666.04 - Introduction to Coalescent Models Biostatistics...

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Introduction to Coalescent Models Biostatistics 666 Lecture 4
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Last Lecture z Linkage Equilibrium Expected state for distant markers z Linkage Disequilibrium Association between neighboring alleles Expected to decrease with distance z Measures of linkage disequilibrium D, D’ and ²or±r 2
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Previously … z DNA sequence variation Types of DNA variants z Allele frequencies z Genotype frequencies Hardy-Weinberg Equilibrium
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Making predictions… z What allele frequencies do we expect? z How much variation in a gene? z How are neighboring variants related?
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Simple Approach: Simulation 1. N starting sequences 2. Sample N offspring sequences ± Apply mutations according to µ 3. Increment time 4. If enough time has passed… ± Generate final sample ± Stop. 5. Otherwise, return to step 1.
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Simulating a Population … Time Sequences
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Today z Introduce coalescent approach Framework for studying genetic variation Provides intuition on patterns of variation Provides analytical solutions
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Aim … z Gene genealogies: Descriptions of relatedness between sequences Analogous to phylogenetic trees for species z The shape of the genealogy depends on population history, selection, etc. z Together with mutation rate, genealogy predicts DNA variation
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Genealogy z History of a particular set of sequences Describes their relatedness Specifies divergence times z Includes only a subset of the population z Most Recent Common Ancestor (MRCA)
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Coalescent approach z Generate genealogy for a sample of sequences. Introduces computational and analytical convenience. z Instead of proceeding forward through time, go backwards!
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History of the Population
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Genealogy of Final Population
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Levels of Complexity z History of the population Includes sequences that are “extinct” z History of all modern sequences Includes sequences that we haven’t sampled z History of a subset of modern sequences Minimalist approach!
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Parameters we will focus on… z Mutation rate ( µ ) z Population Size Haploid population (N chromosomes) Diploid population (2N chromosomes) z Time (t) z Sample size (n) z Recombination rate (r)
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666.04 - Introduction to Coalescent Models Biostatistics...

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