DNA regions (AB or BC) interferes with the formation of a crossover in the other region.

Worked example

Drosophila
Drosophila melanogaster
Drosophila melanogaster is a species of Diptera, or the order of flies, in the family Drosophilidae. The species is known generally as the common fruit fly or vinegar fly. Starting from Charles W...

 males of genotype
Genotype
The genotype is the genetic makeup of a cell, an organism, or an individual usually with reference to a specific character under consideration...

 AaBbCc were crossed with females of genotype aabbcc. This led to 1000 progeny of the following phenotype
Phenotype
A phenotype is an organism's observable characteristics or traits: such as its morphology, development, biochemical or physiological properties, behavior, and products of behavior...

s:
ABC: 244 (parental genotype, shows no recombination)
ABc: 71 (recombinant between B and C)
AbC: 23 (double recombinant)
Abc: 152 (recombinant between A and B)
aBC: 148 (recombinant between A and B)
aBc: 27 (double recombinant)
abC: 79 (recombinant between B and C)
abc: 236 (parental genotype, shows no recombination)


From these numbers it is clear that the B/b locus
Locus (genetics)
In the fields of genetics and genetic computation, a locus is the specific location of a gene or DNA sequence on a chromosome. A variant of the DNA sequence at a given locus is called an allele. The ordered list of loci known for a particular genome is called a genetic map...

lies between the A/a locus and the C/c locus.

There are 23 + 152 + 148 + 27 = 350 progeny showing recombination between genes A and B. And there are 71 + 23 + 27 + 79 = 200 progeny showing recombination between genes B and C. Thus the expected rate of double recombination is (350 / 1000) * (200 / 1000) = 0.07 (or 70 per 1000). .

However, there are actually only 23 + 27 = 50 double recombinants. The coefficient of coincidence is therefore 50 / 70 = 0.71.

Interference is 1 - 0.71 = 0.29.
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