Solution of Mixed-Integer Optimization Problems in Bioinformatics with Differential Evolution Method

The solution of the so-called mixed-integer optimization problem is an important challenge for modern life sciences. A wide range of methods has been developed for its solution, including metaheuristics approaches. Here, a modification is proposed of the differential evolution entirely parallel (DEEP) method introduced recently that was successfully applied to mixed-integer optimization problems. The triangulation recombination rule was implemented and the recombination coefficients were included in the evolution process in order to increase the robustness of the optimization. The deduplication step included in the procedure ensures the uniqueness of individual integer-valued parameters in the solution vectors. The developed algorithms were implemented in the DEEP software package and applied to three bioinformatic problems. The application of the method to the optimization of predictors set in the genomic selection model in wheat resulted in dimensionality reduction such that the phenotype can be predicted with acceptable accuracy using a selected subset of SNP markers. The method was also successfully used to optimize the training set of samples for such a genomic selection model. According to the obtained results, the developed algorithm was capable of constructing a non-linear phenomenological regression model of gene expression in developing a Drosophila eye with almost the same average accuracy but significantly less standard deviation than the linear models obtained earlier.

FMixFN: A Fast Big Data-Oriented Genomic Selection Model Based on an Iterative Conditional Expectation algorithm

Genomic selection is an approach to select elite breeding stock based on the use of dense genetic markers and that has led to the development of various models to derive a predictive equation. However, the current genomic selection software faces several issues such as low prediction accuracy, low computational efficiency, or an inability to handle large-scale sample data. We report the development of a genomic prediction model named FMixFN with four zero-mean normal distributions as the prior distributions to optimize the predictive ability and computing efficiency. The variance of the prior distributions in our model is precisely determined based on an F2 population, and genomic estimated breeding values (GEBV) can be obtained accurately and quickly in combination with an iterative conditional expectation algorithm. We demonstrated that FMixFN improves computational efficiency and predictive ability compared to other methods, such as GBLUP, SSgblup, MIX, BayesR, BayesA, and BayesB. Most importantly, FMixFN may handle large-scale sample data, and thus should be able to meet the needs of large breeding companies or combined breeding schedules. Our study developed a Bayes genomic selection model called FMixFN, which combines stable predictive ability and high computational efficiency, and is a big data-oriented genomic selection model that has potential in the future. The FMixFN method can be freely accessed at https://zenodo.org/record/5560913 (DOI: 10.5281/zenodo.5560913).

Bayesian genomic models boost prediction accuracy for survival to Streptococcus agalactiae infection in Nile tilapia (Oreochromus nilioticus)

Background Streptococcosis is a major bacterial disease in Nile tilapia that is caused by Streptococcus agalactiae infection, and development of resistant strains of Nile tilapia represents a sustainable approach towards combating this disease. In this study, we performed a controlled disease trial on 120 full-sib families to (i) quantify and characterize the potential of genomic selection for survival to S. agalactiae infection in Nile tilapia, and (ii) identify the best genomic model and the optimal density of single nucleotide polymorphisms (SNPs) for this trait. Methods In total, 40 fish per family (15 fish intraperitoneally injected and 25 fish as cohabitants) were used in the challenge test. Mortalities were recorded every 3 h for 35 days. After quality control, genotypes (50,690 SNPs) and phenotypes (0 for dead and 1 for alive) for 2472 cohabitant fish were available. Genetic parameters were obtained using various genomic selection models (genomic best linear unbiased prediction (GBLUP), BayesB, BayesC, BayesR and BayesS) and a traditional pedigree-based model (PBLUP). The pedigree-based analysis used a deep 17-generation pedigree. Prediction accuracy and bias were evaluated using five replicates of tenfold cross-validation. The genomic models were further analyzed using 10 subsets of SNPs at different densities to explore the effect of pruning and SNP density on predictive accuracy. Results Moderate estimates of heritabilities ranging from 0.15 ± 0.03 to 0.26 ± 0.05 were obtained with the different models. Compared to a pedigree-based model, GBLUP (using all the SNPs) increased prediction accuracy by 15.4%. Furthermore, use of the most appropriate Bayesian genomic selection model and SNP density increased the prediction accuracy up to 71%. The 40 to 50 SNPs with non-zero effects were consistent for all BayesB, BayesC and BayesS models with respect to marker id and/or marker locations. Conclusions These results demonstrate the potential of genomic selection for survival to S. agalactiae infection in Nile tilapia. Compared to the PBLUP and GBLUP models, Bayesian genomic models were found to boost the prediction accuracy significantly.

Genomic Prediction and Selection in Support of Sorghum Value Chains

Genomic prediction and selection models (GS) were deployed as part of DataBio project infrastructure and solutions. The work addressed end-user requirements, i.e., the need for cost-effectiveness of the implemented technologies, simplified breeding schemes, and shortening the time to cultivar development by selecting for genetic merit. Our solutions applied genomic modelling in order to sustainably improve productivity and profits. GS models were implemented in sorghum crop for several breeding scenarios. We fitted the best linear unbiased predictions data using Bayesian ridge regression, genomic best linear unbiased predictions, Bayesian least absolute shrinkage and selection operator, and BayesB algorithms. The performance of the models was evaluated using Monte Carlo cross-validation with 70% and 30%, respectively, as training and validation sets. Our results show that genomic models perform comparably with traditional methods under single environments. Under multiple environments, predicting non-field evaluated lines benefits from borrowing information from lines that were evaluated in other environments. Accounting for environmental noise and other factors, also this model gave comparable accuracy with traditional methods, but higher compared to the single environment model. The GS accuracy was comparable in genomic selection index, aboveground dry biomass yield and plant height, while it was lower for the dry mass fraction of the fresh weight. The genomic selection model performances obtained in our pilots are high enough to sustain sorghum breeding for several traits including antioxidants production and allow important genetic gains per unit of time and cost.

Genomic Prediction and Selection for Fruit Traits in Winter Squash

Improving fruit quality is an important but challenging breeding goal in winter squash. Squash breeding in general is resource-intensive, especially in terms of space, and the biology of squash makes it difficult to practice selection on both parents. These restrictions translate to smaller breeding populations and limited use of greenhouse generations, which in turn, limit genetic gain per breeding cycle and increases cycle length. Genomic selection is a promising technology for improving breeding efficiency; yet, few studies have explored its use in horticultural crops. We present results demonstrating the predictive ability of whole-genome models for fruit quality traits. Predictive abilities for quality traits were low to moderate, but sufficient for implementation. To test the use of genomic selection for improving fruit quality, we conducted three rounds of genomic recurrent selection in a butternut squash (Cucurbita moschata) population. Selections were based on a fruit quality index derived from a multi-trait genomic selection model. Remnant seed from selected populations was used to assess realized gain from selection. Analysis revealed significant improvement in fruit quality index value and changes in correlated traits. This study is one of the first empirical studies to evaluate gain from a multi-trait genomic selection model in a resource-limited horticultural crop.

Bayesian genomic models boost prediction accuracy for resistance against Streptococcus agalactiae in Nile tilapia (Oreochromus nilioticus)

Streptococcosis due to Streptococcus agalactiae is a major bacterial disease in Nile tilapia, and development of the resistant genetic strains can be a sustainable approach towards combating this problematic disease. Thus, a controlled disease trial was performed on 120 full-sib families to i) quantify and characterize the potential of genomic selection for S. agalactiae resistance in Nile tilapia and to ii) select the best genomic model and optimal SNP-chip for this trait.In total, 40 fish per family (15 fish intraperitoneally injected and 25 fish as cohabitants) were selected for the challenge test and mortalities recorded every 3 hours, until no mortalities occurred for a period of 3 consecutive days. Genotypes (50,690 SNPs) and phenotypes (0 for dead and 1 for alive) for 2472 cohabitant fish were available. The pedigree-based analysis utilized a deep pedigree, going 17 generations back in time. Genetic parameters were obtained using various genomic selection models (GBLUP, BayesB, BayesC, BayesR and BayesS) and traditional pedigree-based model (PBLUP). The genomic models were further analyzed using 10 different subsets of SNP-densities for optimum marker density selection. Prediction accuracy and bias were evaluated using 5 replicates of 10-fold cross-validation.Using an appropriate Bayesian genomic selection model and optimising it for SNP density increased prediction accuracy up to ∼71%, compared to a pedigree-based model. This result is encouraging for practical implementation of genomic selection for S. agalactiae resistance in Nile tilapia breeding programs.

Environment and ryegrass genetics - multisite trial of advanced breeding populations

Developing a genomic selection (GS) strategy for ryegrass requires field data for training GS models and to gain insight into how ryegrass agronomic performance varies, within and among populations and across locations. Families from five perennial ryegrass breeding populations are being evaluated in eight trials in Northland, Waikato, Hawke's Bay, Manawatu and Canterbury to establish a data set for development of a genomic selection model. Statistically robust variances are evident among families within populations, both for visual scoring of herbage bulk and dry matter measurements. Multi-trial analysis of data showed significant (P