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29.3: Genetic Linkage

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    41136
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    In the simple models we’ve seen so far, alleles are assumed to be passed on independently of each other. While this assumption generally holds in the long term, in the short term we will generally observe a that certain alleles are passed on together more frequently than expected. This is termed genetic linkage.

    The , also known as Mendel’s second law states:

    Alleles of different genes are passed on independently from parent to offspring.

    When this “law” holds, there is no correlation between different polymorphisms and the probability of a haplotype (a given set of polymorphisms) is simply the product of the probabilities of each individual polymorphism.

    In the case where the two genes lie on different chromosomes this assumption of independence generally holds, but if the two genes lie on the same chromosome, they are more often than not passed on together. Without genetic recombination events, in which segments of DNA on homologous chromosomes are swapped (crossing-over), the alleles of the two genes would remain perfectly correlated. With however, the correlation between the genes will be reduced over several generations. Over a suitably long time interval, recombination will completely remove the linkage between two polymorphisms; at which point they are said to be in equilibrium. When, on the other hand, the polymorphisms are correlated, we have Linkage Disequilibrium (LD). The amount of disequilibrium is the difference between the observed haplotype frequencies and those predicted in equilibrium.

    The linkage disequilibrium can be used to measure the difference between observed and expected assortments. If there are two alleles (1 and 2) and two loci (A and B) we can calculate haplotype probabilities and find the expected allele frequencies.

    • Haplotype frequencies

    – P(A1)=x11

    – P(B1)=x12

    – P(A2)=x21

    – P(B2)=x22

    • Allele frequencies

    – P11 = x11 + x12

    – P21 = x21 + x22

    – P12 = x11 + x21

    – P22 = x12 + x22

    • D=P11 *P22P12 *P21
    Dmax, the maximum value of D with given allele frequencies, is related to D in the following equation:

    \[D^{\prime}=\frac{D}{D_{\max }}\nonumber\]

    D' is the maximum linkage disequilibrium or complete skew for the given alleles and allele frequencies. Dmax can be found by taking the smaller of the expected haplotype frequencies P (A1, B2) or P (A2, B1). If the two loci are in complete equilibrium, then D' = 0. If D' = 1, there is full linkage.

    The key point is that relatively recent mutations have not had time to be broken down by crossing-overs. Normally, such a mutation will not be very common. However, if it is under positive selection, the mutation will be much more prevalent in the population than expected. Therefore, by carefully combining a measure of LD and derived allele frequency, we can determine if a region is under positive selection.

    Decay of is driven by recombination rate and time (in generations) and has an exponential decay. For a higher recombination rate, linkage disequilibrium will decay faster in a shorter amount of time. However, the background recombination rate is dicult to estimate and varies depending on the location in the genome. Comparison of genomic data across multiple species can help in determining these background rates.

    29.3.1 Correlation Coefficient r2
    Answers how predictive an allele at locus A is of an allele at locus B

    \[r^{2}=\frac{D^{2}}{P\left(A_{1}\right) P\left(A_{2}\right) P\left(B_{1}\right) P\left(B_{2}\right)}\nonumber\]

    As the value of r2 approaches 1, the more two alleles at two loci are correlated. There may be linkage disequilibrium between two haplotypes, even if the haplotypes are not correlated at all. The correlation coecient is particularly interesting when studying associations of diseases with genes, where knowing the genotype at locus A may not predict a disease whereas locus B does. There is also the possibility where neither locus A nor locus B are predictive of the disease alone but loci A and B together are predictive.


    29.3: Genetic Linkage is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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