# 666.20 - The Lander-Green Algorithm Biostatistics 666...

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The Lander-Green Algorithm Biostatistics 666 Lecture 22

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Last Lecture… Relationship Inferrence z Likelihood of genotype data z Adapt calculation to different relationships Siblings Half-Siblings Unrelated individuals z Importance of modeling error
Today … z The Lander-Green Algorithm z Multipoint analysis in general pedigrees z The basis of modern pedigree analysis packages

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Hidden Markov Model 1 X 2 X 3 X M X 2 I 3 I M I 1 I ) | ( 1 2 I I P ) | ( 2 3 I I P (...) P ) | ( 1 1 I X P ) | ( 2 2 I X P ) | ( 3 3 I X P ) | ( M M I X P IBD states form a Hidden Markov Chain along the chromosome …
Fundamental Calculations z Enumerate possible IBD states z Transition probability for neighboring IBD states z Probability of genotype data given IBD state

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Lander-Green Algorithm z More general definition for I, the "IBD vector" z Probability of genotypes given “IBD vector” z Transition probabilities for the “IBD vectors” = = = 1 1 2 1 1 ) | ( ) | ( ) ( ... I m i i i I m i i i I X P I I P I P L m
Part I “IBD Vectors” Inheritance Vectors Descent Graphs Gene Flow Pattern

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“IBD Vector” Specifications z Specify IBD between all individuals z Must be compact z Must allow calculation of: Conditional probabilities for neighboring markers Probability of observed genotypes
“IBD Vector” z Specify the outcome of each meiosis Which of the two parental alleles transmitted? z Implies founder allele carried by each individual z Implies whether a pair of chromosomes is identical-by-descent

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For any pedigree, consider … z What are the meioses? z What are the possible outcomes for the entire set of meioses?
Example …

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What we are doing . .. z Listing meioses z Alternating outcomes z The outcomes of all meioses define our “IBD vector” V 1 V 2 V 3 V 4 Meiosis 1 Meiosis 2 Meiosis 2
Example … Descent Graph AB CD EF GH This is one representation of inheritance in the pedigree. The 8 founder alleles

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666.20 - The Lander-Green Algorithm Biostatistics 666...

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