Genomic Prediction of Tropical Maize Resistance to Fall Armyworm and Weevils: Genomic Selection Should Focus on Effective Training Set Determination

: Genomic selection (GS) can accelerate variety release by shortening variety development phase when factors that influence prediction accuracies (PA) of genomic prediction (GP) models such as training set (TS) size and relationship with the breeding set (BS) are optimized beforehand. In this study, PAs for the resistance to fall armyworm (FAW) and maize weevil (MW) in a diverse tropical maize panel composed of 341 double haploid and inbred lines were estimated. Both phenotypic best linear unbiased predictors (BLUPs) and estimators (BLUEs) were predicted using 17 parametric, semi-parametric, and nonparametric algorithms with a 10-fold and 5 repetitions cross-validation strategy. n. For both MW and FAW resistance datasets with an RBTS of 37%, PAs achieved with BLUPs were at least as twice as higher than those realized with BLUEs. The PAs achieved with BLUPs for MW resistance traits: grain weight loss (GWL), adult progeny emergence (AP), and number of affected kernels (AK) varied from 0.66 to 0.82. The PAs were also high for FAW resistance RBTS datasets, varying from 0.694 to 0.714 (for RBTS of 37%) to 0.843 to 0.844 (for RBTS of 85%). The PAs for FAW resistance with PBTS were generally high varying from 0.83 to 0.86, except for one dataset that had PAs ranging from 0.11 to 0.75. GP models showed generally similar predictive abilities for each trait while the TS designation was determinant. There was a highly positive correlation (R=0.92***) between TS size and PAs for the RBTS approach while, for the PBTS, these parameters were highly negatively correlated (R=-0.44***), indicating the importance of the degree of kinship between the TS and the BS with the smallest TS (31%) achieving the highest PAs (0.86). This study paves the way towards the use of GS for maize resistance to insect pests in sub-Saharan Africa. the genetically diverse maize panel used in this study, as a base population since it consists of lines adapted to several African agroecologies.


INTRODUCTION
Insect damage on maize plants and stored grains potentially impede food security in Africa (1)(2)(3). The fall armyworm (FAW) and stem borers in the field, and the maize weevil (MW) in storage facilities are some of the most devastating insect pests on the continent causing yield losses ranging from 10 to 90% leading to loss of grain marketability, and consumer health concerns due to the possible contamination of the grain with mycotoxin such as aflatoxins (3)(4)(5)(6). In Africa, tremendous efforts were made during the last two decades to build host plant resistance to insect pests in maize through traditional pedigree (phenotypic)-based selection (PS) with substantial results. Several Africa adapted maize lines were developed and successfully tested for resistance to MW damage on grains MW damage on grains (7)(8)(9)(10)(11)(12). Some of the success stories are from the International Center for Maize and Wheat Improvement (CIMMYT) of Kenya through the Insect Resistant Maize for Africa project (IRMA) that produced several storage pest and stem borer resistant maize lines (7,8,(13)(14)(15). On the other hand, FAW is a recent pest on the continent and was first reported in 2016 in West and Central African countries (16), from where it spread throughout the African continent (17). Hence, although efforts to develop FAW resistant varieties are underway at several institutions including CIMMYT, published reports of FAW resistant varieties are not yet available (18,19).
However, the complex nature of insect resistance traits makes PS slow and expensive, and thus, difficult to implement, especially for resource-constrained breeding programs (20). Application of traditional marker-assisted selection (MAS) is hampered by the necessity to first discover resistanceassociated genomic regions through genetic linkage and GWAS methods, both with several shortcomings, especially for complex traits (21)(22)(23) and have seldom been conducted in African germplasm (8,24), further impeding the application of MAS in the development of insect resistance maize lines in Africa. Moreover, in a previous study, we discovered several quantitative trait nucleotides and genes putatively associated with FAW and MW resistance which confirmed the quantitative nature of these traits, and thus, the difficulty in trying to improve these traits through MAS (25). An alternative to both PS and MAS is genomic selection (GS) which uses whole-genome markers to perform genomic prediction (GP) of breeding values of unphenotyped genotypes from which to select superior candidate genotypes for crossing to produce hybrids or to advance to the next generation (26). GS was reported to achieve up to threefold annual genetic gain in maize improvement when compared to MAS, due to a more efficient accounting of trait-associated QTL, faster selection cycles, and lower phenotyping costs (27)(28)(29)(30)(31)(32)(33).
Several statistical and machine learning GP models with various strengths and weaknesses have been developed to adapt to different contexts partly influenced by the genetic architecture of traits (number and effect size of QTL, proportions of additive and non-additive genetic effects) and reproductive classes of plants (allogamous vs autogamous vs clonally propagated) (34)(35)(36). Therefore, to effectively implement GS in crop improvement programs, it is necessary to employ a holistic approach to determine the best GP strategy for particular breeding targets for given crop species (31,37). Statistical models for GS vary on their prior assumptions and treatment of marker effects (31). Parametric models focus on parameter estimates rather than prediction while nonparametric algorithms give priority to prediction and have fewer assumptions (38). Some parametric methods assume the SNP effects follow a normal distribution with equal variance for all loci which seems unrealistic in practice.
Representative parametric methods are ridge regression best linear unbiased (RR-BLUP) (39) and genomic BLUP (GBLUP) (40). GBLUP was the first GP method developed and replaced the traditional pedigree-based relationship matrix by a genomic information-based matrix to improve prediction accuracies (PA) (41). Parametric methods BayesA (26) and weighted Bayesian shrinkage regression (wBSR) (42), on the other hand, consider a prior distribution of effect with a higher probability of moderate to large effects. Regarding parametric models such as BayesB (43) and BayesCπ (44), assumptions are made that consider the effect of some SNPs to be zero. The Bayesian least absolute shrinkage and selection operator (Bayes LASSO) which is a assumes that the effects of all markers follow a double exponential distribution (45). Also, Zhou et al. (46) developed the Bayesian Sparse Linear Mixed Model (BSLMM) a parametric method that combines the hypotheses of both GBLUP and Bayesian methods and achieves higher PAs than BayesCπ, and BayesLASSO. Nonparametric or semi-parametric approaches like random forest, reproducing kernel Hilbert space (RKHS) (47,48), support vector regression (SVR) (49), and neural networks (NN) (50) are better suited for accounting for non-additive genetic effects (37,38) in contrast with parametric genomic prediction models (23,38,47,51).
Several studies compared the performances of GP models under different conditions. In a simulation study, Meuwissen et al.(26) found that while GBLUP achieved PAs of up to 73.2%, BayesA and BayesB comparatively provided an additional increase of around 9 and 16%, respectively. However, when a population is composed of close relatives and the target traits are controlled by several small effect genes, the different methods perform similarly (52)(53)(54). On the contrary, BayesB and BayesCπ are better when dealing with distant relatives and traits affected by a small number of large-effect loci (23). Kernel methods such as RKHS are robust in predicting non-additive effects and in solving complex multi-environment multi-trait models (55,56). Compared to the above-mentioned parametric methods, deep learning techniques such as SVR, Multilayer Perceptron, and Convolutional Neural Networks models performed poorly in some studies (57,58). However, there are also instances where RKHS, SVR, and NN outperformed one or several of parametric methods, for instance, GBLUP, RRBLUP, and Bayesian algorithms for several traits in several crops including maize (53,59,60). These results are most likely because nonparametric GS models capture more adequately non-additive genetic components which are an essential characteristic of complex traits (23,37,38) and hence could be good candidate tools for the prediction of FAW and MW resistance traits which are controlled by both additive and non-additive gene action (12,61,70,(62)(63)(64)(65)(66)(67)(68)(69).
Additional factors that influence PAs are the sizes of the training sets (TS) and breeding sets (BS) and their genetic relationships, the number of markers used to estimate genomic estimated breeding values (GEBV) of lines, the population structure and extent of linkage disequilibrium (21,23,31,41,71). Since phenotyping is the current bottleneck in plant breeding and one of the disadvantages of GP is the requirement of large TS for high PAs to be achieved, determination of effective TS composition and size is critical for effective implementation of GS in crop improvement programs (21,(72)(73)(74)(75). Also, the best TS determination will depend on the genetic architecture and the extent of population structure of the trait targeted for GP (74), two parameters that are substantially variable among plant breeding traits. Another factor that is a determinant of the predictive ability is the kinship between the TS and the BS (74). Several methods are used for TS optimization and these generally fall into two categories, namely: untargeted and targeted approaches. For the untargeted approach, the TS is determined independently of its genomic information whereas the targeted method considers the genomic relationship between the TS and the BS as a means of maximizing PAs (76). However, deciding the best TS selection method is not straightforward and depends on contexts (77).
Furthermore, in maize, GPs were previously conducted using either genotypic best linear unbiased estimators (BLUEs) (78)(79)(80) or best linear unbiased predictors (BLUPs) (31,41,81) as a means of phenotypic corrections (81). BLUEs are obtained by treating the genotypic effect of a mixed linear model as fixed effects and provide an estimated mean for each individual of a population equal to its true value. On the other hand, BLUPs generated by considering the genotypic factors as radom and allow a shrinkage of the means towards the population mean (82). Whether to use BLUPs or BLUEs in GP is debatable. Phenotypic BLUEs allow avoiding double penalization which BLUPs suffer from. With phenotypic BLUPs, this double penalization is however compensated through maximization of the correlation between predicted and true line values while phenotypic BLUEs do not rely on this shrinkage (81). However, the shrinkage in the BLUP procedure accounts better for outliers and environmental variabilities (83) permitting better estimates of individual genetic effects than BLUEs (82) and, therefore, yield usually more accurate predictions of phenotypic performance (81,83,84). Furthermore, BLUPs are better in handling unbalanced data where, for example, the number of individuals is not the same in different locations or in the different replications of an experiment (51,81). On this basis, the current study was conducted to evaluate the efficacy of different parametric, semiparametric, and nonparametric, statistical, and machine learning GP models in achieving high prediction accuracies (PA) for maize resistance to FAW and MW traits in a diverse panel using both genotypic BLUEs and BLUPs.

Genetic material and field experiments
The panel used in this study consisted of 358 maize lines from a diverse genetic and geographic background sourced from the National Crop Resources Research Institute (NaCRRI/Namulonge, Uganda), the International Institute for Tropical Agriculture (IITA/Ibadan, Nigeria) and The International Maize and Wheat Improvement Center (CIMMYT/Nairobi, Kenya). It consisted of 71 inbred lines developed for various purposes at NaCRRI, 28 and five stem borer (SB)-resistant inbred lines from CIMMYT and IITA, respectively (6,13,14), 19 storage pest (SP)-resistant inbred lines (7,8) and a doubled haploid (DH) panel of 235 lines developed from insect-resistant parents at CIMMYT using six parents of which three were stem borer-resistant and one was a storage pest-resistant inbred line (these were also included in the population) and two were CML elite lines (one, CML132 was included in the panel) (Table S1).
The panel was planted and evaluated in three environments, at the Mubuku Irrigation Experimental Station in Kasese, western Uganda in 2017 (316 lines) during the second rainy season (2017B) and the National Crop Resources Research Institute (NaCRRI), Namulonge, central Uganda in 2018 (92 lines) and 2019 (252 lines) both during the first rainy seasons (2018A and 2019A, respectively). Detailed information on these locations is presented in Table 1. Table 1. Geographical, climatic, and soil characteristics of the planting locations (85). Each combination of location and season was considered an environment amounting to three environments. An augmented experimental design was adopted in all three environments using six checks in 2017B, two in 2018A, and four in 2019A replicated in all the blocks (12 blocks in 2017B, five blocks in 2018A, and 10 blocks in 2019A) containing unreplicated lines. The experiment in 2018A was replicated twice.

FAW and MW resistance phenotyping
After germination, plants were left unprotected to allow sufficient natural pressure of fall armyworm (FAW) population to build up. FAW damage scoring in all three environments was carried out two months after planting when adequate natural FAW infestation and pressure had manifested, and scoring was based on a visual assessment on a scale of 1 (no or minor leaf damage) to 9 (all leaves highly damaged) as described by (86) and illustrated in Figure S1 (18).
Rearing and bioassay of MW were performed as described in previous experiments carried out at NaCRRI (87,88). Weevils were reared prior to the bioassay to obtain enough insects aged between 0 to 7 days for infestation. During rearing, standard conditions were provided for weevils to ensure proper acclimatization during the experiment. Rearing was carried out by creating a weevil-maize grain culture of 300 to 400 unsexed insects and 1.5 Kg of grains contained in 3000 cm 3 plastic jars incubated for 14 days in the laboratory at a temperature of 28±2°C and relative humidity of 70±5%, to enhance oviposition. The lids of the jars were perforated and a gauze-wire mesh of pore size smaller than one mm was fitted on each lid to allow proper ventilation while preventing the weevils from escaping.
After harvest and shelling, 30 grams of grains from each line of the panel were weighed from a bulk of all three environments with the aim of having three replicates per genotype. However, due to lack of enough seed for some of the genotypes, only 64 lines could generate three replicates while 123 provided two and 132 only one. Each of these samples was wrapped in polythene bags and kept at -20°C for 14 days to eliminate any weevil infestation prior to the start of the experiment. After this disinfestation process, samples were left to thaw and transferred into 250 cm 3 glass jars and infested with 32 unsexed weevils. After 10-days incubation to allow oviposition, all dead and living adult insects were removed. One month after infestation (MAI), each sample was removed from its jar, and the grains and the flour were separated and their weights were recorded. The total number of holes inflicted by the weevils on the grains was counted along with the number of grains affected by such damages. Also, the number of dead and living weevils was recorded. After these measurements were collected, the grains were returned to their respective jars and all the measurements were repeated at two and three MAI. The collected data were used to infer for each sample, the cumulative grain weight loss (GWL), the cumulative number of emerged adult weevil progenies (AP), the final number of damage-affected kernels (AK), the total number of holes on grains (NH), and the cumulative weight of the flour produced (FP).

Statical analyses of the phenotypic data
For GP analyses, both best linear unbiased estimators (BLUEs) and predictors (BLUPs) were generated using the general linear model with only phenotype option of the software Trait ASSociation through Evolution and Linkage (TASSEL) (89) and the ranef function of the R package (90) lme4 (91), respectively. The mixed linear model for generating BLUEs (all factors considered as fixed) and BLUPs (all factors considered as random) for MW traits (GWL, AP, AK, NH, and FP) was as follows: The mixed model for generating BLUEs (all factors considered as fixed) and BLUPs (with all factors considered as random) for FAW damage scores across environments model was: Where: in the two equation is the intercept.

MW resistance traits
To estimate GP accuracies for MW resistance, 37% (126 out of 341) of lines from the panel which had both genotypic and phenotypic data on grain weight loss (GWL), adult progeny emergence (AP), and number of affected kernels (AK) were used as the TS. The remaining 215 lines with no phenotypic data were considered as the breeding set (BS) for which the genomic-estimated breeding values (GEBV) were predicted.

FAW damage resistance
To determine TS and BS sizes and compositions for the evaluation of maize resistance to FAW damage, two strategies, namely: random-based TS (RBTS) and pedigree-based TS (PBTS) were used.

Random-based TS determination
For the RBTS, first, 126 (37%) lines used for GPs of MW resistance traits were used as the TS to predict the GEBVs of the remaining lines. To build the second TS, the 215 (67%) lines used earlier as BS were considered as a TS. Then random selections of 75 and 85% of the lines in the entire panel were performed to determine the third and fourth TS to predict the GEBVs of the remaining lines.

Pedigree-based TS determination
The PBTS strategy is presented in Table 2. For the first dataset (FAW.Ped1), the 235 (68.91%) doubled haploid (DH) lines were used as a TS and the remainder as a BS. Regarding the second dataset, the TS and BS were switched to consider the TS in FAW.Ped1 as BS, and BS in FAW.Ped1 as the TS. The third dataset, FAW.Ped3, had a TS composed of the 294 (86.22%) that were stem borer (SB) and storage pest (SP) resistance lines not from the International Center for Maize and Wheat Improvement (CIMMYT) whilst the CIMMYT SB and SP resistant lines constituted the BS. In the last dataset, FAW.Ped4, the 235 DH lines, and the SB and SP lines from CIMMYT and the International Institute for Tropical Agriculture (IITA) amounting to 287 (84.16%) genotypes were considered as the TS and the remaining from NaCRRI lines were considered as the BS (Table 2).

Genomic prediction algorithms
The GP analyses were performed using the BLUEs and BLUPs of the phenotypes and the 28919 single nucleotide polymorphism (SNP) markers that remained after duplicate removal (DRSNPs) and distributed across all the 10 chromosomes of the entire maize genome. Generation of the SNPs from this maize panel and duplicate removal were described in our previous study (25). The analyses were based on 17 prediction methods (a set of statistical and machine learning models, parametric, semi-parametric, and nonparametric methods) available in 12 GP algorithms implemented on the Genomic Prediction 0.2.6 plugin of the KDCompute 1.5.2.beta (https:// kdcompute.igss-africa.org/kdcompute/home), an online database developed by Diversity Array Technologies (DArT, https://www. diversityarrays.com) for the analysis of DArT marker data. The 12 algorithms were drawn from five R packages designed for GP analyses: The The BRNN (Bayesian regularization for feed-forward neural networks) package (101) fits a two-layer neural network (102,103). BRNN uses the Nguyen and Widrow algorithm (104) to assign initial weights and the Gauss-Newton algorithm to perform the optimization.
The ridge regression best linear unbiased predictor (rrBLUP) packages can either estimate marker effects by ridge regression or alternatively, BLUPs can be calculated based on an additive relationship matrix or a Gaussian kernel. This package also implements the Mixed Model Solution (MMS) that calculates the maximum-likelihood (ML) or restricted-ML (REML) solutions for mixed models to perform GP (105). The R package missForest uses the function missForest that implements Breiman's random forest algorithm for classification and regression (106). On the KDCompute 1.5.2.beta platform, the user can choose either Square root or Regression options for the classification of the number of variables randomly sampled as candidates at each split (https://kdcompute.igss-africa.org/ kdcompute/plugins). The 16 methods used in this study and their statistical characteristics are presented in Table 3.

Cross-validations and PA estimation
To calculate the predictive accuracies of each of the 17 methods, a cross-validation approach was performed using the data for the TS with 10 folds and five repetitions amounting to 50 replications. The PAs were estimated as the correlation coefficient (R 2 ) averaged across the 50 cross-validation replications between the observed phenotypic values and the predicted genomic-estimated breeding values (GEBV) (https://kdcompute.igss-africa.org/kdcompute/ plugins).

Higher PAs achieved with BLUPs for FAW and MW resistance traits as compared with BLUEs across GP algorithms
Both genotypic BLUEs and BLUPs for resistance to FAW and MW traits such as AK, AP, and GWL were used in GPs. Generally, BLUPs produced better predictions than BLUEs by at least two orders of magnitude in terms of PAs (Figure 1). The PAs realized with BLUEs ( Figure S2) varied from -0.246 for FAW (mms_ML) to 0.299 for AP (BayesB), while PAs for BLUEs ranged from 0.668 for AP (mmer_NR) to 0.823 for AP (missForest_Reg). The differences in terms of accuracies between BLUEs and BLUPs were high despite the highly significant (P<0.001) correlations between BLUEs and BLUPs for each trait ranging from 0.93 for FAW to close to 1 for MW resistance traits such as AP, AK, and GWL (Figure 1), therefore, only results for BLUPs of resistance traits will be presented hereafter.

PAs for MW resistance traits using BLUPs
The PAs were generally high for the tested MW traits, mostly above 0.668 across the 12 GP models that were successfully run on the datasets (Figure 2), however, RKHS failed  Table 3 for GP algorithms).
to work on the AK trait. The highest PAs were achieved for AP with missForest_reg (0.823), followed by BRR (0.805) and RKHS (0.804) with the lowest prediction accuracy of 0.667 obtained through the mmer_NR algorithm ( Figure 2). The PAs achieved for GWL ranged from 0.742 for missForest_Sqt to 0.795 for mmer_NR, while for AK, they varied from 0.749 for missForest_sqrt to 0.779 for BRR ( Figure 2). Generally, Bayesian models predicted better than both mixed model and machine learning methods, although the differences were small ( Figure S3).

PA for FAW resistance using BLUPs
The different maize resistance to FAW datasets showed high predictive abilities achieved through 10 of the 17 GP algorithms used in the study. Regarding the RBTS approach, the PAs were the lowest with the dataset that had a TS composed of 37% (lowest size) of the panel and the highest with the largest TS (85% of the panel). Even with a TS of 37%, the PAs were still high, ranging from 0.694 to 0.714 for mms_ML and BLR methods, respectively ( Figure 3). However, it should be noted that with equal TS sizes and composition (37% of the panel), higher PAs were achieved for MW resistance  Table 3 for GP algorithms).
traits such as GWL, AP, and AK than for FAW resistance ( Figure S3). The PA for the TS of 63% varied from 0,833 for BL method to 0.838 for the missForest_Sqt, thus, there was a small variation among methods. Similarly, there was minimal variation among GP algorithms on the dataset with a 75% TS whose PAs varied from 0.838 for mms_REML to 0.843 for MissForest_Reg. The same trend was obtained on the dataset with a TS of 85% of the panel, with PAs ranging from 0.843 for the BRR model to 0.847 for the missForest_Reg method. Furthermore, there was a high and significant (P<22e -16 ) positive correlation of 0.92 (Figure 4) between the PAs and TS sizes for FAW datasets for the RBTS Figure 4. Pearson correlation between training set (TS) sizes and prediction accuracies across the 10 genomic prediction models conducted on RBTS and PBTS datasets for fall armyworm resistance (FAW).
denoting a steady improvement of the PAs as the TS sized increased. However, the PAs for FAW resistance reached a plateau at TS size above 63% of the panel ( Figure 5).
Although the PAs do not vary much among GP algorithms, especially when the analyses involved larger TS sizes equal or bigger than 63% of the panel, the Machine learning methods slightly outperformed other GP algorithms for almost all the traits, except for the TS of 37% where Bayesian methods such as BLR and BayesC showed a slight advantage over the former ( Figure S4).
The PAs for FAW resistance datasets with PBTS were generally high, mostly above 0.82 ( Figure 6). For the first dataset (FAW.Ped1) with a TS of 68.91% of the panel (see Table 2), the PAs varied between 0.828 for BLR to 0.835 for missForest_Sqt. Regarding FAW.Ped2 (TS=31.09%), the PAs ranged from 0.862 for BayesC to 0.864 for mms_REML.   Figure 4). In these datasets, the PAs were more influenced by the composition of the TS and its pedigree relationship with the BS (see Table 2). Using the doubled haploid (DH) lines as TS (FAW.Ped1) and viceversa (FAW.Ped2) or DH and stem borer (SB) and storage pest (SP) resistant lines as TS (FAW.Ped4) permitted achieving higher PAs from all the 10 algorithms than when considering the CIMMYT SB and SP resistant lines as BS and the remainder as a TS (FAW.Ped3), where only Machine learning algorithms missForest_reg and missForest_Sqt achieved high PAs. Furthermore, the composition of the TS and its relationship with the BS determined which GP methods achieved the highest PAs with Machine learning algorithms working best on FAW.Ped1 and FAW.Ped3, linear mixed model approaches outperforming Bayesian and Machine Learning algorithms on FAW.Ped2 and FAW.Ped4, and Bayesian methods ranking either second or third on all datasets ( Figure S5). It should be noted that the PBTS strategy generally achieved better PAs than the RBTS irrespective of the size of the TS, except for the FAW.Ped3 dataset (Figures 3 and 6).  Table 2 for the PBTS strategy and Table 3 for GP algorithms).

DISCUSSION
Tropical maize germplasm is characterized by rapid linkage disequilibrium (LD) decay with high diversity (107). These genetic characteristics make genomic selection (GS) a promising approach to integrate into African breeding programs (108). Given the diversity of GP models and their differential performances depending on crops and trait architectures and other other parameters such as the size of the training set (TS) and it its relationship with the breeding set (BS) (31,37), this study aimed at assessing the feasibility of genomic selection for maize resistance to FAW and MW through estimation of the genomic prediction accuracies achieved by parametric, semiparametric, and nonparametric genomic prediction (GP) algorithms for both traits using both BLUES and BLUPs of these phenotypes, and random and pedigree-based TS determination strategies.

Higher PAs for BLUPs compared to BLUEs for both FAW and MW resistance traits
With an RBTS of 37% of the panel, PAs were higher (at least two-fold) across both FAW and MW resistance traits, and for all GP models when trait BLUPs were used as phenotypes compared to BLUES, although there were high Pearson correlations between these two categories of phenotypic data for each trait. Generally, BLUPs were reported to have higher predictability than BLUEs owing to better accounting for outliers and environmental variabilities permitted by the shrinkage procedure in BLUPs which results in more accurate estimates of individual genetic effects (81)(82)(83)(84). Furthermore, most of the predictive differences between BLUPs and BLUEs might have stemmed from BLUPs being more suitable than BLUEs in fitting data recorded from unbalanced experiments (51,81) as it was the case for both FAW damage scores across environments and MW bioassay in this study. Therefore, for all subsequent analyses with higher RBTS sizes and the PBTS strategy for FAW, only BLUPs were focused on in this study and will be further discussed.

High PAs achieved for FAW and MW resistance traits using moderately sized training sets
The obtained PAs were high for both MW and FAW resistance traits even with TS of moderate sizes confirming the potential of genomic selection (GS) in Africa adapted germplasms (28)(29)(30)33). With a TS of 37% of the entire panel, high PAs (above 0.70) for MW resistance traits, grain weight loss (GWL), adult progeny emergence (AP), and the number of affected kernels (AK), and for FAW resistance were achieved in agreement with the moderate to high heritability values for these traits as earlier reported (21,31,41). These results are significantly important considering that one of the disadvantages of GS is the requirement of large TS which negatively impacts the reduction of phenotyping cost (73,75).
The PAs increased up to above 0.85 in proportion to the increase in TS (RBTS approach) size for FAW resistance which was the only trait phenotyped on all the lines of the panel. It would be interesting to phenotype other lines of the panel that were not evaluated for MW resistance traits to establish larger TS which may improve the PAs (31,76,109,110). Very few reports of GP are available for maize resistance to biotic stresses. Similar and higher PAs were achieved for maize resistance to chlorotic mottle virus (up to 0.95) and maize lethal necrosis (reaching 0.87) in tropical germplasm (78). However, lower PAs of up to 0.59 were obtained in a study that assessed the predictability of maize resistance to the European corn borer (111) in temperate germplasm. Similarly, Gowda et al.(80) reported moderate PAs (close to 0.60) for maize resistance to the biotic stress, the maize lethal necrosis in tropical maize populations.

GP algorithms performed differently on FAW and MW maize resistance traits
In this study, several GP models including statistical and Machine Learning algorithms, parametric, semi-parametric, and nonparametric approaches were used to predict FAW and MW resistance traits. These GP algorithms, as expected, performed differently on the different traits although the predictive variations were generally minimal, especially when large TS were involved, similar to earlier model benchmarking reports (112,113). Bayesian models (parametric: BLR and BRR, and semi-parametric: RKHS) performed better on MW traits, GWL, AP, and AK, while nonparametric Machine Learning algorithms (missForest) and, to a lesser extent, linear mixed model (especially in the PBTS approach), achieved the highest PAs on FAW datasets. The differential performances of the different GP algorithms on the resistance traits evaluated in this study could be due to differences in the genetic structures (extent of additive vs. nonadditive gene action) of the respective traits (23,38,47,51). Maize resistance to FAW, which was moderately heritable across environments (25), would be expected to be controlled by both additive and nonadditive genetic factors (62,63,70), whereas, MW resistance traits such as GWL, AP, and AK with heritability values above 90% (25) were most likely characterized by a prevalence of additive gene action (64,68) in the current panel.

Influence of the size and the composition of TS and BS on PAs
Two factors, the relative sizes of the TS and BS (RBTS approach) and their kinship (PBTS approach), affected the PAs across FAW resistance datasets which corroborated earlier reports Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 15 July 2020 doi:10.20944/preprints202007.0336.v1 (31,74,76,109,110,114,115). A net increase in PAs for maize resistance to FAW was realized when the size of the TS was increased from 37% (0.694 to 0.714) to 63% (0.833 to 0.838) similar to earlier reports on wheat yield (116). This increase was followed by a slight gain in predictability at 75% (0.837 to 0.843) and 85% (0.843 to 0.847). Similar to results in the current study, PAs were reported to reach a plateau and not increase significantly when TS reached a certain size (21,75,(116)(117)(118). Consequently, future GS programs for maize resistance to FAW could be designed around TS composed of a minimum of 60% of the entire breeding germplasm to achieve high genetic gains. These results were further supported by the highly significant (p>2.2e-16) positive correlation (R=0.92) between TS size and PAs. Similarly, positive correlations between the number of lines in the TS and the PAs, and plateau for the PAs were also reported by Edwards et al. (116).
The composition of the TS and its relationship with the BS are determinant factors for the genomic predictability of complex traits (74,(119)(120)(121). In the current study, using the PBTS approach, these parameters were more important than the size of the TS since higher PAs were achieved in FAW.Ped2 (0.862 to 0.864) with a TS of 31.09% than in all other FAW PBTS datasets including FAW.Ped3 (0.114 to 0.750) with the largest TS of 66.22%. In fact, FAW.Ped3 achieved the lowest PAs among all the PBTS FAW datasets. These results were further illustrated by the significantly (p<13e-08) negative correlation (R=-0.33) between the sizes of the PBTS and the achieved PAs.
However, it is not very clear why the prediction between the BS FAW.Ped3 (47 CIMMYT SB and SP resistant lines) and the TS (DH, IITA SB, and NaCRRI lines) led to lower PAs in FAW.Ped3. A possible explanation is that these two sets were distantly related since only two and one CIMMYT SB and SP resistant lines, respectively, were used as parents to develop the DH lines. Spindel et al. (118) argued that high PAs can be achieved with small-sized TS when lines in the TS and the BS are closely related, since such TS would have sampled the full genetic diversity of the population. However, the more distantly related the TS and the BS are, the larger the required TS size to reach high PAs (118). Using the CIMMYT SB and SP resistant lines as a TS would most likely lead to lower PAs since such a TS would be additionally disadvantaged by small size (47 lines). The DH lines in the current study are involved as a TS in most of the best performing GP datasets evaluated in the current study (both in the RBTS and PBTS approaches) and as unique lines in the BS of the best performing pedigree-based BS (FAW.Ped2). This DH population would be of interest in future breeding activities targeted at improving insect resistance in maize (23,(122)(123)(124) and potentially useful for GS of complex traits with low to moderate heritability (125).

Conclusion
This study assessed the influence of the size and composition of the training set on the genomic predictability of maize resistance to fall armyworm (FAW) and maize weevil (MW) in a diverse Africa adapted maize population using several parametric and non-parametric genomic prediction models. Prediction accuracies for maize resistance to FAW and MW traits were relatively high, even with a moderate training set size. For FAW resistance, although the prediction accuracies were positively correlatedwith the size of the training set, the composition and the relationship of the training set with the breeding set were more influencial in predicting line performance. Also, TS determination-related parameters were more important than the type of genomic prediction models in predicting FAW and MW resistance traits. Therefore, future genomic selection programs for maize resistance to insect pests such as the Fall armyworm and the maize weevil in Africa should put more effort in designing effective training set for improved genetic gains coupled with short breeding cycles and accelerated variety release. Such programs would greatly benefit from using the genetically diverse maize panel used in this study, as a base population since it consists of lines adapted to several African agroecologies.