Question

Linkage Disequilibrium

a) Mention two processes that may cause LD.

b) Why may the extent of LD vary over a chromosome?

c) After how many generations have the LD between two loci with a recombination rate of 0.1 declined to 50% of the starting LD?

d) Calculate LD between two biallelic loci (alleles A/a and B/b) in a population that has just been formed by mixing equal number of individuals from two source populations with the following allele frequencies: Population 1: pA=90%, pB=70%; Population 2: pA=60%, pB=30%.

e) What will happen with LD over time in the admixed population between (i) two loci located on two different chromosomes, and (ii) two tightly located loci?

Answer 1

a) Linkage disequilibrium is caused by effect of non random mating in small population, low recombination rate

Recombination and genetic drift

In a finite-size population we observe LD because its variance is larger than zero. Again, the smaller the effective population size the larger is the variance. An extreme reduction in population size, like a very strong bottleneck, can therefore increase LD due to the loss of haplotypes. The associated increase of genetic drift will increase LD. Especially long-distance LD is a sign of population reduction which can be best detected by comparing two populations: one ancestral and one derived. Population expansion, on the other hand, is characterized by a fast decay of LD. New haplotypes are introduced into the population and thin out haplotype combinations

Selection
A novel, advantageous allele under strong positive Darwinian selection will quickly rise in frequency, carrying along neighboring neutral alleles (selective sweep). This results in a dramatic loss of local heterozygosity and an unusually strong LD of linked neutral sites with the beneficial site. The LD across the selected site vanishes after the fixation of the Lecture X: Linkage Disequilibrium Lecture WS Evolutionary Genetics Part I – Richard Merrill 7 beneficial allele, while the LD on either side of the selected locus remains. If recombination occurs during the sweep, chromosomal segments that otherwise would have been lost from the population may recombine with the haplotype carrying the advantageous mutation thus rescuing the present genetic variation. The higher the recombination rate between a locus and the centre of the selective sweep the less its variation will be affected.

b) Genetically distant loci are more likely to recombine and more recombination lowers LD so it varies over chromosomes, LD decreases with genetic distance

c)

C 50% Die LD decreases AD = 50 -0.5. loo t = ? pote(t-ot Do 50 =(1-0.g)t 100 => 0.5 = (0.9€ (taking natural logs on > 46.693 to 40.105) both sides) t = 6.6 generations.

d)

6A = 90% PA = 0.6 = 0.9 PB = 70 % PB = 0.3 = 0.7 BB- bag tolab Petre Rab+ Pas D = PAB - PAB PAR a difference between frequency of gametes. carrying the pair of alleles A and B at - two loci PAPB 2 product of two alleles. PA I PAT IP2A & P B = 1 PB + 1 P2B PAB 1 PLA PLB + I BAP2B. Coefficient of LD in a mixture - D = I (PA - PRA) (Pig Pes) =] (0.9 -0.6) (0.47-0.3) 2 t x D:3x04 = 0.03

e) Migration and admixture The mixing of individuals from different subpopulations that have different allele frequencies creates LD. If two subpopulations both fixed unequal allele combinations, such as AB and ab, respectively, any mixture of individuals would create LD, although each subpopulation on its own has none. This can be directly seen with a simple example. Assume two populations each with segregating alleles A and a at one locus and B and b at the second locus – within each population the loci are in linkage disequilibrium. Therefore, the frequency of the AB haplotype is equal to the expectation p1Ap1B and p2Ap2B in both populations.Whenever allele frequencies differ for both loci (e.g. by the effect tof genetic drift) D will be non-zero. Population subdivision therefore generates LD even if each population is in linkage equilibrium. This is called the two-locus Wahlund effect. As a consequence, migration between divergent populations increases LD in each population. For single major migration bouts, the timing of migration can in principle be estimated by the decay of LD generated during the migration event

i) when genes on different chromosomes LD will decrease over generations due to higher probabilty of crossing over

ii) tightly linked loci will be linked will cause high rates of LD