kernel function

Predicting quantitative traits is a fundamental aspect of plant and animal breeding. Genomic selection is a precise and efficient approach that estimates genetic merit using high-density single nucleotide polymorphisms (SNPs). However, most genomic selection procedures primarily focus on additive effects to calculate the genomic estimated breeding value (GEBV) for selection candidates. Nonetheless, incorporating non-additive effects offers several advantages: (i) it enhances the accuracy of GEBV predictions and subsequent selection responses, (ii) it facilitates optimized mate allocation among selection candidates, and (iii) it enables improved utilization of non-additive genetic variation through tailored crossbreeding or purebred breeding strategies. One of the most challenging factors affecting the accuracy of genomic evaluation is the selection of an appropriate statistical method to estimate marker effects with high accuracy. The most common parametric methods for genomic evaluation are the genomic best linear unbiased predictor (GBLUP) and Bayesian methods, which use the co-variance structure between individuals and regression of phenotype on markers to predict the genetic values ​​of individuals, respectively. However, in recent years, non-parametric methods of machine learning have been widely used for genomic evaluation in animal and plant breeding programs. This study aimed to evaluate and compare the accuracy of genomic predictions using GBLUP and support vector machine (SVM) methods. The SVM models employed various kernel functions, including linear (SVM-lin), Gaussian radial (SVM-rad), polynomial (SVM-pol), and cyclic (SVM-sig). Both purely additive and additive + dominance deviation gene action models were considered under varying levels of dominance variance.

A simulated genome comprising six chromosomes with a total length of 600 cM was used for this study. Each chromosome contained 1,000 evenly spaced SNPs and 100 randomly distributed quantitative trait loci (QTLs). Phenotypic variance ( ) and narrow-sense heritability ( ) were set to 1 and 0.4, respectively. Dominance variance ( ) levels were evaluated at 0.10, 0.15, 0.20, 0.25, 0.30, and 0.35. Prediction accuracy was calculated as the Pearson correlation coefficient between the true genetic value (TGV) or true breeding value (TBV) and their respective genomic estimates (GEGV or GEBV). The correlations were represented as  and , respectively. In addition, the practical significance of differences in prediction accuracy among the studied statistical methods was assessed using Cohen’s d effect size during 100 replicates.

The conventional GBLUP method consistently exhibited higher prediction accuracy for both GEBV and GEGV across all scenarios. Among the SVM approaches, the SVM-rad and SVM-sig kernels showed superior performance in predicting GEGV under both purely additive and additive + dominance deviation models. However, for GEBV prediction, their performance declined with increasing dominance variance. When dominance variance exceeded 0.30, SVM-lin and SVM-sig demonstrated prediction accuracy comparable to or slightly better than SVM-rad. The differences in prediction accuracy between GBLUP and SVM-rad were minimal (d=0.218) in the purely additive model but reached their peak (d=0.492 and d=0.404) in the additive + dominance deviation model at the highest dominance variance ( ). This disparity occurred because, as dominance variance increased, the GBLUP method exhibited slightly greater changes in accuracy compared to the SVM-rad method. Furthermore, with higher dominance variance, the difference in prediction accuracy for GEBV between the SVM methods and both GBLUP and SVM-rad substantially decreased. For example, in the purely additive model ( ), Cohen’s d was 2.608 and 2.336, respectively, while in the additive + dominance deviation model ( ), d dropped to 0.309 and 0.189, respectively. Using the additive + dominance deviation model significantly improved GEBV prediction accuracy, particularly when dominance variance contributed substantially to phenotypic variance. This improvement is due to dominance deviation, which arises from interactions between alleles at a locus. While additive effects are represented as breeding values, which partially incorporate dominance effects, genomic evaluations that explicitly consider dominance effects can further enhance GEBV accuracy.

The choice of kernel function in SVM models plays a pivotal role in the accuracy of GEBV and GEGV predictions. Overall, when applying the nonparametric SVM method to fit markers to phenotypes, the Gaussian radial kernel function is recommended for optimal performance. However, as the dominance variance increased, the performance of SVM-lin and SVM-sig methods improved significantly and the performance gap with GBLUP and SVM-rad decreased. This indicated the potential capacity of SVM in investigating non-additive effects, especially in situations where the contribution of dominance in explaining phenotypic variance increases.

In recent years by growing technology, new methods have been substantially developed to solve nonlinear problems such as river flow forecasting. Among the available various methods, Support Vector Machine (SVM) and Adaptive Neuro-Fuzzy Inference System (ANFIS) models have been recently used by many researchers. In this study, these methods were used to predict the monthly flow of NazluChai and Sezar Rivers during 1956-2016 period. Firstly, the data were prepared in two modes: (a) using flow data and considering the role of memory; (b) influencing the periodic term. Modeling was done by 80% of the data (576 months) for training and the remaining 20% (144 months) for testing. The root mean square error (RMSE), Nash-Sutcliffe (NS) and mean absolute relative error (MARE) metrics were used to evaluate the performance of the proposed models. The results showed that the SVM method with the RBF kernel function had the best performance in predicting monthly flow of the studied rivers. In addition, the periodic term significantly increased the prediction accuracy of the SVM-RBF model. Also, the performance of the ANFIS method was improved by using the periodic term and this model had the least error in estimating the monthly flow of the Saesar and Nazlu chi Rivers in M6 and M7 patterns, respectively. In general, the results of this study showed that the SVM method performs better than the ANFIS model in monthly flow prediction and the selection of appropriate kernel function has a direct effect on its efficiency.

Traditional method in flood frequency analysis is parametric approach. This method lacks the ability to describe multimodal and Asymmetric densities. In order to overcome this problem¡ the nonparametric models can be used. Two methods of nonparametric approach are: fixed and variable kernel density. In fixed kernel density method¡ the probability density function can be estimated by selecting a kernel function and optimal bandwidth and in variable kernel density method the probability density function can be estimated by selecting a kernel function and bandwidth at each observation point. Cross validation and Rule of thumb are common methods for estimating the optimum bandwidth. In this paper¡ besides mentioned methods Plug in bandwidth method is used and nonparametric flood frequency analysis is performed using annual maximum flood data of the Dez river. Finally results were compared with parametric method. According to RMSE¡ it is concluded that plug in bandwidth is the most accurate method for estimating optimum bandwidth. As well as Nonparametric method based on variable kernel density is more accurate than fixed kernel density and both types of these models are more accurate than LP3 distribution.

In this research, a first order Markov chain model was applied to simulate soil salinity in nine standard depths and 10 classes in the cultivated pistachio areas of Ardakan city. Transition probability matrix, kernel and uniform distribution were used to simulate 500000 soil profiles. Results indicate kernel function could reproduce soil salinity values with statistical criteria (i.e. mean, standard deviation, skewness and kurtosis) more closely to the observed data when compared to data simulated by uniform function. Moreover, simulation processes from down-up is more accurate than that of up-down method. Overall, Makov simulation technique is able to consider the relationship between different classes.

There are two parametric and nonparametric approaches for frequency analysis of hydrological data. Current methods of frequency analysis are based on the parametric methods. Moments، maximum likelihood and probability weighted moments are from various parametric methods for frequency analysis. In this research، maximum likelihood and L-moment methods are used for precipitation frequency analysis. L-moment is a new method for frequency analysis and one of the specific kinds of probability weighted moments. The results of frequency analysis with L-moment are compared with maximum likelihood method and kernel functions of nonparametric methods of normal، log-normal، rectangular and triangular kernel function. In this research، monthly and annual precipitations are fitted to thirteen distribution functions such as Logistic، Generalized Extreme Value and etc. with estimation of L-moment and maximum likelihood methods. The results showed that L-moment parametric method is best fitted to monthly and annual data due to mean relative deviation and mean square relative deviation goodness of fit tests compared to maximum likelihood parametric method. The L-moment parametric method is also best fitted to Boushehr، Jask and Mashhad annual data due to mean relative deviation and mean square relative deviation goodness of fit tests compared to kernel nonparametric methods with rectangular، triangular and normal functions. Therefore، L-moment method is a suitable method for frequency analysis of other hydrological parameters such as flood and drought for planning of water resource management and hydrological analysis.