The ‘V’ in the Tajima D equation is: The variance of the difference expected between P- K / a under the standard neutral model. The variance cannot be expressed in any simple form, and the reason for doing so is to create a test statistic that would be Normally distributed with mean 0 and variance equal to 1 in the limit of infinite data. For any real sample, the distribution of the difference is not Normally distributed,and it often makes sense to derive the distribution by simulation rather than use tables. This is particularly true if there is recombination in the data set, as the confidence intervals tabulated in the paper assume no recombination, which (generally) makes the test conservative if there is recombination.

Genetic Linkage

Two pops may have the same allele frequencies but different chromosome frequencies.

Conditions for Linkage Equilibrium (Two locus case) Frequency of B is the same on chromosome A and a Frequency of haplotypes AB, ab, Ab, aB can be calculated from allele frequencies A=p, a=q, B=t, and b=s. f(AB) = pt f(ab) = qs f(Ab) = ps f(aB) = pt 3) Coefficient of linkage disequilibrium (D) = 0 f(AB) x f(ab) - f(Ab) x f(aB) = D ps x qt - pt x qs = 0 (ranges from -0.25 to +0.25)

Hardy Weinberg Principle for Two Loci Chromosome frequencies remain unchanged across generations if loci are in linkage equilibria. If loci are in linkage disequilibria, the chromosome frequencies will move closer to linkage equilibrium each generation. What Creates Linkage Disequilibrium in a Population? selection, drift, and population admixture

Effects of Selection on Chromosome Frequencies ab/ab = body size of value 10 each additional A or B adds 1 value predators eat all individuals of size 12 or less 65.28% survive

Locus A and B are in disequilibrium among the survivors Freq a = (0.1536 + 0.1536) / .6528)/2 = 0.24 Freq b = (0.0576 + 0.0576) / .6528)/2 = 0.09 Freq ab = .24 x .09 = .02 however! 65.28% survive Locus A and B are in disequilibrium among the survivors

Genetic Drift, followed by selection can cause linkage disequilibrium

Admixture

Recombination Breaks Down Linkage Disequilibria The rate of decline in LD increases with r

LD declines over time (rate depending on r) r = D sqrt(pqst)

All allele combinations All allele combinations Concept of Linkage Law of Independent Assortment ab = 0.25 A B b Meiosis All allele combinations in gametes equally probable aB = 0.25 a Ab = 0.25 AB = 0.25 Probability of recombination = 0.5 ab = 0.25 A a B b All allele combinations in gametes equally probable Meiosis aB = 0.25 Ab = 0.25 AB = 0.25

All allele combinations All allele combinations Linked Loci Probability of recombination = 0.3 ab = 0.35 A a Meiosis aB = 0.15 B b All allele combinations in gametes NOT equally probable Ab = 0.15 AB = 0.35 Probability of recombination = 0.1 ab = 0.45 A a B b Meiosis All allele combinations in gametes NOT equally probable aB = 0.05 Ab = 0.05 AB = 0.45

Why important? Concept: The closer two loci are on a chromosome, the lower the probability of recombination. Why important? (1) Affects rate that LD is broken down. (2) Allows one to determine the linear order of genes on a chromosome (make a genome map). (3) Maps allow for the localization of genes, mutant phenotypes, and QTL in the genome.

Selection at a single locus affects other loci under LD Selection has an effect on frequency of B alleles

new mutations are linked to deleterious sites or arise LD may retard rate of evolution If: new mutations are linked to deleterious sites or arise in the ‘wrong’ chromosomal backgrounds A comparison of substitution rates between D. simulans and D. melanogaster for synonomous and non-synonomous sites

Where did CCR5 D32 come from? There is strong linkage disequilibrium between CCR5 and two neutral marker loci.

Pg = (1 - c - m)g Prob recombination Prob mutation Probability that D32-197-215 has remained unchanged across generations: Pg = (1 - c - m)g Prob recombination Prob mutation Estimated p = 0.848, m = 0.001, c = 0.005 g = 27.5 ~ 27.5 x 25 = 688 yrs

How does LD help identify genes that may be under positive natural selection? For neutral alleles: Genetic drift is the primary evolutionary mechanism. So: If LD is detectable, indicates that an allele is young. Expect magnitude of LD is proportional to the age of an allele. If LD is not detectable, indicates that an allele is old. Expect old and frequent alleles, or old and rare alleles, But do not expect young, high frequency alleles. Indicates alleles at the locus may be under selection.

G6PD polymorphism and deficiency Countries with malaria

LD is higher for the G6PD-202A allele suggests positive selection Probability that 2 randomly chosen “a” chromosomes have the same snps across a physical distance