Tutorial #8 by Ma’ayan Fishelson

1. Allele Recoding Tutorial #8 by Ma’ayan Fishelson

2. Computational Difficulties • Algorithms that perform multipoint likelihood computations sum over all the possible ordered genotypes for each person. • When highly polymorphic markers are analyzed, any person who is untyped at these markers will have a very large number of possible genotypes. • The computations become increasingly difficult with regards to both memory and time requirements.

3. Possible Savings • All alleles that do not appear in the genotype of any typed person can be lumped together in a single new allele. • What would be the gene frequency of this allele ? • Perform genotype elimination: • Ignore genotypes incompatible with phenotypes. • Delete genotypes of parents which are incompatible with children’s genotypes. • Vitesse does even better !

4. Allele-Recoding in Vitesse • In order to reduce the computational complexity, a set-recoding scheme which recodes each person’s genotypes has been implemented in Vitesse (a program for Genetic Linkage Analysis). • The number of genotypes that need to be summed over is decreased.

5. k 1/1 1/2 Key Idea • Consider an untyped individual k who has only two typed descendants, and a locus with 4 alleles. • Q: • Which alleles need to be specified • individually ? • Can we distinguish between alleles 3 & 4 ? • (These alleles don’t appear in any of the • genotypes of k’s typed descendants). • A: • There’s no need to distinguish between alleles 3 & 4. • There’s also no need to consider allele 2 separately, • because person k couldn’t have passed it to her 2nd • typed descendant.

6. Transmitted & Non-Transmitted Sets • For each untyped person, sets of alleles with identical roles as recombination indicators are combined into a single representative allele.

7. Transmitted & Non-Transmitted Sets(cont.) • There are 2 sets of alleles: ‘transmitted’ and ‘non-transmitted’. • In terms of recombination indicators, a person’s non-transmitted alleles are indistinguishable from one another.

8. Some Notations… • Assume there are n alleles at a marker. An untyped person will initially have an ordered genotype list consisting of n x n orderedpairs of alleles formed by {1,…n}X{1,…,n}. • The set of maternal alleles (Ma) – the set of alleles inherited from the mother. • The set of paternal alleles (Pa) is defined in a similar way. • The set of paternal transmitted alleles – Pt. • The set of paternal non-transmitted alleles – Pn • In a similar way for the maternal alleles.

9. Transmitted Alleles An allele is transmitted if : • The allele appears in the ordered genotype list of a typed descendent D of P, as inheritable from. • There is some path from P to D containing only untyped descendants in the pedigree, so D is the “nearest” typed descendant on that path.

10. Non-Transmitted Alleles The remaining alleles are defined to be non-transmitted.

11. Example 2 1 5 4 6 3 1/2 7 8 • Assume a locus • with 4 alleles. 10 11 9 3/3 2/2

12. Example (2) 2/3 2/3 {2/2, 2/3, 3/3} 8 7 Mt = {2,3} Mn = Ø 11 9 10 3/3 2/2 Mt = Ø Mn = {2,3}

13. Example (3) 2 1 Mt = {1,2,3} Mn = {4} 4 5 6 3 1/2 8 7 Mt = {2,3} Mn = Ø 10 11 9 3/3 2/2 Mt = Ø Mn = {2,3}

14. Clarifications: • The term ‘transmitted’ doesn’t mean that transmission necessarily occurred. • A person’s transmitted / non-transmitted set may be empty. • An untyped parent may have more (but not fewer) transmitted alleles than its untyped offspring. • An untyped parent will have fewer non-transmitted alleles than its untyped offspring, unless the offspring’s non-transmitted set is empty.

15. Fuzzy Inheritance • Regular Inheritance case: if a parent has the genotype A|B and its child has allele C, then C is inherited from the parent if A=C or B=C. • Set-Recoding: A,B,C are sets. C is inherited from the parent if or . • Set-recoding of typed loci: (A|B = {A}|{B})

16. 2 {6}/{4,5} 1 {1}/{2,3} 3 {1,2,3}/{4,5} Example – fuzzy inheritance

17. 2/3 3/2 2/4 2/2 1/1 1/2 3/4 1/2 1/2 2/3 Another Example… • A locus with 5 alleles.