Lecture 22: Signatures of Selection and Introduction to Linkage Disequilibrium November 12, 2012
Last Time Sequence data and quantification of variation Infinite sites model Nucleotide diversity (π) Sequence-based tests of neutrality Tajima s D Hudson-Kreitman-Aguade Synonymous versus Nonsynonymous substitutions McDonald-Kreitman
Today Signatures of selection based on synonymous and nonsynonymous substitutions Multiple loci and independent segregation Estimating linkage disequilibrium
Using Synonymous Substitutions to Control for Factors Other Than Selection d N /d S or Ka/Ks Ratios
Types of Mutations (Polymorphisms)
Synonymous versus Nonsynonymous SNP First and second position SNP often changes amino acid UCA, UCU, UCG, and UCC all code for Serine Third position SNP often synonymous Majority of positions are nonsynonymous Not all amino acid changes affect fitness: allozymes
Synonymous & Nonsynonymous Substitutions Synonymous substitution rate can be used to set neutral expectation for nonsynonymous rate d S is the relative rate of synonymous mutations per synonymous site d N is the relative rate of nonsynonymous mutations per non-synonymous site ω = d N /d S If ω = 1, neutral selection If ω < 1, purifying selection If ω > 1, positive Darwinian selection For human genes, ω 0.1
Complications in Estimating d N /d S Multiple mutations in a codon give multiple possible paths Two types of nucleotide base substitutions resulting in SNPs: transitions and transversions not equally likely CGT(Arg)->AGA(Arg) CGT(Arg)->AGT(Ser)->AGA(Arg) CGT(Arg)->CGA(Arg)->AGA(Arg) Back-mutations are invisible Complex evolutionary models using likelihood and Bayesian approaches must be used to estimate d N /d S (also called K A /K S or K N /K S depending on method) (PAML package) http://www.mun.ca/biology/scarr/transitions_vs_transversions.html
dn/ds ratios for 363 mouse-rat comparisons Most genes show purifying selection (dn/ds < 1) Some evidence of positive selection, especially in genes related to immune system interleukin-3: mast cells and bone marrow cells in immune system Hartl and Clark 2007
McDonald-Kreitman Test Conceptually similar to HKA test Uses only one gene Contrasts ratios of synonymous divergence and polymorphism to rates of nonsynonymous divergence and polymorphism Gene provides internal control for evolution rates and demography
Application of McDonald- Kreitman Test: Aligned 11,624 gene sequences between human and chimp Calculated synonymous and nonsynonymous substitutions between species (Divergence) and within humans (SNPs) Identified 304 genes showing evidence of positive selection (blue) and 814 genes showing purifying selection (red) in humans Positive selection: defense/immunity, apoptosis, sensory perception, and transcription factors Purifying selection: structural and housekeeping genes Bustamente et al. 2005. Nature 437, 1153-1157
Genes showing purifying (red) or positive (blue) selection in the human genome based on the McDonald-Kreitman Test Bustamente et al. 2005. Nature 437, 1153-1157
How can you differentiate between effects of selection and demographic effects on sequence variation? Will this work for organellar DNA?
Extending to Multiple Loci So far, only considering dynamics of alleles at single loci Loci occur on chromosomes, linked to other loci! The fitness of a single locus ripped from its interactive context is about as relevant to real problems of evolutionary genetics as the study of the psychology of individuals isolated from their social context is to an understanding of man s sociopolitical evolution Richard Lewontin (quoted in Hedrick 2005) Size of region that must be considered depends on Linkage Disequilibrium
Gametic (Linkage) Disequilibrium (LD) Nonrandom association of alleles at different loci into gametes Haplotype: Genotype of a group of closely linked loci LD is a major factor in evolution LD itself provides insights into population history Estimation of LD is critical for ALL population genetic data
Nomenclature and concepts Two loci, two alleles Frequency of allele i at locus 1 is p i Frequency of allele i at locus 2 is q i p 1 p 2 A 1 A 2 B 1 B 2 q 1 q 2 n i= 1 n p = i q i= 1 i = 1
Nomenclature and concepts Genotype is written as A 1 B 1 A 2 B 2 A 1 A 2 B 1 B 2 A 1 and B 1 are in coupling phase A 1 and B 2 are in repulsion phase
Gametic Disequilibrium Easiest to think about physically linked loci, but not necessarily the case Meiosis A 1 B 1 A 2 B 2 A 1 B 1 A 1 B 2 A 2 B 1 A 2 B 2 p 1 q 1 p 1 q 2 p 2 q 1 p 2 q 2 What Are Expected Frequencies of Gametes in a Population Under Independent Assortment?
What are expected frequency of Gametes with complete linkage? p 1 p 2 A 1 A 2 B 1 B 2 q 1 q 2 Meiosis A 1 B 1 A 2 B 2 A 1 B 1 A 1 B 2 A 2 B 1 A 2 B 2 x 11 x 12 x 21 x 22
Linkage disequilibrium measure, D Independent Assortment: With LD: Substituting from above table: D = x x x x 11 22 12 21
Problem: D is sensitive to allele frequencies Can t have negative gamete frequencies Maximum D set by allele frequencies Example, if D is positive: p 1 =0.5, q 2 =0.5, Dmax=0.25 but p 1 =0.1, q 2 =0.9, D max =0.09 Solution: D' = D/D max ranges from -1 to 1 D max Calculation: If D is positive, D max is lesser of p 1 q 2 or p 2 q 1 If D is negative, D max is lesser of p 1 q 1 or p 2 q 2
LD can also be estimated as correlation between alleles r = r can also be standardized to a -1 to 1 scale It is equivalent to D in this case p 1 D p 2 2 q q 1 2 p p q q r ' = 1 2 1 2 = D p 1 D p max 2 q q 1 2 D'
Recombination Shuffling of parental alleles during meiosis A 1 B 1 A 2 B 2 A 1 B 1 A 1 B 2 A 2 B 2 A 2 B 1 Occurs for unlinked loci and linked loci Rate of recombination for linked markers is partially a function of physical distance
What is the expected recombination rate for unlinked loci? Meiosis A 1 B 1 A 2 B 2 A 1 B 1 A 1 B 2 A 2 B 1 A 2 B 2 c Coupling n r n r = Where n r is number of repulsion phase gametes, and n c is number of coupling phase gametes + n c Repulsion Repulsion Coupling
LD is partially a function of recombination rate Expected proportions of gametes produced by various genotypes over two generations First generation (Second generation) Where c is the recombination rate and D 0 is the initial amount of LD
Recombination degrades LD over time D = x' x' x' x' 1 11 22 12 21 = ( x cd )( x cd ) ( x cd )( x cd ) 11 0 22 0 12 0 21 0 D = 1 c) 1 D t ( D ct 0 D = e D = ( 1 c) t t 0 D0 Where t is time (in generations) and e is base of natural log (2.718)
Effects of recombination rate on LD Decline in LD over time with different theoretical recombination rates (c) Even with independent segregation (c=0.5), multiple generations required to break up allelic associations Genome-wide linkage disequilibrium can be caused by demographic factors (more later)