Genomic selection (GS) has revolutionized breeding practices by integrating genotype and phenotype data to predict genomic estimated breeding values (GEBVs), offering the potential to accelerate breeding cycles and intensify and enhance early-stage selections. This approach relies on the concept of linkage disequilibrium (LD) between genetic markers and quantitative trait loci (QTL) within populations. LD is the non-random association between alleles at different loci and provides valuable insights into recombination rates. This study aimed to investigate the influence of recombination on haplotype sizes and LD, assess the impact of additive (A) versus additive + epistasis (A+I) genetic models on GS prediction accuracy, and demonstrate how haplotype resolution in the training set (TS) impacts the prediction accuracy of GS. For this, we used biparental (MP2) and multiparent (MP6-8) populations, where the only difference between them was the recombination rate. Results revealed a direct relationship between LD decay and the number of recombination opportunities within populations, with smaller haplotype blocks observed in populations experiencing more recombination. The use of A+I models increased heritability but did not improve prediction accuracy. Finally, populations with smaller haplotype sizes in the TS exhibited enhanced prediction accuracy. This study demonstrates the effect of haplotype size on GS accuracy, and its uniqueness lies in its focus on populations where the sole differentiating factor is haplotype size. It offers an important tool for breeders in designing GS strategies, providing valuable guidance for future breeding efforts.
Article
The Effect of Haplotype Size on Genomic Selection Accuracy and Epistasis: An Empirical Study in Rice
https://doi.org/10.21203/rs.3.rs-3895233/v1
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In classical breeding schemes, selecting the best individuals is typically based on their phenotypic values, which serve as a surrogate of their breeding value. In contrast, genomic selection (GS) combines genetic information encoded in an individual’s genotype with phenotypic data to predict the genomic estimated breeding values (GEBVs) of individuals in the population (Meuwissen et al., 2001). GS can potentially enhance genetic gain by shortening breeding cycles, intensifying selection, and improving the accuracy of early-stage selections (Heslot et al., 2015; Crossa et al., 2017). Numerous studies have demonstrated the increased genetic gains achieved by leveraging genotypic information, especially in the early generations when phenotypic data is limited (Calus et al., 2008; Meuwissen et al., 2001; VanRaden, 2008).
GS relies on the linkage disequilibrium (LD) between genetic markers and quantitative trait loci (QTL) within a population. LD represents the non-random association between alleles at different loci and provides insights into the rate of recombination within a population (Andrade et al., 2019; Goddard and Hayes, 2007; Vos et al., 2017; Wall and Pritchard, 2003). Various methods, such as the Pearson Correlation Coefficient r2, estimate LD and its decay between marker pairs (Weir, 2008). LD, measured in terms of r2, plays a crucial role in constructing haplotype blocks, which are segments of the genome that are inherited together (Devlin and Risch, 1995). Recombination events lead to the breakdown of haplotype blocks into smaller units, and these changes in haplotype structure can significantly impact various genetic phenomena, potentially leading to an increased response to selection (Battagin et al., 2016; Tourrette et al., 2019). The rate of LD decay in a population is context-dependent and greatly influenced by the germplasm being evaluated. Features of interest include the genetic diversity, mating history, selective pressures, mutation rates, recombination frequencies, and demographic factors (Ardlie et al., 2002; Slatkin, 2008).
While additive genetic effects of genes are often the primary focus in GS studies (Falconer and Mackay, 1996; Meuwissen et al., 2001), the inclusion of epistatic effects has yielded varying results. Some studies have reported increased prediction accuracies when epistasis is included in the model (Hu et al., 2011; Luo et al., 2001), while others have found no advantage in prediction accuracy (Lorenzana and Bernardo, 2009). Epistasis, involving the interaction of multiple genes, introduces complexity into the genetic models used for GS. Understanding the relationship between epistasis and recombination is crucial, and empirical investigations are needed to assess the effect of recombination on the manifestation of epistatic effects.
A notable gap in empirical research concerns the influence of haplotype size and rate of LD decay on GS prediction accuracy, as previous investigations have relied on simulation-based approaches. This study aims to address this gap and focuses on three main objectives: i) investigate the influence of recombination on haplotype sizes and LD decay, ii) assess the impact of additive versus additive + epistasis genetic effect models on GS prediction accuracy, and iii) demonstrate how haplotype resolution in the training population impacts the prediction accuracy of GS in rice.
3.1 Experimental material and genotyping
Four bi-parental rice populations (MP2), named MPA, MPB, MPC, and MPD, were developed using eight elite US parents. The combination of parents and the development methodology of the MP2 was explained by Cerioli et al. (2022). Four-way populations (MP4) were obtained by crossing pairs of F1 individuals from the MP2 populations: MPA x MPB (MP4-AB), MPA x MPC (MP4-AC), MPA x MPD (MP4-AD), MPB x MPC (MP4-BC), MPB x MPD (MP4-BD) and MPC x MPD (MP4-CD). Multi-parent populations consisting of six or eight parent combinations (MP6-8) were generated using F1 individuals from the MP4 populations. A set of 430 MP2, 1,026 MP4, and 324 MP6 lines were genotyped and used for this study. For the MP2 materials, a single F3 plant was sampled for genotyping, serving as the seed source for all subsequent generations. In the MP4 and MP6-8 populations, an F4 plant was derived and genotyped.
Additionally, data from preliminary yield trials (PYTs) from the LSU Rice Breeding Program performed at the H. Rouse Caffey Rice Research Station (HRCRRS) in Rayne, LA, during 2020, 2021, and 2022 was also used for this work. These PYTs consisted of 2,929 F2:F4 and F3:F5 lines, of which 1,263 correspond to the PYTs from 2020, 943 from 2021, and 733 from 2022. All PYT entries were genotyped with a single leaf sample from the plot in the field.
Genotyping of the PYT materials, MP2, MP4, and MP6-8, was conducted using the LSU500 AmpSeq custom marker set that was described by Cerioli et al. (2022) through the genotyping service provider Agriplex Genomics (https://agriplexgenomics.com). This SNP array is an optimized set of informative markers used routinely for genotyping US rice germplasm that has proven useful for breeding purposes.
Markers used to calculate LD decay were quality-controlled using the “raw. data” function from the package snpReady (Granato et al., 2017), with filtering set for minor allele frequency (MAF) > 0.05 and a call rate of 0.95. The final dataset was transformed from nucleotide genotype coding (e.g., 'A', 'C', 'T', 'G') to numeric coding (0= homozygote class 1, 1= heterozygotes, and 2= homozygote class II, respectively). This conversion allowed for efficient computation and interpretation of the genetic data within the statistical analysis framework.
Additionally, the additive and epistatic genomic relationship matrices (i.e., Ga and GI, respectively) were calculated using the LSU500 marker set. The Ga was obtained using the “A.mat” function from the sommer R package markers were also filtered for a MAF >0.05 (Covarrubias-Pazaran, 2019), which implemented the equation proposed by VanRaden (2008) to account for genetic relatedness among individuals. Then, the second-order epistatic kinship (additive x additive) was obtained using the “E.mat” function from the same package and is computed as the Hadamard product of the genomic additive relationship matrix (Henderson, 1985).
3.2 Phenotypic data
All tested lines were grown at the HRCRRS (Crowley, LA, 30°14′30″ N, 92°20′46″ W), following the recommended nutrition and water management practices from the Louisiana Rice Production Handbook (Saichuk, 2014). The trials were planted in 1.42 m wide plots and 4.12 m long with a heavy-duty grain drill (Almaco Equipment, Nevada, IA), using a seeding rate of 78 kg.ha-1, and 2 cm was the planting depth. Days to heading was measured as the number of days elapsed from the emergence of the plants until the day in which 50% of the plants within the plot present panicles emerging from the sheath of the flag leaf. The determination of grain yield (kg.ha-1) was carried out by harvesting the entire plot through a Delta Plot (Wintersteiger AG) combine harvester and a Harvest Master Grain Meter (Juniper Systems), which was used to collect the weight and moisture (%) of the grain. Moisture values from each plot were adjusted to 120 g.kg-1 of water content. Samples of 100 g were milled in a PAZ laboratory mill (Zaccaria USA) and were used to measure the whole milling percentage (%) expressed as grams per kilogram of whole milled kernels over rough rice seed. Chalk percentage (%) was measured with SeedCount (Next Instruments) and corresponded to the percentage of the chalky area of the milled grain. Days to heading, grain yield, whole milling percentage, and chalk percentage were collected for MP2 and MP6-8 materials and all PYTs; this data was not collected for the MP4 materials which were omitted from the phenotypic evaluation.
430 MP2 genotypes were tested in 2020; from those, 220 were evaluated in 2021 in two different environments (i.e., different planting dates in the same location). 318 and 178 MP6-8 genotypes were also evaluated in two environments (i.e., other planting dates in the same location) during 2021 and 2022, respectively. During 2020, 2021, and 2022, three different PYTs were grown as regular breeding activities within the LSU Rice Breeding Program. These PYTs represent different forms of herbicide resistance within the long grain materials, namely the “Conventional,” “Clearfield ®” and “Provisia ®”, hereafter PYT CN, PYT CL, and PYT PV respectively (Table 1).
Table 1. Name of the trials used for this study, description, number of genotypes, year of evaluation, and the dates of emergence and harvest. The grey color indicates the multi-parent (MP6-8) or bi-parental (MP2) materials developed and used for this study, and the white color shows the use of Preliminary Yield Trials (PYTs) that are part of the regular breeding activities and were used as part of this research.
3.3 Statistical-genetics Analysis
All the analyses were performed using the statistical programming language R (R Core Team, 2021). The sommer package (Covarrubias-Pazaran, 2019) was utilized for calculating LD as well as the linear mixed model equations (LMME) for estimating genetic heritability values, obtaining the best linear unbiased estimators and predictors (BLUEs and BLUPs, respectively), and the GEBVs.
3.3.1 LD decay and haplotype size
The calculation of LD involves estimating the Pearson correlation coefficient r2, which measures the non-random association of alleles at different loci. LD decay, conversely, refers to the decrease in linkage disequilibrium over physical distance. This study assessed LD decay by calculating r2 between pairs of genetic markers using the “LD.decay” sommer function that incorporates a marker matrix and a map providing the physical distances between markers in kilobase pairs (i.e., kbp).
The LD statistics were computed per chromosome for the MP2, MP4, and MP6-8 materials using the LSU500 marker set. Subsequently, the LD values were aggregated across all 12 chromosomes. To visualize the LD decay pattern, the r2 was plotted against the physical distance in kbp. Only significant correlations (p < 0.001) were retained to focus on meaningful associations to calculate the average and median LD values. Haplotype sizes in terms of mean and media, along with selected percentiles (10th, 25th, 75th, and 90th), were calculated using distances (in kbp) between significant pairs of markers. In this study, LD was estimated within the MP2 populations as a whole and separately within the MP6-8, aligning with conventional practices in GS (Meuwissen et al., 2001; Heffner et al., 2009). As part of a practical approach, information from populations was combined.
3.3.2 Phenotypic data analysis and statistical models for genomic predictions
Outliers from the phenotypic data were removed using the “outlierTest” function in the car package (Fox and Weisberg, 2019) in R, which uses the Bonferroni outlier test. For the statistical analysis of the trials, a two-step approach was performed. The subsequent statistical analysis was carried out in three steps. First, a spatial adjustment was performed based on rows and columns using two-dimensional splines. For this step, the “SpATS” package from sommer was used. The best linear unbiased estimators (BLUEs) for the traits in consideration for every line were extracted using the function “predict. mmer” from the same package. Hence, the SpATS mixed model for each trial is formulated as follows (Equation 1):
where the vector y contains the phenotypic observations, arrayed as rows within columns, β is a vector of fixed terms that includes the intercept, and X is the associated design matrix. The expression for the smooth spatial surface is enclosed by the fixed (unpenalized) term Xsβs and the random (penalized) component Zss. The vector u comprises mutually independent sub-vectors of random row and column effects accounting for discontinuous field variation, expressed as u = [ur|uc] with a design matrix Z. Additionally, the vector g contains the fixed effect of the genotypes and Zg represents the design matrix for genotypes. The vector e represents the error term with a distribution e ~ N (0, σ2e).
In the second step, a multi-environment trial (MET) analysis was performed, adding the planting date and year as fixed effects (Equation 2):
Here y* represents the adjusted means from the first step, (Equation 1); p is the planting date effect with X as the correspondent design matrix, s is the year effect with T as the design matrix, and u is the random term for genotypes with Z as the design matrix. The best linear unbiased predictors (BLUPs) from each genotype were extracted using the predict.mmer function mentioned above.
To perform the genomic predictions, we used Additive (A; reduced model) and Additive + Epistasis models (A+I; full model), as follows (Equation 3):
2.3.3 Heritability and k-fold cross validation (CV) predictive ability
Narrow-sense genetic heritability (h2) was calculated for the A and A+I models described above for each of the traits, as the ratio between the additive variance component and the sum of the additive and residual error component (A model), in the case of the A+I model, the epistatic variance component was added in the denominator of the equation, as is defined in Equation 4:
where σa2 is the additive genetic variance from the A or the A+I model, σi2 is the genomic epistatic variance, and σe2is the residual variance. These calculations were conducted for each of the traits and each trial. Subsequently, the computed heritability values were averaged within each population, encompassing MP2, MP6-8, and PYTs.
To evaluate prediction accuracy, a cross-validation (CV) approach was employed (Gianola et al., 2009; Meuwissen et al., 2001) using the A or A+I as the LMME to assess their predictive performance in each trial. A k-fold cross-validation scheme was used, with five replicates and five folds, totaling twenty-five predictions per scenario. Consequently, the GEBVs were obtained for all individuals in the validation population. The CV predictive ability was calculated as the Pearson Correlation (R) between the adjusted phenotypes (BLUP) and the computed GEBVs.
3.1 Comparison of LD-decay and haplotype sizes between MP2, MP4, and MP6-8 concerning recombination cycles
The multi-parent (MP) materials used in this study were developed from eight elite founder varieties from the southern US exhibiting high yield potential, disease resistance, and grain quality. Four bi-parental (MP2), six 4-way (MP4), and two multi-parent (MP6-8) populations were developed (Fig. 1), with the relatedness of these populations presented in Supplemental Figure S1. The MP2, MP4, and MP6-8 materials exhibited two, four, and five generations of recombination, respectively. The study incorporated 430 MP2, 1034 MP4, and 324 MP6-8 lines, all of which were genotyped using the LSU500 marker array (Cerioli et al., 2022). After quality control, the number of polymorphic markers was 422 for MP2, 357 for MP4, and 410 for MP6-8.
The specific design of these populations and the absence of selection provided a unique opportunity to explore the influence of additional recombination on LD decay and haplotype size within each population. Pearson r2 was used to estimate LD between each marker pair along the 12 rice chromosomes in the MP2, MP4, and MP6-8 materials (Fig. 2). The average level of LD was higher in the MP2 materials (r2 = 0.22), intermediate for the MP4 (r2 = 0.19) and lower for the MP6-8 materials (r2 = 0.18). As expected, the LD-decay was directly related to the number of cycles of recombination within each population, with the most rapid decay and the smallest haplotype block sizes observed in the MP6-8 (Table 2).
The mean and median of the minor allele frequency (MAF) for polymorphic markers within each population class were 0.31 and .32 for MP2, 0.31 and 0.34 for MP4, and 0.30 and 0.31 for MP6-8, demonstrating no significant change in MAF over the generations.
Table 2. Mean, median, and quartile (10, 25, 75, and 90%) haplotype size (kbp) within MP2, MP4, and MP6-8 materials.
3.2 Trait heritability and cross-validation for MP2 and MP6-8 materials for Additive versus Additive + Epistasis effects
Phenotypic trials were conducted for the MP2 and MP6-8 materials to evaluate grain yield, days to heading, chalk percentage, and whole milling percentage. MP2 materials were assessed in 2020 and 2021 in one and two environments, respectively (i.e., two planting dates), while the MP6-8 lines were tested in 2021 and 2022, with two planting dates each year. For both groups, BLUP scores were calculated for each line based on their phenotypic values, and narrow sense genetic heritability (h2) was estimated under two scenarios: one considering additive (A) effects exclusively and another accounting for both additive and epistatic effects (A+I) (Table 3).
Table 3. Heritability (h2) for grain yield, chalk percentage, days to heading, and whole milling percentage across all MP2 and MP6-8 trials considering Additive (A) only versus Additive + Epistatic (A+I) effects.
Incorporating epistatic effects along with additive effects increased the estimated heritability. For MP2 materials, with larger haplotype blocks, adding epistatic effects led to a 2.9% increase in average heritability compared to additive effects alone. In contrast, the MP6-8 materials, with smaller haplotype blocks, exhibited a 55.26% increase in average heritability. These findings underscore the positive effect on heritability of including epistatic interactions in the analysis, and demonstrate that the extent of the effect depends on the recombinational profile (haplotype block structure) of the population.
Prediction accuracy of the A versus the A+ I model was evaluated using CV within the MP2 and MP6-8 populations, calculated as the Pearson Correlation between the phenotypic BLUPs and the GEBVs for each trial (Fig. 3). In both populations, the prediction accuracies did not increase when A+I effects were added to the model. However, when both additive and epistatic effects were incorporated into the model, there was a 3.89% decrease in CV accuracy compared to using only A effects for the MP2 materials. In contrast, for the MP6-8 materials, the impact of including epistasis in the model was more pronounced, resulting in a 15.33% decrease in CV accuracy when A+I effects were considered.
When comparing CV predictive accuracies within each population, the MP2 populations consistently exhibited superior prediction accuracy for all traits compared to MP6-8, as illustrated in Figure 3. This is consistent with the observed heritability results (Table 3).
3.3 Prediction accuracies of the MP2 and MP6-8 populations as training sets and validation sets
To compare prediction accuracies across populations, the MP6-8 (smaller haplotypes) population was used as a TS to predict phenotypes in the MP2 (larger haplotypes) materials and the MP2 was used as a TS to predict phenotypes in the MP6-8. These comparisons allowed direct comparisons of the effect of haplotype size on prediction accuracy, considering that both populations are derived from the same set of parents and the observed allele frequencies within each population are the same. Prediction accuracies were again calculated as the Pearson Correlation Coefficient (r) between the phenotypic BLUPs and the GEBVs for each trait (Fig. 4).
Results indicated that prediction accuracies were equivalent or higher when MP6-8 was used as the TS to predict MP2 phenotypes, compared to using MP2 as the TS to predict MP6-8 phenotypes. Notably, the difference in prediction accuracy was minimal for days to heading (2.43%), a trait that is controlled by relatively few genes in these populations, compared to the highly quantitative traits, such as grain yield, chalk percentage, and whole milling percentage, where improvements of 18.55%, 78.68%, and 43.85%, respectively, were observed when MP6-8 materials were used to predict MP2 phenotypes.
3.4 Predictive ability of MP2 and MP6-8 materials as TS to predict overall breeding program germplasm
The suitability of using MP2 and MP6-8 materials as TS to predict the grain yield of historical data from the regular breeding program (Prediction Set, PS) was explored. The PS consisted of data from preliminary yield trials conducted in 2020, 2021, and 2022 as part of the LSU rice breeding pipeline, in combination with either MP2 or MP6-8 as the TS.
This study utilized various PYTs, each corresponding to different sets of trials with slight variations in the degree of relatedness between the lines. Each PYT is associated with a distinct herbicide-resistant trait found in rice (Famoso et al., 2019). Specifically, three different PYTs were employed each year, namely CN (Conventional), CL (Clearfield®), and PV (Provisia®). For each, the narrow sense genetic heritability (h2) and CV accuracy for yield were estimated (Table 4).
Table 4. Heritability (h2) and CV accuracy for grain yield for each PYT evaluated for this study.
To evaluate the efficacy of MP2 as a TS, PYT data corresponding to the same years of testing (i.e., 2020 and 2021) were utilized to calculate the correlation between the GEBVs and the observed phenotypic BLUEs. A similar approach was applied when MP6-8 was used as a TS to predict PYT in 2021 and 2022. The correlation between predicted GEBVs and observed phenotypic BLUEs for grain yield was computed for each case, as illustrated in Figure 5.
The bar plot depicted in Figure 5 illustrates the prediction accuracy of the MP2 and MP6-8 TS to predict the yield performance of the PYT materials. MP2 trials of 2020 and 2021 were used to predict the 2020 and 2021 PYTs, respectively. Conversely, the 2021 and 2022 MP6-8 trials were used to predict 2021 and 2022 PYTs. The combined bar represents the prediction accuracy of each TS (MP2 or MP6-8 materials) to predict the whole PYTs in each case, which is 0.34 and 0.40 when using the MP2 or MP6-8 as TS to predict the PYTs, respectively. We used a single year's data to minimize environmental year effects to directly compare MP2 and MP6-8 TS for predicting the breeding program germplasm. The prediction accuracy of the 21 MP2 TS was 0.19, and the accuracy of the 21 MP6-8 was 0.25. Thus, we observed that the MP6-8 TS has a higher prediction accuracy across and within years when predicting the overall breeding program germplasm.
4.1 Factors affecting GS accuracy.
Several key factors influence genomic prediction accuracy, including 1) the size of the TS and its relatedness with the PS (Combs and Bernardo, 2013; Hickey et al., 2014), 2) the heritability and architecture of the trait (Hayes et al., 2010), 3) the marker density and the LD between the markers and the trait (Heffner et al., 2009; Meuwissen et al., 2001), and 4) the environmental similarities between the TS and the PS (Cuevas et al., 2016; Jarquín et al., 2017; Monteverde et al., 2018). By considering these factors, breeders and researchers can optimize the accuracy of genomic selection models, leading to more effective breeding programs.
Previous simulation studies in cattle and chicken (Johnsson et al., 2022), wheat (Taagen et al., 2022), rice, and mustard (Tourrette et al., 2019) have investigated the impact of recombination rates and LD on prediction accuracy. These studies concluded that a higher recombination rate can increase long-term genetic gain by increasing additive genetic variance but may reduce GS accuracy.
In this study, we aimed to examine the influence of haplotype sizes and LD within the TS on GS prediction accuracy. One of the primary challenges impeding empirical studies in the past was the scarcity of materials possessing the requisite characteristics related to recombination and LD while maintaining consistent control over all other relevant factors affecting GS accuracy. Thus, most of these previous attempts heavily relied on simulation rather than empirical data. This work contributes to a deeper understanding of the genetic parameters that influence GS in our context.
4.2 Suitability of the MP populations to explore the effect of haplotype size and LD on GS accuracy.
The MP2 and MP6-8 populations have specific characteristics that make them suitable for observing differences in prediction accuracy, primarily attributed to haplotype size. The populations 1) are of similar size, with MP2 and MP6-8 consisting of 420 and 324 genotypes, respectively; 2) share the same set of founder parents and have similar average MAF across populations (MP2 MAF=0.31 and MP6-8 MAF= 0.30); 3) have been characterized using the same marker set (LSU500); 4) demonstrate consistent heritability values (h2); 5) have been evaluated for the same traits in trials conducted at the same locations under similar environmental conditions, minimizing differences between TS and PS. Considering the above characteristics of the populations used in this study, the only notable difference of interest for this study is the difference in recombination rate.
4.3 Haplotype size, linkage disequilibrium, and prediction accuracy.
Haplotype blocks represent genomic regions characterized by a cluster of neighboring SNPs that tend to be inherited as a unit (Hess et al., 2017). Recombination events play a key role in shaping these blocks, fragmenting them into smaller units. The MP2 and MP6-8 populations used in this study were developed based on specific crossing strategies, increasing opportunities for recombination within the MP6-8 materials (Fig. 1). The increased recombination resulted in smaller haplotype blocks within the MP6-8 populations compared to the MP2 populations (Table 2). The similarity of the MP2 and MP6-8 materials for many key factors affecting GS accuracy presented a unique opportunity to study the effect of haplotype size on prediction accuracy empirically. Across all traits, a clear trend emerged confirming that smaller haplotype size in the TS resulted in higher prediction accuracy. This trend was observed with higher prediction accuracies when using MP6-8 as a TS to predict MP2, compared to using the MP2 as a TS to predict MP6-8. A similar result was observed when predicting the overall breeding program germplasm, with higher prediction accuracies when MP6-8 was used as a TS compared to MP2 as the TS.
The results of this study support similar findings reported in beef cattle and multiple crop datasets (Weber et al., 2023; Won et al., 2020). These studies suggested that as haplotype size increases, there is a greater opportunity for the true effect of underlying loci within the haplotype block to be masked. An example would be the presence of two linked loci where one locus has a positive effect and the other has a negative effect on a trait of interest. If these loci are in strong LD with each other, the overall haplotype effect could be neutral; however, if these loci were recombined, the true effect of each could be realized, potentially enhancing prediction accuracy.
4.4 Additive only versus Additive + Epistatic effects for GS.
The performance of a given phenotype is affected by genetic factors such as additive, dominance, and epistatic genetic effects. The genotypic value for quantitative traits is primarily attributed to additive effects of genes, with epistasis being a key component but of controversial significance (Mackay, 2014). GS methods mainly consider additive genetic effects, as the additive genetic effects affect many genes that can be accumulated and stably inherited and contribute significantly to quantitative trait variation, while non-additive genetic effects are the effects of gene interactions that can change by allele recombination and thus cannot be stably inherited (Liu et al., 2022; Meuwissen et al., 2001).
Additive genetic variance is the main source of variation contributing to selection response in breeding programs, as evidenced by heritability. Epistatic variation generally contributes less to the quantitative trait variation than additive genetic variance (Hem et al., 2021; Hill et al., 2008). Monnahan and Kelly (2015) demonstrated that epistasis significantly contributed to the total genetic variance of the floral traits in Mimulus guttatus. We hypothesized that haplotype size would directly affect the epistasis variance components, as more genetic loci would be independently segregating. To explore the effect of epistasis effect within a breeding program, we compared the heritability and prediction accuracy when using an A-only or AI model. We observed increased genetic heritability when epistatic effects were added to the model for all populations and traits (Table 3). Including epistasis in the model had a larger impact within the MP6-8 population (55.26 % increase) than within the MP2 population (2.9% increase). These results support our hypothesis that as haplotype size decreases, the epistasis effect increases.
Previous studies comparing different GS approaches considering epistasis have concluded that modeling epistasis does not improve prediction accuracy (Jiang and Reif, 2020; Muñoz et al., 2014; Su et al., 2012; Varona et al., 2018). Our study yielded similar results in which our GS prediction accuracy using CV did not increase when using A+I models compared to A-only models (Figure 3), and in multiple cases, the prediction accuracy was reduced. Onogi et al. (2021) and Su et al. (2012) had similar results in beef cattle and pigs, respectively. They concluded that additive-by-additive genetic interactions significantly contributed to genetic variance, but adding these effects did not influence the predictive accuracy. Notably, despite these insights, there remains a scarcity of empirical studies in this domain, highlighting the need for further research to advance the understanding of the role of epistatic effects in GS.
This study aimed to empirically investigate the impact of recombination and haplotype size on the accuracy of GS. Our findings demonstrate that increased recombination and reduced haplotype block sizes within the TS increase prediction accuracy. Recombination reduces haplotype block sizes, exposing genetic effects that larger haplotypes might otherwise conceal. This heightened resolution, in turn, bolsters the precision of genomic predictions for quantitative traits. Moreover, increased recombination amplifies non-additive genetic effects, as reflected in genetic variance components.
Nonetheless, the heightened presence of epistatic effects did not exert a significant influence on prediction accuracy. This work's uniqueness is the similarity of the materials and data used across all factors that influence GS prediction accuracy, with the only variation being in haplotype size. The practical significance of this work will be useful in designing optimal breeding schemes that consider the practical and logistical aspects of the breeding process, coupled with quantitative genetic theory and empirical validations for optimal TS design.
ACKNOWLEDGMENTS:
The author thank
AUTHOR CONTRIBUTIONS:
Maria G. Montiel: Conceptualization; Data curation; Formal analysis; Investigation; Writing – original draft. Jose Moreno-Amores: Data curation. Brijesh Angira: Data curation; Investigation; Writing – review&editing. Tommaso Cerioli: Data curation; Investigation. Kelly R. Robbins: Conceptualization; Methodology; Supervision; Writing – review & editing. Susan R. McCouch: Conceptualization; Investigation; Writing – review & editing. Adam N. Famoso: Conceptualization; Funding acquisition; Investigation; Methodology; Project administration; Supervision; Writing – review & editing. Roberto Fritsche-Neto: Conceptualization; Supervision; Writing – review & editing.
COMPETING INTEREST
The authors declare no conflict of interest.
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Tables 1 to 4 are available in the Supplementary Files section.
There is no duality of interest