Genetic Linkage

Genetic linkage is the tendency of genes or other DNA sequences on the same chromosome to be inherited together. Closely spaced sequences are generally less likely to be separated by recombination during meiosis than sequences farther apart. Linkage therefore connects the physical arrangement of genetic information with patterns of inheritance and provides the foundation for mapping genes through breeding experiments and family studies. (genome.gov)

Chromosomal basis

In a diploid organism, a pair of homologous chromosomes carries corresponding genetic positions, or loci, although the two chromosomes may carry different alleles at those positions. During meiosis, homologous chromosomes pair, and chromosomal crossing over can exchange DNA between their nonsister chromatids. Such exchanges produce new combinations of alleles. Closely spaced loci have fewer opportunities for a crossover between them and consequently tend to retain their original combinations. (facweb.furman.edu)

Linkage qualifies the scope of independent assortment, rather than contradicting the segregation of alleles at an individual locus. Loci on different chromosomes ordinarily assort independently, whereas loci close together on one chromosome do not. Widely separated loci on the same chromosome can nevertheless behave as though they assort independently because multiple crossovers obscure their physical connection. Thus, sharing a chromosome does not necessarily mean that two loci will show detectable linkage in a two-locus experiment. (facweb.furman.edu)

A linkage group is a set of loci whose inheritance relationships place them on the same chromosome. A chromosome can contain many such loci, with strong detectable linkage between neighboring markers even when markers near opposite ends show little detectable pairwise linkage. (facweb.furman.edu)

Linkage phase and recombinant combinations

For two loci with alleles $A/a$ and $B/b$, a double heterozygote can have either of two arrangements:

• Coupling, or cis phase: $AB/ab$. One homolog carries $A$ and $B$, while the other carries $a$ and $b$.
• Repulsion, or trans phase: $Ab/aB$. One homolog carries $A$ and $b$, while the other carries $a$ and $B$.

The slash separates the two homologous chromosomes. These arrangements have the same two-locus genotype, $AaBb$, but different combinations of alleles along each chromosome. Such combinations are examples of haplotypes. (facweb.furman.edu)

For an $AB/ab$ parent, $AB$ and $ab$ are the parental, or nonrecombinant, combinations, while $Ab$ and $aB$ are recombinant combinations. For an $Ab/aB$ parent, those classifications are reversed. “Recombinant” therefore describes a combination relative to the parental phase, not an intrinsic property of an allele. (passel2.unl.edu)

Complete linkage describes inheritance without recombination between the loci under consideration; incomplete linkage allows recombinant combinations. Observing no recombinants in a finite sample does not establish that recombination is impossible: very close loci may simply yield too few recombinants to be detected. (facweb.furman.edu)

Measuring linkage

The recombination fraction, usually written $r$ or $\theta$, is the probability that an informative transmission produces a recombinant combination at two loci. When recombinant and nonrecombinant offspring can be identified directly, it is estimated as

A classical testcross mates a double heterozygote with an individual homozygous for recessive alleles at both loci. Under appropriate dominance and viability assumptions, each offspring’s phenotype reveals the allele combination transmitted by the heterozygous parent. (passel2.unl.edu)

For example, consider a hypothetical $AB/ab \times ab/ab$ cross producing:

The estimated recombination fraction is

This constructed example illustrates the calculation; it is not a reported experimental result.

Under the standard model of Mendelian transmission without segregation distortion, the theoretical recombination fraction lies between 0 and 0.5. A value below 0.5 indicates linkage when supported by sufficient data. A value of 0.5 is compatible both with loci on different chromosomes and with sufficiently distant loci on the same chromosome; it does not prove physical separation onto different chromosomes. Sampling variation can make an observed proportion differ from its underlying probability. (ndsu.edu)

Genetic maps and map distance

A genetic map, or linkage map, places loci in order and assigns distances based on recombination. Its usual unit is the centimorgan (cM). Over a short interval, a recombination fraction of 0.01 corresponds approximately to 1 cM, so the hypothetical 14% recombination example gives a first approximation of 14 cM. The unit is named after Thomas Hunt Morgan. (genome.gov)

Genetic distance is not the same as physical distance in DNA base pairs. Recombination rates vary along chromosomes, so equal physical intervals need not have equal genetic lengths. There is no universal conversion from centimorgans to base pairs. (genome.gov)

Multiple crossovers and three-point mapping

Two-point measurements can underestimate genetic distance because multiple crossovers may restore the parental combination at the two outer markers. A recombinant event within the interval can therefore remain invisible when only those endpoints are examined. Although the recombination fraction cannot exceed 0.5 under the standard model, a chromosome’s genetic map can extend well beyond 50 cM. (ndsu.edu)

A three-point cross follows three loci simultaneously. In suitable testcross data, comparing parental combinations with double-crossover combinations identifies the middle locus. Double-crossover offspring are included in the recombination count for each adjacent interval, allowing a better estimate of the map than the outer markers alone provide. Larger maps are assembled by connecting overlapping intervals. (ndsu.edu)

Crossovers are not always independent events. Crossover interference describes how a crossover changes the probability of another nearby crossover. In classical three-point analysis, the coefficient of coincidence compares observed with expected double crossovers; interference is conventionally calculated as one minus that coefficient. This affects how recombination observations are interpreted as map distances. (facweb.furman.edu)

Linkage analysis in families

Human linkage studies examine whether a marker and a trait are transmitted together through families more often than expected under independent assortment. Unlike an experimental cross, a family study may leave parental phase or some genotypes uncertain. The analysis therefore evaluates the probabilities of possible inheritance patterns rather than merely counting visibly recombinant offspring. (pubmed.ncbi.nlm.nih.gov)

A LOD score, short for “logarithm of the odds,” compares the likelihood of the observed data under linkage with its likelihood under no linkage:

Here $L$ is the likelihood function, evaluated under a specified inheritance model. Positive scores favor linkage at the tested recombination fraction; negative scores favor the no-linkage model. A score of 3 represents a likelihood ratio of 1,000 to 1, not a direct statement that linkage has a 99.9% probability. Newton E. Morton established the influential sequential LOD-score framework in 1955. (pubmed.ncbi.nlm.nih.gov)

Genetic mapping can locate a chromosomal region containing a gene involved in an inherited trait. It does not, by itself, identify which sequence change is responsible or establish its biological mechanism. A nearby marker may track the responsible variant simply because the two are inherited together. (genome.gov)

Linkage versus linkage disequilibrium

Genetic linkage and linkage disequilibrium are related but distinct:

• Linkage concerns recombination and joint transmission of loci through meiosis.
• Linkage disequilibrium, or LD, concerns the nonrandom association of alleles in a population.

For two alleles $A$ and $B$, one measure of LD is

where $p_{AB}$ is the frequency of the $AB$ haplotype and $p_A$ and $p_B$ are the individual allele frequencies. If $D=0$, the observed haplotype frequency equals that expected from the allele frequencies. Physical linkage can help preserve an association, but the definition of LD is statistical rather than simply positional. (genome.gov)

This distinction separates two mapping strategies: family linkage mapping follows transmissions across observed generations, whereas population association mapping uses correlations among variants represented in population haplotypes. The International HapMap Project characterized such population patterns to support studies of genetic variation and disease. (genome.gov)

Historical development

The chromosome-based understanding of linkage developed through experiments in Thomas Hunt Morgan’s fruit-fly laboratory. In 1913, Alfred H. Sturtevant published the first genetic linkage map, using inheritance data to infer the relative positions of genes on a chromosome. The important conceptual step was that recombination frequencies could reveal an ordered arrangement of genes without directly observing their molecular locations. (caltech.edu)

Later human genetic mapping extended this principle to inherited DNA markers. Linkage maps helped researchers locate genes responsible for disorders such as cystic fibrosis and Duchenne muscular dystrophy and formed an important component of the Human Genome Project. (genome.gov)

Limitations and interpretation

Linkage evidence depends on informative observations. If the parental allele combinations cannot be distinguished, a transmission may provide little or no information about recombination. Testcross interpretation also depends on whether the scored offspring accurately represent the gametes produced: differences in survival or phenotype identification can alter the observed class frequencies. (passel2.unl.edu)

Two-point data have limited power to distinguish distant loci on one chromosome from loci on different chromosomes. Three-point and larger maps recover information by introducing intermediate markers, but finite samples still leave uncertainty in gene order and distance estimates. Genetic maps describe recombination relationships; physical sequence maps describe molecular positions. Neither should be treated as an interchangeable measurement of the other. (ndsu.edu)

References

1. Linkagegenome.gov
2. Linkage: Chapter 5facweb.furman.edu
3. Haplotypegenome.gov
4. Two Point Test Cross Mappingpassel2.unl.edu
5. Centimorgan (cM)genome.gov
6. Understanding Our Genetic Inheritance: The U.S. Human Genome Project—The First Five Yearsgenome.gov
7. Sequential tests for the detection of linkagepubmed.ncbi.nlm.nih.gov
8. Genetic Mapping Fact Sheetgenome.gov
9. What is Linkage Disequilibrium?genome.gov
10. A Haplotype Map of the Human Genomegenome.gov