Optimal peeling order for pedigrees with incomplete genotypic information. (English) Zbl 1124.62071

Belonogova, Nadezhda M.; Axenovich, Tatiana I.

Comput. Biol. Chem. 31, No. 3, 173-177 (2007).

Summary: The likelihood approach is common in linkage analysis of large extended pedigrees. Various peeling procedures, based on the conditional independence of separate parts of a pedigree, are typically used for likelihood calculations. A peeling order may significantly affect the complexity of such calculations, particularly for pedigrees with loops or when many pedigree members have unknown genotypes. Several algorithms have been proposed to address this problem for pedigrees with loops. However, the problem has not been solved for pedigrees without loops until now.
We suggest a new graph theoretic algorithm for optimal selection of peeling order in zero-loop pedigrees with incomplete genotypic information. It is especially useful when multiple likelihood calculation is needed, for example, when genetic parameters are estimated or linkage with multiple marker loci is tested. The algorithm can be easily introduced into the existing software packages for linkage analysis based on the Elston-Stewart algorithm for likelihood calculation. The algorithm was implemented in a software package PedPeel, which is freely available at http://mga.bionet.nsc.ru/nlru/.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
92D10	Genetics and epigenetics
05C90	Applications of graph theory
92D15	Problems related to evolution

Keywords:

pedigree likelihood; graph theory; software

Software:

PedPeel

References:

[1]	Axenovich, T.I., Zorkoltseva, I.V., Liu, F., Kirichenko, A.V., Aulchenko, Y.S. Breaking loops in large complex pedigrees. Hum. Hered., submitted for publication.
[2]	Axenovich, T.I.; Zorkoltseva, I.V.; Akberdin, I.R.; Beketov, S.V.; Kashtanov, S.N.; Zakharov, I.A.; Borodin, P.M., Inheritance of litter size at birth in farmed arctic foxes (alopex lagopus, canidae, carnivora), Heredity, 98, 2, 99-105, (2007)
[3]	Cannings, C.; Thompson, E.A.; Skolnick, E.H., Probability functions on complex pedigrees, Adv. appl. prob., 10, 26-61, (1978) · Zbl 0431.92019
[4]	Elston, R.C.; Stewart, J., A general model for the genetic analysis of pedigree data, Hum. hered., 21, 6, 523-542, (1971)
[5]	Fernandez, S.A.; Fernando, R.L., Technical note: determining peeling order using sparse matrix algorithms, J. dairy sci., 85, 1623-1629, (2002)
[6]	Harbron, C., A pedigree-based algorithm for finding efficient peeling sequences, IMA J. math. appl. med. biol., 12, 1, 13-27, (1995) · Zbl 0832.92010
[7]	Kruglyak, L.; Daly, M.J.; Reeve-Daly, M.P.; Lander, E.S., Parametric and nonparametric linkage analysis: a unified multipoint approach, Am. J. hum. genet., 58, 1347-1363, (1996)
[8]	Lander, E.S.; Green, P., Construction of multilocus genetic linkage maps in humans, Proc. natl. acad. sci. U.S.A., 84, 2363-2367, (1987)
[9]	Lange, K.; Boehnke, M., Extensions to pedigree analysis. V: optimal calculation of Mendelian likelihoods, Hum. hered., 33, 291-301, (1983)
[10]	Lange, K.; Goradia, T.M., An algorithm for automatic genotype elimination, Am. J. hum. genet., 40, 250-256, (1987)
[11]	O’Connell, J.R.; Weeks, D.E., An optimal algorithm for automatic genotype elimination, Am. J. hum. genet., 65, 1733-1740, (1999)
[12]	Pardo, L.M.; MacKay, I.; Oostra, B.; van Duijn, C.M.; Aulchenko, Y.S., The effect of genetic drift in a Young genetically isolated population, Ann. hum. genet., 69, 288-295, (2005)
[13]	Thomas, A., Optimal computations of probability functions for pedigree analysis, IMA J. math. appl. med. biol., 3, 167-178, (1986) · Zbl 0612.92008
[14]	West, D.B., Introduction to graph theory, (2001), Prentice Hall