Free Access
Genet. Sel. Evol.
Volume 36, Number 1, January-February 2004
Page(s) 29 - 48
Genet. Sel. Evol. 36 (2004) 29-48
DOI: 10.1051/gse:2003049

The effect of using approximate gametic variance covariance matrices on marker assisted selection by BLUP

Liviu R. Totira, Rohan L. Fernandoa, b, Jack C.M. Dekkersa, b, Soledad A. Fernándezc and Bernt Guldbrandtsend

a  Department of Animal Science, Iowa State University, Ames, IA 50011, USA
b  Lawrence H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University, Ames, IA 50011, USA
c  Department of Statistics, The Ohio State University, Columbus, OH 43210, USA
d  Danish Institute of Animal Science, Foulum, Denmark

(Received 19 September 2002; accepted 13 May 2003)

Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15 000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between $0.1\%$ and $13.5\%$ for Method A, between $1.7\%$ and $23.8\%$ for Method B, and between $7.6\%$ and $28.9\%$ for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.

Key words: marker assisted selection / BLUP / gametic variance covariance matrix

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© INRA, EDP Sciences 2004