marker-assisted selection in wheat - ictsd

176Marker-assisted selection – Current status and future perspectives in crops, livestock, forestry and fishto derive co-variances between QTL effects,yielding best linear unbiased prediction(BLUP) of breeding value for both polygenicand QTL effects. Random effects ofpaternal and maternal QTL alleles are addedto the standard animal model with randompolygenic breeding values. The varianceco-variancestructure of the random QTLeffects, also known as the gametic relationshipmatrix (GRM), is based on probabilitiesof identity by descent (IBD), and is nowderived from co-segregation of markers andQTL within a family. Probabilities of IBDderived from pedigree and marker data linkQTL allele effects that are expected to beequal or similar, therefore using data fromrelatives to estimate an individual’s QTLeffects. For example, if two paternal halfsibsi and j have inherited the same paternalallele for markers that flank the QTL (withrecombination rate r), they are likely IBDfor the paternal QTL allele and the correlationbetween the effects of their paternalQTL alleles will be (1-r) 2 . The method isappealing, but computationally demandingfor large-scale evaluations, especially whennot all animals are genotyped and complexprocedures must be applied to derive IBDprobabilities.Genetic evaluation using LD markersMost QTL projects have moved towardsfine mapping where the final result is amarker or marker haplotype in LD withthe QTL, if not the direct mutation. Ahaplotype of marker alleles close enoughto the putative QTL is likely to be inLD with QTL alleles. Such a marker testprovides information about QTL genotypeacross families, and is in a sense notvery different from a direct marker. Themost convenient way to include genotypicinformation from marker haplotypesin genetic evaluation systems is throughthe random QTL model. In their originalpaper, Fernando and Grossman (1989)derived IBD from genotype data on singlemarkers and recombination rates betweenmarker and QTL. However, the randomQTL model is more versatile, and co-variancesbased on IBD probabilities can alsouse information beyond pedigree, based onLD. The latter can be derived from markeror haplotype similarity, e.g. based on anumber of marker genotypes surroundinga putative QTL. Meuwissen and Goddard(2001) proposed using both linkage and LDinformation to derive IBD-based co-variances(termed LDL analysis). Lee and vander Werf (2005) showed that with densermarkers, the value of linkage information,and therefore pedigree, reduces. Hence,when QTL positions become more accuratelydefined, genetic information fromclose markers (within a few cM) can beused increasingly to derive LD-based IBDprobabilities, thereby defining co-variancesbetween random QTL effects without theneed for a family structure or informationthrough pedigree.Lee and van der Werf (2006) have shownthat LD information results in a very denseGRM. Genetic evaluation, which is usuallybased on mixed model equations that arerelatively sparse, is currently not feasiblecomputationally for the LDL method fora large number of individuals and alternativemodels are needed. One approach isto model population-wide LD by simplyincluding the marker genotype or haplotypeas a fixed effect in the animal modelevaluation, as suggested by Fernando(2004). An advantage of modelling population-wideLD effects as fixed rather thanrandom is that fewer assumptions aboutpopulation history are needed. A disadvantageis that estimates are not “BLUPed”,i.e. regressed towards a mean depending on