The validation crosses were initially divided into six random sets of equal size, and for each validation set, the prediction accuracy for cross values was obtained as the Pearson correlation between the reference and the predicted cross values. GCA prediction accuracy was obtained as the Pearson correlation between the reference and the predicted GCAs on the 67 Group A individuals and 42 B available for validation, with no replicates due to small population sizes.
In order to investigate the effect of taking pedigree information into account when imputing the missing molecular data with BEAGLE 4. To investigate the effect of marker density on prediction accuracy, we varied the number of SNPs used to construct the genomic matrices of GBLUP from SNPs to using the same number simultaneously in both parental groups.
For a given level of SNP density, we made 26 replicates of random samples of SNPs, using the same replicates for all the traits. In order to study whether filtering SNPs based on their percentage of missing data affected prediction accuracies, the variation in the number of SNPs was also implemented using the SNPs with the lowest percentage of missing data, with three replicates of random SNPs with same percentage of missing data for each level of numbers of SNP. An ANOVA similar to the one explained above was performed to assess whether the effect of SNP filtering minimized the percentage of missing data on the prediction accuracies of the cross values.
Secondly, to study the effect of increasing the selection intensity, we also applied RRGS to a number of selection candidates per population larger than the number of progeny-tested individuals per population. Correlations were computed over the nine crosses common to both sites. As a consequence, in Marchal et al. In this study we considered that heterosis in bunch production was a consequence of the multiplicative interaction between the negatively correlated bunch number and bunch weight, both assumed here to have complete additive genetic determinism.
Marker alleles were simulated from the start and QTL for bunch weight and bunch number were assigned after the first generations of random mating. The variance-covariance matrices were:. This was obtained as the mean selection accuracy of the 67 A and 42 B individuals, computed from the prediction error variances as described in Marchal et al.
For RRS, the A individuals and B included in the progeny tests were randomly chosen from the populations of candidates. For RRS with genomic preselection, the A individuals and B individuals included in the progeny tests were those with the highest genomic estimated GCA among each population of candidates.
To investigate how the number of A and B candidates subjected to genomic preselection affected the performance of the selected hybrids, we first considered candidates per parental population and then increased the number from to , with a step of For each level of number of candidates, 20, replicates were made by generating random populations of candidates for each replicate. All analyses were conducted using R software version 3. Molecular coancestries between training and validation individuals were similar in Group A and Group B, the mean value of the maximum molecular coancestries between validation individuals and training individuals being 0.
Using the pedigrees when imputing the missing SNP data increased the prediction accuracy of cross values for two traits, OP oil-to-pulp ratio and FFB fresh fruit bunches , but did not affect the other traits see Fig. For OP, the prediction accuracy increased by 4. In our oil palm case study, RRGS was superior to traditional RRS as it allowed accurate selection of individuals without progeny tests. It led to a significant increase in the annual selection response, through generations of selection based on markers alone and, to a lesser extent, through an increase in the selection intensity.
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In our oil palm example, the annual selection response of this RRGS best strategy reached 0. Therefore, it seemed that genotyping more individuals would have been useless here. However, the number of hybrids to genotype should be dependent on the heterozygosity in the parental populations. With a higher level of heterozygosity in the parental population, the phenotypic variation within crosses would likely increase, making more relevant hybrid genotyping of hybrids in order to capture this variation.
Aspects other than just the expected annual selection response need to be taken into account when choosing an optimal breeding scheme. Furthermore, the efficiency cost and operational complexity must be considered. Other breeding schemes could thus offer interesting alternatives, with good compromises between costs, operational complexity, expected annual selection response, risk regarding this expectation and evolution of inbreeding. Indeed, it was among the best four breeding schemes in terms of annual selection response 0.
The relative importance of the decrease in generation interval and the increase in selection intensity depends on the characteristics of the species.
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This makes the species an excellent candidate for the implementation of early genomic evaluation, with RRGS having a high potential compared to RRS. By contrast, oil palm breeding populations have a quite narrow genetic base, with effective sizes under 10 [ 27 ], and this creates relatively small additive variances, therefore reducing the interest of increasing the number of candidates.
Our results confirmed the usefulness of GS for oil palm, in line with the simulation results of Wong and Bernardo [ 14 ]. However, we extended their results to a more general situation, closer to actual oil palm breeding program conditions, by applying GS to complex breeding populations and by considering two antagonistic traits, i. BN and ABW, which are crucial in oil palm breeding. The accuracies we obtained in this previous study when applying GS to full-sibs of the training individuals could be compared with the accuracies we obtained here on the full-sibs of the progeny-tested individuals.
We previously obtained mean accuracies of 0. This was likely due to the fact that our previous training population was smaller than that used here The consistency between the empirical results and our present simulations suggests that the actual genetic architecture for BN and BW could be close to the average scenario of our simulations, i. This would result in a high computation time that would be hard to manage in a simulation study due to the many replicates, and memory problems.
However, this should not be a problem here as the mixed models were used to predict GEBV, not to estimate genetic parameters. According to these authors, this occurred because the Mendelian sampling terms i.
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We assumed the different trend existing in our study was related to the drop in accuracy observed for non-progeny-tested individuals, which occurred because the calibration of the GS model was based on the progeny tests of only individuals per population. Consequently, our estimates of Mendelian sampling terms were likely not as accurate as those obtained in animal species.
Good genetic variability management is necessary to avoid inbreeding depression in parental populations, which has been reported in oil palm [ 10 , 29 , 30 ], and to maintain the genetic progress potential over the long term. Therefore, the RRGS breeding schemes we presented here should be combined with methods to explicitly manage genetic diversity and inbreeding.
The simplest inbreeding management method is to increase the number of selected individuals, which would slow down the increase in inbreeding, possibly with only a small reduction in selection response [ 28 ].
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Another option that does not necessarily lead to gain losses is optimal contribution selection [ 32 ] and its extension in the GS context [ 33 ]. This involves the use of the genetic value of individuals and their relationships with other individuals to determine their contribution to the following generation, in order to maximize genetic gain at a desired inbreeding rate under the assumption of random mating among selections. A step further is mate selection [ 34 , 35 ], where the optimum contribution is applied to mates among all candidates, so that selection and mating are simultaneously handled for improved management of inbreeding beyond what is expected by random mating.
Mate selection optimizes the number of parents to be selected, the actual matings between them and the distribution of the contribution in the offspring of these mates, in order to maximize the expected selection response in the following generation while respecting a restriction on the expected increase in inbreeding. Here we studied a GS approach to select individuals within two parental populations for their crossbred performance, as in several animal studies [ 6 , 36 — 38 ] and in maize [ 39 ].
This multiplicative interaction between complementary component differences in the parents is a heterosis model without dominance, but heterosis in a multiplicative trait can also be due to the multiplicative interaction of component dominance [ 7 ]. In this case, dominance in the component traits generates heterosis in the complex trait, to a greater extent than the dominance in the components, due to the multiplicative nature of the complex trait. Here we did not study the effect of this type of genetic determinism or a combination of the two types. This would require further investigation, which could be done by modifying the script used for our simulations and including dominance effects in the GS models see for instance Su et al.
Presumably their result applied in the case where selection was highly accurate, such as when based on progeny tests, which was not the case here when selection was made on markers alone using a GS model calibrated with a small training set. Reciprocal recurrent genomic selection RRGS appeared as a valuable method to achieve a long-term increase in the performance for a trait showing heterosis due to the multiplicative interaction between additive and negatively correlated components. In our oil palm case study, RRGS was superior to traditional RRS in terms of annual selection response as it could decrease the generation interval and increase the selection intensity.
With genotyped hybrids, calibration every four generations and candidates per generation and population, selection response of RRGS was RRGS without genotyping hybrid individuals, with calibration every two generations and candidates was a relevant alternative, as a good compromise between the annual response, risk around the expected response, increased inbreeding and cost. DC carried out the simulations, performed the statistical analysis of the results and drafted the manuscript.
LS and JMB contributed to the writing of the paper. MD participated in the statistical analysis. All authors read and approved the final manuscript. National Center for Biotechnology Information , U. Abstract Background To study the potential of genomic selection for heterosis resulting from multiplicative interactions between additive and antagonistic components, we focused on oil palm, where bunch production is the product of bunch weight and bunch number.
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Results We concluded that RRGS could increase the annual selection response compared to RRS by decreasing the generation interval and by increasing the selection intensity. Conclusions RRGS appeared as a valuable method to achieve a long-term increase in the performance for a trait showing heterosis due to the multiplicative interaction between additive and negatively correlated components, such as oil palm bunch production. Background Genomic selection GS [ 1 ] is the state-of-the-art method of marker-assisted selection for complex traits.
senjouin-kikishiro.com/images/xevewix/654.php Methods Simulation overview The overall simulation process is summarized in Fig. Open in a separate window. Simulation of the equilibrium base population We simulated a population over discrete generations with a constant size of individuals having an equal contribution to the following generation and reproducing by random mating with the exclusion of selfing.
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The model was of the following form: Analysis of results We distinguished between two types of factors: Table 3 Ranking of breeding schemes according to their mean annual response. Selection accuracy The selection accuracy with RRS was very high and remained constant over generations, i. Additive variance The additive variance decreased with generations, which is a well-known effect of selection and genetic drift. Inbreeding As expected, inbreeding increased with the generation turnover see Fig.
Discussion We showed that reciprocal recurrent genomic selection RRGS was a valuable method to achieve a long-term increase in the performance for a trait showing heterosis due to the multiplicative interaction between additive and negatively correlated components. Genomic selection model Here we studied a GS approach to select individuals within two parental populations for their crossbred performance, as in several animal studies [ 6 , 36 — 38 ] and in maize [ 39 ].
Conclusions Reciprocal recurrent genomic selection RRGS appeared as a valuable method to achieve a long-term increase in the performance for a trait showing heterosis due to the multiplicative interaction between additive and negatively correlated components. Footnotes Competing interests The authors declare that they have no competing interests. Contributor Information David Cros, Email: Prediction of total genetic value using genome-wide dense marker maps.
Genomic measures of relationship and inbreeding.
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