Introduction

Another possibility is to find the most probable consistent correction with respect to a Bayesian formulation of the problem. In this case, the output of the software is a list of individuals for which predicted genotypes differ from their genotyping data and such that the corresponding joint probability for the whole problem is maximum.

The problem, its formulation as a weighted constraint satisfaction problem, and some experimental results on simulated and real large animal pedigrees (up to 129516 individuals) are described in:

M. Sanchez, S. de Givry, and T. Schiex
Mendelian error detection in complex pedigrees using weighted constraint satisfaction techniques (preprint)
In Constraints journal, special issue on bioinformatics, 13(1), 2008.

S. de Givry, I. Palhiere, Z. Vitezica, and T. Schiex
Mendelian error detection in complex pedigree using weighted constraint satisfaction techniques
In ICLP-05 workshop on Constraint Based Methods for Bioinformatics, page 9p., Sitges, Spain, 2005.

Download and installation

Version 0.9.8 can be found here: version 0.9.8 for Linux and Windows (executables only).

On Linux computers (it should work on other systems also), after downloading, extract the zipped source codes:

unzip toulbar2-1.0.1.zip

Then, enter in the source code directory and compile using cmake/ccmake (set option MENDELSOFT_ONLY to ON):

cd toulbar2-1.0.1
ccmake .
cmake .  
make

It will generate an executable called mendelsoft in directorty bin/Linux. Note that if you already have an executable toulbar2, it does the same as mendelsoft plus some extra solving options.

On Windows computers, compile all the .cpp files together using Visual C++ with the following macro definitions:

-DMENDELSOFT -DWCSPFORMATONLY -DNARYCHAR -DINT_COST -DDOUBLE_PROB -DWIN32 -D_DEBUG -D_WINDOWS -DWINDOWS -DNDEBUG

Warning! On Windows computers, the maximum precision for probability encoding should be lower than 4. See below.

Input File Format

• a pedigree number (locus)
• an individual identification number (different from zero), or id
• father's id number
• mother's id number
• sex
• first allele number
• second allele number

If you assume there are no errors with a particular genotyping data, then the data can be made mandatory by using negative allele numbers.

Running MendelSoft with a parsimony criterion

mendelsoft simple.pre

5 informative individuals found (either genotyped or having a genotyped descendant).
Read pedigree with 5 individuals, 3 founders, 4 alleles, 4 genotypings and 3 generations.
Cost function decomposition time : 0 seconds.
Preprocessing Time               : 0.01 seconds.
0 unassigned variables, 0 values in all current domains (med. size:0, max size:10) and 0 non-unary cost functions (med. degree:0)
Initial lower and upper bounds: [1, 2] 50.000%
New solution: 1 (0 backtracks, 0 nodes, depth 1)
Correction: 2 (1)
Optimum: 1 in 0 backtracks and 0 nodes ( 2 removals by DEE) and 0.001 seconds.
end.

Use option -w (or without the minus sign for previous version 0.8a or older) to save a consistent pedigree corresponding to the last correction found into a file called pedigree_corrected.pre in the current directory. Try the following command:

mendelsoft simple.pre -w

mendelsoft simple.pre w

NEW! Use option --save=filename to modifiy the output file name.

Executing mendelsoft without any parameter gives a help message with available options. It is possible to speed up the search by giving an initial strict upper-bound on the maximum number of genotyping data to be removed. If this upper-bound is lower than or equal to the optimum, then mendelsoft will return no solution. Try the following command:

mendelsoft simple.pre -ub=1

mendelsoft simple.pre 1

5 individuals found with a genotyped descendant..
No solution found by initial propagation!
end.

Running MendelSoft with a Bayesian formulation

mendelsoft simple.pre -w -bayes

mendelsoft simple.pre wy

5 informative individuals found (either genotyped or having a genotyped descendant).
Read pedigree with 5 individuals, 3 founders, 4 alleles, 4 genotypings and 3 generations.
Bayesian MPE (genotyping error rate: 0.05, genotype prior: 0, precision(1-10^-p): 7, normalization: 1e+07, ub: 274677317)
Cost function decomposition time : 8e-06 seconds.
Preprocessing time: 0.000853 seconds.
0 unassigned variables, 0 values in all current domains (med. size:0, max size:10) and 0 non-unary cost functions (med. degree:0)
Initial lower and upper bounds: [136646016, 136646017] 0.000%
New solution: 136646016 energy: 13.665 prob: 1.163e-06 (0 backtracks, 0 nodes, depth 1)
Correction: 5 (1)
Optimum: 136646016 energy: 13.665 prob: 1.163e-06 in 0 backtracks and 0 nodes ( 3 removals by DEE) and 0.001 seconds.
end.

It is possible to select the way of correcting the erroneous genotypings and also predicting the missing genotypes in the output file pedigree_corrected.pre, by adding a value (0,1, or 2) just after the option w:

• -w=0 (or w0 for previous version 0.8a): remove erroneous genotypings in the output file (default case).
• -w=1 (or w1): correct erroneous genotypings to their prediction (in conjunction with option -bayes (or y) for the Bayesian formulation).
• -w=2 (or w2): correct erroneous genotypings to their prediction and infer missing genotypes for informative individuals (non-informative individuals are not genotyped and have no genotyped descendant in the pedigree).

By default, we assume 5% of genotyping errors and equivalent allele frequencies. See the help message obtained by executing mendelsoft without any parameter to change these defaults. For instance, try the following command line, having only 1% of genotyping error uniform prior and an allele probability distribution equal to ( allele1: 0.4, allele2: 0.4, allele3: 0.1, allele4: 0.1 ):

mendelsoft simple.pre -w -bayes -genoError=0.01 -precision=7 -problist= 4 0.4 0.4 0.1 0.1

mendelsoft simple.pre wy 0.01 7 2 0.4 0.4 0.1 0.1

Warning! On Windows computers, the maximum precision for probability encoding should be lower than 4. Try

mendelsoft simple.pre -w -bayes -genoError=0.01 -precision=4 -problist= 4 0.4 0.4 0.1 0.1

mendelsoft simple.pre wy 0.01 4 2 0.4 0.4 0.1 0.1

Check genotype priors, deduced from the selected allele probability distribution, using verbose option -v=1 (or v for previous version 0.8a).

You can penalize genotyping removals for individuals which have many genotyped children (only with a Bayesian formulation). Use option -u=[threshold] (or u[threshold] for previous version 0.8a) with a threshold number of genotyped children. mendelsoft adds a penalty weight (logarithmically proportional to the number of genotyped children) on genotyping removals if the number of genotyped children for the corresponding individuals is strictly greater than the threshold. At each correction output line, the penalized likelihood is decomposed into the original likelihood and the total penalty term (given in parenthesis).

NEW! If the problem is large and difficult to solve, you can add one or a combination of the following options:

• -l (performs several searches with an increasing complexity)
• -hbfs (performs hybrid best-first search with optimality gap information)
• -p=3 (applies more problem simplifications in preprocessing)

Weighted Constraint Satisfaction Problems

J. Larrosa, and T. Schiex
In the quest of the best form of local consistency for Weighted CSP
In Proc. of IJCAI-03, pages 239-244, Acapulco, Mexico, 2003.

S. de Givry, M. Zytnicki, F. Heras, and J. Larrosa
Existential arc consistency: Getting closer to full arc consistency in Weighted CSPs
In Proc. of IJCAI-05, pages 84-89, Edinburgh, Scotland, 2005.

J. Larrosa, E. Morancho, and D. Niso
On the practical applicability of Bucket Elimination: Still-life as a case study
Journal of Artificial Intelligence Research. 23 :421-440, 2005.

C. Lecoutre, L. Sais, S. Tabary, and V. Vidal
Last Conflict based Reasoning
In Proc. of ECAI-06, pages 133-137, Trento, Italy, 2006.

For more information, see the old SoftCSP web site and the new Cost Function web site

Please report bugs or problems to: Simon de Givry Email: simon.de-givry _AT_ inra.fr Last Update: May 23nd 2019