There is various method of linkage mapping :
11.1.    Mapping through the number of crossovers observed during the meiosis 1
Crossing over is a feature of the germ cell. During meiosis I crossing over takes place in pachytene stage of meiosis I. By observing the chromatid in prophase I of meiosis I. We can map the distance between two genes based upon the number of the cell showing a particular number of cross over.

Let’s imagine that you are observing meiosis in germ cell and following numbers are given to you 70 gametes out of 100 produces because of no cross over, 23 gametes out of 100 are produced because of single cross over.  5 gametes out of 100 are produced because of a double cross over. 2 gametes out of 100 are produced because of triple cross over.

The distance between A and B gene is 0.42 M. This can be also represented as 42 cM is equal to one map unit. Thus the distance between A and B genes is 42 map unit.
When crossing over number is given then we calculate it by the average number of crossovers between A and B. In this method, we do not consider the parental and recombinant, we consider only crossing over the number.
11.2.    Gene Mapping through chiasmata Frequency
The genetic maps of chromosomes are based on the average number of crossovers that occur during meiosis. The actual number of crossover can’t be predicted. Genetic map distances are estimated by calculating the frequency of recombination between genes in experimental crosses. 

11.3.    Mapping by test cross:-
If two genes are 100% linked the dihybrid ratio deviates from 9: 3 : 3 : 1 and reduced to monohybrid ratio of  3:1 and only two types of gametes are produced instead of four types of gametes. These linked genes do not strictly obey Mendel’s principle of independent assortment; rather, they tend to be inherited together as a unit.
When the heterozygous Red and long plant is test crossed with the dwarf and short plant the test cross yielded the following results.

This frequency of recombinants i.e. 0.08 M is used to generate what is known as genetic maps, linkage maps. The frequency of recombination of greater than 50% and the two loci would be assumed either to not be located on the same chromosome or instead to be on the same chromosome but quite distantly separated.
To develop the understanding of linkage we can compare the inheritance of two linked genes with the inheritance of two genes that assort independently. 

New combinations of alleles in the above gamete formation is the result of an independent assortment of genes present on different chromosomes. Here genes are not linked so we get 50% parental and 50% recombinant.
Following conclusion can be drawn from the above experiment 
1.    Linked Genes do not assort Independently
The principle of segregation states that each individual diploid organism possesses two alleles at a locus that separate in meiosis, with one allele going into each gamete. 
The principle of independent assortment states that during the process of separation, the two alleles at a locus act independently of alleles at other loci. The independent separation of alleles results in recombination, the sorting of alleles into new combinations. 
11.4.    Recombination 
Recombination means the combination of alleles in the gametes produced by progeny(F1) is different from the gametes produce by its parents. Mendel derived his principles of segregation and independent assortment by observing the progeny of genetic crosses, but he had no idea of the chromosome and what brings the recombination in the progeny. At that time there was no idea of crossing over. Later the chromosome theory of heredity reveals that genes are found on chromosomes.

Linked Genes Segregate together and Crossing Over Produces Recombination Between Them  
Genes that are close together on the same chromosome usually segregate as a unit and are therefore inherited together. The frequency of crossing over between two closely placed genes is low. This implies that the chances of separation of two closely linked genes are low. The number of chiasmata observed between non-sister chromatid of the homologous chromosome is very less and the number is not more than five which indicate that the chances of separation of two close genes are less.

Representation of Genes on Chromosomes
The representation of genes on chromosomes. A cross between an individual homozygous for dominant alleles at two linked loci and another individual homozygous for recessive alleles at those loci (XX YY × xx yy) is represented as below.

In this notation, each line represents one of the two homologous chromosomes. Inheriting one chromosome from each parent, the F1 progeny is represented by

a)    Complete linkage:- Genes are located very close together on the same chromosome and do not exhibit crossing over that means only non-recombinant gametes will be produced, the recombination frequency is zero.
b)    Independent assortment of two genes will result in 50% of the gametes being recombinant and 50% being non-recombinant, as would be observed for genes on two different chromosomes. Independent assortment may also be observed for genes on the same chromosome if they are far enough apart that one or more crossovers occur between them in every meiosis. 
11.4.1.    Test Cross for linkage
The linkage can be identified by a test cross also. When a heterozygous individual is test-crossed with a homozygous recessive individual (Aa Bb × aa bb). The following results can be obtained. If two genes are unlinked 
If two genes are unlike that means they are present on the separate chromosome the F1 produce four types of gametes that are also in equal frequency. That means the gametic ratio of F1 generation is 1:1:1:1.  When this F1 generation plant is test crossed with the recessive plants, the phenotypic and genotypic ratio is same that is typical dihybrid ratio of testcross  1:1:1:1. 
This is because of the independent assortment of genes as genes are present on a different chromosome. They separate independently from each other and give rise to all possible allelic combinations. If two genes are linked 
The effect of crossing over on the inheritance of two linked genes. Crossing over, which takes place in prophase I of meiosis, is the exchange of genetic material between nonsister chromatids. After a single crossover has taken place, the two chromatids that did not participate in crossing over are unchanged; gametes that receive these chromatids are non-recombinants. The other two chromatids, which did participate in crossing over, now contain new combinations of alleles; gametes that receive these chromatids are recombinants.
In each meiosis a single crossover takes place, then, two nonrecombinant gametes and two recombinant gametes will be produced. The result is as same as that produced by independent assortment; so, when crossing over between two loci takes place in every meiosis, it is impossible to determine whether the genes are on the same chromosome and crossing over took place or whether the genes are on different chromosomes.

Recombination Frequency
The percentage of recombinant progeny produced in a cross is called the recombination frequency, which is calculated as follows:-

11.5.    Mapping through two-point test cross
Two point test cross is when we calculate the distance between two genes present on the same chromosome with the help of test cross called as two-point test cross.
If two genes are linked the test cross ratio is not 1:1:1:1. It deviated significantly from it. This is because of genes which are close together on the same chromosome usually segregate as the unit and are therefore inherited together. There is a least tendency to form all possible allelic combination in equal number. The frequency of crossing over between two closely placed genes is low. This implies that the chances of separation of two closely linked genes are low. This allows the deviation of gametic ratio from 1:1:1:1. Thus the F1 generation forms the unequal type of gametes. When these unequal gametes combine with the gametes produced by recessive parents the ratio deviates from the typical dihybrid test cross ratio of 1:1:1:1 to 1:1. 
Along with wings, grey body female is cross with vestigial wings black body male. All the male and female are long wings and a grey body. This indicates that the long wings grey body trait are dominant over vestigial wings black body. 
When the F1 generation is test crossed with the recessive parent the F2 generation is obtained. In F2 generation the ratio is not equal to 1:1:1:1 this indicates the genes are linked. Here we take two genes thus called as two-point test cross.

11.5.2.    The drawback in Two point test cross
A double crossover between two genes gives parental genotype and not regarded as recombinant even though recombination has occurred twice. This is a major drawback in the two-point test cross as it gives inaccurate map distance between two genes since not all crossovers can be counted as recombinants. That means in two-point test cross we are not counting all the cross over the product. This gives an inaccurate map distance.

11.6.    Three-Point Cross
A three-point test cross is a cross of a triple heterozygous with a triple homozygous recessive. The potential advantage of the three-point testcross over two point test cross is the presence of a third allelic pair between the two genes enables the detection of the double crossover event. In a double crossover, the middle gene will change positions relative to the outside genes.  Three-point cross is used to determine the loci of three genes in an organism genome. It can be used to order three loci on a chromosome.
Gene mapping using three-point test cross 
A double crossover between linked genes gives only parental gametes, thus inaccurate map distances between genes result since not all crossovers were counted while mapping the genes on the chromosome. 
    The procedure of three-point test crosses
1.    Some of the offspring to get a total number of progeny.
2.    The highest frequency is identified as parental genotypes.
3.    The lowest frequency is identified as double recombinant genotypes.    
4.    Now we have to identify the order of genes. The order of genes can be identified by comparing double recombinant genotypes with the parental genotypes.
5.    Draw a map of the chromosome, and divide the spaces between loci into two 'regions'.    
6.    Now map the distance.    
7.    For the first region, identify the two classes of single recombinant offspring where a recombination event has occurred in this area. Sum the offspring of these classes and the offspring of the double recombinant classes will give a recombinant value for that region.

8.    The map distance for this region is 

9.    Repeat steps 6 and 7 for the second 'region' to give this region a map distance.

11.6.1.    Three-point test cross in Drosophila
In the case of Drosophila, there is a problem by applying the principles we used in the above example. The following table gives the results we will analyze. 

Step 1:     Determine the parental genotypes. 
The genotypes found most frequently are the parental genotypes. From the table, it is clear that the v cv+ ct+ 
    v+ cv ct genotypes were the parental genotypes.  
Step 2:     Determine the gene order 
The double-crossover genotypes are the least frequent.  To determine the gene order, compare the parental genotypes with double crossover genotypes. 
Step 3:     Determining the linkage distances. 

•    v - ct distance calculation. 

Step 4.  Draw the map. 

As we talked about the dependency of one cross over another. The occurrence of one cross over inhibits the occurrence of the second cross over in the vicinity of the first. This is known as interference.
    I  =  1 - C 
11.6.2.    Coefficient of Coincidence
To measure interference, we first calculate the coefficient of coincidence (C) which is the ratio of an observed double cross over frequency to expected double cross over frequency.  


For the v ct cv data, the interference value is 33% [100*(8/12)].

Most often, interference values fall between 0 and 1. Values less than one indicate that interference is occurring in this region of the chromosome.
Expected double cross over (EDCO)  =  (Single C.O frequency between ct and cv)  x  (S co frequency between valid ct)
Expected double cross over (EDCO)  =  6.4  x  13.2  =  84.48

For the v and ct loci, the recombinants are v ct and v+  ct+. There are 89 + 94 + 3 + 5 = 191 of these recombinants among 1448 flies, so recombination frequency  is 13.2 percent.
For ct and cv, the recombinants are cv  ct+ and cv+ ct. There are 45 + 40 + 3 + 5 = 93 of these recombinants among the 1448, so recombination frequency is 6.4 percent.

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