In a dihybrid testcross in Drosophila, Thomas Hunt Morgan found a deviation from Mendel’s law of independent assortment. He postulated that the two genes were located on the same pair of homologous chromosomes. This relation is called linkage.

Linkage explains why the parental gene combinations stay together but not how the recombinant (nonparental) combinations arise. Morgan postulated that, in meiosis, there may be a physical exchange of chromosome parts by a process now called crossing over. A result of the physical breakage and reunion of chromosome parts, crossing over takes place at the four-chromatid stage of meiosis. Thus, there are two types of meiotic recombination. Recombination by Mendelian independent assortment results in a recombinant frequency of 50 percent. Crossing over results in a recombinant frequency generally less than 50 percent.

As Morgan studied more linked genes, he discovered many different values for recombinant frequency and wondered if these values corresponded to the actual distances between genes on a chromosome. Alfred Sturtevant, a student of Morgan’s, developed a method of determining the distance between genes on a linkage map, based on the RF. The easiest way to measure RF is with a testcross of a dihybrid or trihybrid. RF values calculated as percentages can be used as map units to construct a chromosomal map showing the loci of the genes analyzed. In ascomycete fungi, centromeres also can be located on the map by measuring second-division segregation frequencies.

Single nucleotide polymorphisms (SNPs) are singlenucleotide differences in sequences of DNA. Single sequence length polymorphisms (SSLPs) are differences in the number of repeating units. SNPs and SSLPs can be used as molecular markers for mapping genes.

Although the basic test for linkage is deviation from independent assortment, such a deviation may not be obvious in a testcross, and a statistical test is needed. The χ² test, which tells how often observations deviate from expectations purely by chance, is particularly useful in determining whether loci are linked.

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Some multiple crossovers can result in nonrecombinant chromatids, leading to an underestimation of map distance based on RF. The mapping function, applicable in any organism, corrects for this tendency. The Perkins formula has the same use in fungal tetrad analysis.

In genetics generally, the recombination-based map of loci conferring mutant phenotypes is used in conjunction with a physical map such as the complete DNA sequence, which shows all the gene-like sequences. Knowledge of gene position in both maps enables the melding of cellular function with a gene’s effect on phenotype.

The mechanism of crossing over is thought to start with a double-stranded break in one participating chromatid. Erosion leaves the ends single stranded. One single strand invades the double helix of the other participating chromatid, leading to the formation of heteroduplex DNA. Gaps are filled by polymerization. The molecular resolution of this structure becomes a full double-stranded crossover at the DNA level.