The recombination rate (r) between linked loci A and B is...

The recombination rate $(r)$ between linked loci $A$ and $B$ is $0.10 .$ In a population, we observe the following haplotypic frequencies: \[ \begin{array}{ll} A B & 0.40 \\ a B & 0.10 \\ A b & 0.10 \\ a b & 0.40 \end{array} \] a. What is the level of linkage disequilibrium as measured by $D$ in the present generation? b. What will $D$ be in the next generation? c. What is the expected frequency of the $A b$ haplotype in the next generation? d. Using a spreadsheet computer software program, make a graph of the decline in $D$ over 10 generations.

The recombination rate $(r)$ between linked loci $A$ and $B$ is $0.10 .$ In a population, we observe the following haplotypic frequencies:
\[
\begin{array}{ll}
A B & 0.40 \\
a B & 0.10 \\
A b & 0.10 \\
a b & 0.40
\end{array}
\]
a. What is the level of linkage disequilibrium as measured by $D$ in the present generation?
b. What will $D$ be in the next generation?
c. What is the expected frequency of the $A b$ haplotype in the next generation?
d. Using a spreadsheet computer software program, make a graph of the decline in $D$ over 10 generations.

Key Concepts

Decay of LD Over Generations

The decay of linkage disequilibrium over generations is typically modeled by the equation D_t = (1 - r)^t * D_0, where D_t is the disequilibrium after t generations, D_0 is the initial disequilibrium, and r is the recombination rate. This reflects that each generation of recombination reduces the non-random association between alleles, causing D to decline exponentially until it approaches zero.

Haplotype Frequencies

Haplotype frequencies represent the proportions of different combinations of alleles that occur at multiple loci on the same chromosome. They are essential for calculating measures such as linkage disequilibrium because the observed frequencies of haplotypes are compared with the expected frequencies if alleles were combined randomly, providing insights into the underlying genetic structure of the population.

Graphical Representation

Graphing the decline in linkage disequilibrium over several generations is an effective way to visualize the exponential decay governed by the recombination rate. By plotting D against the number of generations, one can observe how recombination progressively erodes the association between alleles. Spreadsheet software can be used to compute D for each generation using the decay formula and then create a graph that illustrates this trend over time.

Linkage Disequilibrium

Linkage disequilibrium (LD) is a measure of the non-random association of alleles at different genetic loci. It quantifies how frequently combinations of alleles occur together compared to what would be expected if the loci were independently assorted. The parameter D is typically calculated from the frequencies of the haplotypes, and it reflects the degree to which allelic associations deviate from equilibrium expectations.

Recombination Rate

The recombination rate (r) is the probability that a crossover event occurs between two loci during meiosis, thereby reshuffling the alleles and creating new haplotypic combinations. It plays a crucial role in reducing linkage disequilibrium over generations by breaking apart associations between linked alleles, with the magnitude of the reduction depending on the recombination fraction.

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