marker-assisted selection in wheat - ictsd

212Marker-assisted selection – Current status and future perspectives in crops, livestock, forestry and fishfor each animal, including animals that didnot have production records (Westall andvan Vleck, 1987). Genetic evaluations forthese animals are derived via the numeratorrelationship matrix, which is included in themodel. In addition, a “permanent environmental”effect is computed for each animalwith records to account for similaritiesamong multiple records of the same cowthat are not due to additive genetic effects.As noted previously, analysis of QTLeffects has generally been based on analysisof genetic evaluations or DYD, which arethe adjusted means of the daughter recordsof a bull but which, unlike genetic evaluations,are not regressed. However, thestatistical properties of DYD are not wellunderstood, and QTL effects derived fromanalysis of DYD are still biased (Israeland Weller, 1998). Theoretically, it shouldbe possible to derive unbiased QTL estimatesif these effects are incorporated intoa genetic evaluation scheme based on analysisof the actual records, such as the animalmodel. In practice, the inclusion of QTLeffects into genetic evaluation models iscomplicated by three main factors:• actual QTL location is unknown, andthere is only partial linkage betweengenetic markers and QTL;• linkage phase between genetic markersand QTL differs among individuals, andis generally unknown;• only a small fraction of the population isgenotyped.An analysis including only genotypedindividuals is not a viable option as it willgenerally not be possible to derive accuratefixed effects, such as herd-year-seasons,from this sample.Fernando and Grossman (1989) proposedmodifying the individual animalmodel described above to a “gametic”model that assumes the two QTL allelesof each individual are random effects sampledfrom a distribution with a knownvariance. They developed a method to estimatebreeding values for all individualsin a population, including QTL effectsvia linkage to genetic markers, providedthat all animals are genotyped and theheritability and recombination frequencybetween the QTL and the genetic markerare known. This model is suitable for anypopulation structure and can also incorporatenon-linked polygenic effects and other“nuisance” effects such as herd or block.The basic model assumes only a singlerecord per individual, but can be adaptedreadily to a situation of multiple recordsper animal. This method is also denoted“marker-assisted BLUP” or “MA-BLUP”.Each individual with unknown ancestorsis assumed to have two unique allelesfor the QTL, which are “sampled” from aninfinite population of alleles. For animalsthat are not genotyped, the probability ofreceiving either allele from either parent willbe equal. However, if both the parent andprogeny are genotyped for a linked geneticmarker, then the probability of receiving aspecific parental allele for a QTL linked tothe genetic marker will be a function of theprogeny marker genotype and recombinationfrequency. Based on these probabilities,Fernando and Grossman (1989) demonstratedhow a variance-co-variance matrixcould be constructed for the QTL gameticeffects. They further described a simplealgorithm to invert this matrix analogousto Henderson's method for invertingthe numerator relationship matrix. Thismethod has been extended to handle multiplemarkers and traits (Goddard, 1992).Cantet and Smith (1991) demonstrated thatthe number of equations could be significantlyreduced by analysis of the reducedanimal model.