bugNumerical Library for Haploid Genetics - Bugs: bug #34879, ld_sub_geno () should calculate...


bug #34879: ld_sub_geno () should calculate recursively

Submitter:  Joel J. Adamson <trashbird1240>
Submitted:  Tue 22 Nov 2011 02:57:50 PM UTC
Category:  Library Severity:  3 - Normal
Item Group:  None Status:  None
Privacy:  Public Assigned to:  trashbird1240
Open/Closed:  Open
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Tue 22 Nov 2011 03:18:41 PM UTC, comment #1: 

Check to make sure this reduces to Bennett's Equation.

Joel J. Adamson <trashbird1240>
Group administrator
Tue 22 Nov 2011 02:57:50 PM UTC, original submission:  

ld_sub_geno () does not calculate the full linkage disequilibrium among a set of loci, it calculates a subset of it.  We can use the following recursive algorithm to calculate the right value (where U is the set of loci we're interested in, and |U| is its size):

  1. If |U| = 0, or |U| = 1 then return 0
  2. If |U| = 2 then use the standard linkage disequilibrium
  3. If |U| > 2 then split off a locus and use the following formula

  E[X_i \Pi_{j \in U/i} (X_j - p_j) ] - p_i D_U/i

  with recursion on the last term.  U/i is the set difference of U and i, X_i is an indicator variable giving the status to the locus (on or off) and E represents expectation (genotypic average).

For each such calculation we will need the genotypic frequency (for averaging) and the allele frequencies of the constituent alleles (can be calculated once).

Joel J. Adamson <trashbird1240>
Group administrator


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