Simplifications of marker-assisted genetic evaluation and accounting for non-additive interaction effects

Abstract

A computing simplification was applied to marker-assisted genetic evaluation of quantitative traits including additive and non-additive effects of QTL as well as residual polygenic effects. Different situations including QTL and the residual polygenic effect estimated as a sum or separately, and with or without non-additive effects integrated in models were evaluated. The computing simplification was used in combinations with different models and parameterizations. An example data was adopted to illustrate the simplified computing strategy and was compared with the computing method of direct inversion. Identical results were obtained from both computing strategies. The main advantage of the simplification is that it does not require inversion of nonadditive relationship matrices and relationship matrices of QTL, and the number of random effects in mixed model equations is the same as any animal model with only additive effects.Key Words: molecular markers, gametic models, QTL, non-additive effects, computing simplification Zusammenfassung Titel der Arbeit: Vereinfachungen der markerunterstützten Zuchtwertschätzung und Erfassung nichtadditiver Interaktionseffekte Eine computerunterstützte Vereinfachung der Marker-gestützten genetischen Evaluierung quantitativer Merkmale einschließlich additiver und nicht-additiver Effekte von QTL sowie polygener Restvarianz wurde angewendet. Verschiedene Situationen mit QTL und polygenen Effekten wurden in ihrer Summe betrachtet oder separat sowie mit oder ohne nicht-additive Effekte integriert in den Modellen ausgewertet. Die rechnerische Vereinfachung wurde in den Kombinationen mit unterschiedlichen Modellen und Parametrisierungen verwendet. Beispieldaten wurden angenommen, um die vereinfachte rechnerische Strategie zu veranschaulichen, und wurden mit der Methode der direkten Inversion verglichen. Identische Resultate konnten von beiden rechnerischen Strategien erreicht werden. Der Vorteil der Vereinfachung ist, dass sie eine Inversion der Verwandtschaftsmatrizen für nicht-additive und QTL Effekte nicht erfordert. Die Zahl zufälliger Effekte in den Gleichungen der gemischten Modelle ist identisch mit nur additiven Effekten im Tiermodell.Schlüsselwörter: Molekulare Marker, gametische Modelle, QTL, Nicht-additive Effekte, rechnerische Vereinfachung Introduction In linear model genetic evaluations, the independent variables are usually results in a probability distribution of QTL genotype rather than a specific genotype. Estimation of QTL effects in a linear model requires the use of uncertain QTL genotypes as independent variables. Three types of linear models are often used for the estimation:(1) Mixture model: This type of model is based on a mixture of QTL genotypic distributions. It was proposed by LANDER and BOTSTEIN (1989) for QTL interval mapping and was a direct solution for this kind of evaluation. (2) Regression model: The model was proposed by HALEY and KNOTT (1992). It takes the expectation of

Bayesian analysis of ordinal categorical data under a mixed inheritance model

“…A number of authors suggested that utilization of marker-assisted selection (Meuwissen & Van Arendonk 1992, Liu & Mathur 2005 and marker-assisted introgression (Dominik et al 2007), especially for traits with low heritability, can considerably increase selection efficiency and maximize genetic progress. Unfortunately, molecular detection of important loci is still relatively expensive and labor-consuming.…”

Computing the condensed conditional gametic QTL relationship matrix and its inverse

“…The concept of reducing the size of G was proposed by MEUWISSEN and GODDARD (1996) for multiple markers: parents and offspring sharing the same marker haplotype were both assigned the same gametic QTL effect by assuming that the probability of double recombination was equal to zero for informative animals (transmission probabilities were rounded to 0, 0.5 or 1.0). In reality, marker information (and therefore the transmission probability for each marker) is variable and may have any value between zero and one; the values approach zero or one for more informative markers (LIU and MATHUR, 2005). The condensing algorithm presented by TUCHSCHERER et al (2004) leads to the same result as the reducing algorithm when transmission probabilities of one and zero occur and no recombination takes place.…”