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Plants competing for available resources is an unavoidable phenomenon in a field. We conducted studies in cassava ( Manihot esculenta Crantz) in order to understand the pattern of this competition. Taking into account the competitive ability of genotypes while selecting parents for breeding advancement or commercialization can be very useful. We assumed that competition could occur at two levels: (i) the genotypic level, which we call interclonal, and (ii) the plot level irrespective of the type of genotype, which we call interplot competition or competition error. Modification in incidence matrices was applied in order to relate neighboring genotype/plot to the performance of a target genotype/plot with respect to its competitive ability. This was added into a genomic selection (GS) model to simultaneously predict the direct and competitive ability of a genotype. Predictability of the models was tested through a 10-fold cross-validation method repeated five times. The best model was chosen as the one with the lowest prediction root mean squared error (pRMSE) compared to that of the base model having no competitive component. Results from our real data studies indicated that <10% increase in accuracy was achieved with GS-interclonal competition model, but this value reached up to 25% with a GS-competition error model. We also found that the competitive influence of a cassava clone is not just limited to the adjacent neighbors but spreads beyond them. Through simulations, we found that a 26% increase of accuracy in estimating trait genotypic effect can be achieved even in the presence of high competitive variance., (Copyright © 2018 Elias et al.)

Cassava ( Manihot esculenta Crantz) is an important staple food in sub-Saharan Africa. Breeding experiments were conducted at the International Institute of Tropical Agriculture in cassava to select elite parents. Taking into account the heterogeneity in the field while evaluating these trials can increase the accuracy in estimation of breeding values. We used an exploratory approach using the parametric spatial kernels Power, Spherical, and Gaussian to determine the best kernel for a given scenario. The spatial kernel was fit simultaneously with a genomic kernel in a genomic selection model. Predictability of these models was tested through a 10-fold cross-validation method repeated five times. The best model was chosen as the one with the lowest prediction root mean squared error compared to that of the base model having no spatial kernel. Results from our real and simulated data studies indicated that predictability can be increased by accounting for spatial variation irrespective of the heritability of the trait. In real data scenarios we observed that the accuracy can be increased by a median value of 3.4%. Through simulations, we showed that a 21% increase in accuracy can be achieved. We also found that Range (row) directional spatial kernels, mostly Gaussian, explained the spatial variance in 71% of the scenarios when spatial correlation was significant., (Copyright © 2018 Elias et al.)