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Grouping loci

Grouping loci. Criteria Maximum two-point recombination fraction Example - r ij ≤ 0.40 Minimum LOD score - Z ij For n loci, there are n ( n -1)/2 possible combinations that will be tested Expect  probability of false positives Significant probability value - p ij

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Grouping loci

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  1. Grouping loci Criteria • Maximum two-point recombination fraction • Example -rij≤ 0.40 • Minimum LOD score - Zij • For n loci, there are n(n-1)/2 possible combinations that will be tested • Expect  probability of false positives • Significant probability value - pij • Example pij ≤ 0.00001

  2. Locus ordering • Ideally, we would estimate the likelihoods for all possible orders and take the one that is most probable by comparing log likelihoods • That is computationally inefficient when there are more than ~10 loci • Several methods have been proposed for producing a preliminary order

  3. Locus ordering Number of orders among k loci Number of triplets among k loci

  4. Three-point Analysis Number of unique orders among k loci For three loci (k = 3 )

  5. Three-point analysis

  6. Non-Additivity of recombination frequencies rBC rAB C B A rAC The recombination frequency over the interval A – C (rAC) is less than the sum of rAB and rBC : rAC < rAB + rBC. This is because (rare) double recombination events (a recombination in both A - B and B - C) do not contribute to recombination between A and C.

  7. Non-Additivity of recombination frequencies P00=(1-rAB)(1-rBC) P10=rAB(1-rBC) rAC=rAB(1-rBC)+(1-rAB)rBC rAC=rAB+rBC-2rABrBC P01=(1-rAB)rBC C C C C B B B B A A A A P11=rABrBC

  8. Interference • Interference means that recombination events in adjacent intervals interfere. The occurrence of an event in a given interval may reduce or enhance the occurrence of an event in its neighbourhood. • Positive interference refers to the ‘suppression’ of recombination events in the neighbourhood of a given one. • Negative interference refers to the opposite: enhancement of clusters of recombination events. • Positive interference results in less double recombinants (over adjacent intervals) than expected on the basis of independence of recombination events. rAC=rAB+rBC-2CrABrBC

  9. A B C a b c Interference Coefficient of coincidence C = coefficient of coincidence Expected number of double crossovers = rABrBCN Interference I = 1 - C

  10. DH population N=100, locus order ABC Observed Count: 14 24 10 22 16 4 8 2

  11. Interference • No interference • C = 1 and Interference = 1-C = 0 • Complete interference • C = 0 and Interference = 1-C = 1 • Negative interference • C > 1 and Interference = 1-C < 0 • Positive interference • C < 1 and Interference = 1-C > 0

  12. Three locus analysis, DH population For the ABC locus order NR SC2 DC12 SC1 SC1 DC12 SC2 NR

  13. MLE of two-locus recombination fractions For the ABC locus order Regardless of locus order the MLEs of rare

  14. B a C B A C X X b A c b a c Ordering Loci by Minimizing Double Crossovers Rarest genotypes are double recombinants The order of loci is BAC

  15. Ordering Loci by using recombination fractions MLEs of rare Order B C Largest r is rBC = 0.3 B A C A C Smallest r is rAC = 0.1

  16. Minimum Sum of Adjacent Recombination Frequencies (SARF) (Falk 1989) r = recombination frequency between adjacent loci ai and aj for a given order: 1, 2, 3, …, l -1, l The B-A-C order gives MIN[SARF] and the minimum distance (MD) map Simulations have shown that SARF is a reliable method to obtain markers orders for large datasets

  17. Minimum Product of Adjacent Recombination Frequencies (PARF) (Wilson 1988) r = recombination frequency between adjacent loci ai and aj for a given order: 1, 2, 3, …, l -1, l The B-A-C order gives MIN[PARF] and the minimum distance (MD) map SARF and PARF are equivalent methods to obtain markers orders for large datasets

  18. Maximum Sum of Adjacent LOD Scores(SALOD) Z = LOD score for recombination frequency between adjacent loci aiand aj for a given order: 1, 2, 3, …, l -1, l The B-A-C order gives MAX[SALOD] SALOD is sensitive to locus informativeness

  19. Minimum Count of Crossover Events (COUNT) (Van Os et al. 2005) X = simple count of recombination events between adjacent loci ai and aj for a given sequence: 1, 2, 3, …, l -1, l The B-A-C order gives MIN[COUNT] COUNT is equivalent to SARF and PARF with perfect data. COUNT is superior to SARF with incomplete data

  20. Locus Order- Likelihood Approach r1 = Recombination fraction in interval 1 r2= Recombination fraction in interval 2 C = Coefficient of coincidence pi = fi /n fi = Expected frequency of the ith pooled phenotypic class I = 1, 2, …, k k = No. of pooled phenotypic classes

  21. Three locus analysis, DH population For the ABC locus order NR SC2 DC12 SC1 SC1 DC12 SC2 NR

  22. MLE of two-locus recombination fractions For the ABC locus order Regardless of locus order the MLEs of rare

  23. ABC ORDER BAC ORDER ACB ORDER

  24. ABC ORDER

  25. BAC ORDER

  26. ACB ORDER

  27. Likelihood method The B-A-C order gives highest likelihood and LOD under a no interference C=1 model Most multipoint ML mapping algorithms use no interference models

  28. Ordering Loci • GMENDEL (Liu and Knapp 1990) minimizes SARF (Minimum Sum of Adjacent Recombination Frequencies ) • PGRI (Lu and Liu 1995) minimizes SARF (Minimum Sum of Adjacent Recombination Frequencies ) or maximizes the likelihood. • RECORD (Van Os et al. 2005) minimizes COUNT (Minimum Count of Crossover Events)

  29. Ordering Loci • JoinMap 4 (Van Ooijen, 2005) • minimizes the least square locus order using a stepwise search (regression) • Monte Carlo maximum likelihood (ML). Very fast computation of high density maps

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