Hétérosis et variétés hybrides en amélioration des plantes (Synthèses) (French Edition)

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African populations were also subject to inbreeding and selection for yield. Table S1 lists the number of A and B individual progeny tested per parental group in the two sites, as well as their status genotyped or not, present in only one site or in both.

Figures S1 and S2, for groups A and B, respectively with training individuals in blue and validation individuals in red. In Group A, the mean maximum genealogical coancestry [ 29 ] between each validation individual and the training individual f max V-T , ranged from 0 to 0. In Group B, f max V-T ranged from 0 to 0.

The validation sets were therefore closely related to the training set, which corresponds to the way GS would be applied in oil palm breeding to predict the breeding value of individuals of the same generation or of the following generation compared to the progeny tested individuals or the genetic values of crosses between them. They both have deep well drained soils developed over reworked Toba Tuffs haplic arenosols and dystric cambisol types in Site 1 and haplic acrisols type in Site 2.

The same standard cultural practices were used in both sites, and the same protocol was used for recording data. Table S1 summarizes the characteristics of the experimental designs in the two sites. The data from Site 1 are also described in detail in Cros et al. The total number of crosses in Site 2 was with data for bunch production for bunch quality but only were used as the validation set, the others being excluded because they were also present in Site 1 9 crosses or because their parents were not genotyped. All the data used were collected on tenera thin-shelled commercial type individuals.

The plant material belongs to the PalmElit www. PalmElit is a leading oil palm breeding and seed production company. Phenotypic data on hybrid individuals were available for three bunch production traits: Data from palms aged three to seven were used for bunch production traits. Data from palms aged five and six were used for bunch quality traits.

Between-site phenotypic correlations were estimated on the nine crosses common to both sites. The correlations were on average 0. Coefficient of variation CV and skewness in the two sites and between-site correlations for the reference adjusted for experimental design cross values of the seven traits studied. Correlations were computed over the nine crosses common to both sites. The reverse adapter contained the flowcell attachment region and the Hha I-compatible overhang sequence.

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Next, PCR equimolar amounts of amplification products from each sample in the well microtiter plate were bulked and applied to c-Bot Illumina bridge PCR followed by sequencing on Illumina HiSeq From the total number of good barcoded reads ,, out of ,, , the pipeline found , tags, aligned with Bowtie2 software. The tag mapping and the polymorphism calling identified , polymorphic sites. The data were further processed with VCFtools [ 34 ]. Indels and SNPs that were not biallelic were discarded. Data points with a sequencing depth of less than five were set to missing. Using a custom R script [ 35 ], the SNPs appearing as outliers in terms of mean depth i.

This resulted in 19, SNPs. The molecular dataset was split into two, one for Group A and the other for Group B. The SNPs that mapped on the unassembled part of the genome were discarded, as the imputation of sporadic missing data required known positions. Mendelian segregation between parents and offspring was checked and the inconsistent data points were set to missing. The depth per data point was on average The mean depth per SNP was The mean minor allele frequency MAF was 0.

The percentage of missing data was on average Molecular coancestries between genotyped individuals were calculated according to Lynch [ 38 ] and Li et al. For each validation individual, the maximum coancestry with the training individuals was computed, and the mean value over all the validation individuals was calculated. The proportion of dominance variance between crosses over the total genetic variance between crosses was calculated for Site 2 from the TBLUP model including genealogical information.

The additive genomic relationship matrices G. In order to investigate the usefulness of estimating the dominance effects SCAs , the predicted cross values where obtained with or without SCA, i.

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.

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. For the remainder of the study, we consequently only used the molecular dataset imputed with the pedigree. Prediction accuracies of cross values of the genomic model GBLUP according to the imputation method and trait concerned. All SNPs were used for predictions.

Background

Values are means over six sets of training crosses. The prediction accuracies of the cross values were the same whether or not the predicted cross values included the SCA specific combining ability term. The proportion of SCA variance between crosses in total genetic variance between crosses reached a maximum for FB For the remainder of the study, we only present the results obtained for cross values prediction accuracies when the SCA term was not used in the prediction.

When SNPs were used, the prediction accuracy of the cross values ranged from very low to intermediate 0. The variation in GS prediction accuracy for intermediate marker densities indicated that some SNP subsets enabled higher prediction accuracy than when all the markers were used not shown. With to SNPs, the increase reached In the other traits, this method of SNP sampling led to prediction accuracies with to SNPs similar to random sampling. Percentage of missing molecular data in group a left panel and group b right panel according to the method used to sample SNPs random sampling, solid black line, or selecting SNPs with the lowest percentage of missing data, red line.

Vertical bars are standard deviations. Using all SNPs, they ranged from 0. The prediction accuracies of the cross values were usually closer to the GCA prediction accuracies obtained in Group B than in Group A. As expected, the magnitude of the increase was affected by the number of A and B individuals subjected to preselection, although the number of B candidates had a greater effect than the number of A candidates. Thus, with a fixed number of A candidates subjected to genomic preselection, increasing the number of B candidates from to increased the FFB from 2.

Increase in production of fresh fruit bunches FFB in the crosses selected in Site 2 progeny tests if preliminary genomic preselection had been applied in the parental populations. The increase in FFB is expressed as a percentage of the FFB performance of the hybrids selected using the current method with no genomic preselection.

Axes show the number of A and B selection candidates subjected to genomic preselection. Values are means over 20, replicates. We found that a reciprocal recurrent genomic selection GS breeding scheme can be implemented in oil palm, applying a genomic preselection among parental populations to identify individuals with highest genetic value in hybrid crosses, before progeny testing them to make the final selection on all traits.

Genomic preselection increases the genetic gain compared to the current RRS breeding scheme thanks to higher selection intensity. GS can be used for several key components of palm oil yield, in particular bunch production and the percentage of oil in the mesocarp. The efficiency of the genomic preselection observed for several traits resulted from two facts. Second, the GS prediction accuracies could be significantly higher than the prediction accuracies of the pedigree-based control model PBLUP , indicating that GS was able to capture genetic differences within full-sib families of parents i.

In this case, GS enables identification of the best individuals of the best families, as currently done among the progeny tested individuals. According to the results of the simulation, the extra gain in FFB of selected hybrids obtained by using genomic preselection reached, when for instance A candidates and B candidates were genotyped, Considering that most oil palm breeding companies are also large scale palm oil producers with tens of thousands of hectares or more, and given the GBS price per sample, the associated extra genotyping costs would be quickly recovered by the increase in annual income per hectare.

The question of the additional gain that would be obtained with conventional RRS by using the extra cost of GS to progeny test more A and B parents remains, but given the much higher costs of progeny tests compared to the GBS price, the increase in selection intensity would likely be negligible compared to what can be achieved with GS. This study allowed us to extend the promising empirical results of Cros et al. The prediction accuracies obtained here are therefore more relevant for the practical implementation of the method than the previous prediction accuracies, and as a result, it was possible to use them to obtain a realistic first empirical estimate of the additional genetic gain that could be obtained with GS in oil palm.

The additional gain obtained here thanks to genomic preselection compared to the conventional method is close to the values obtained in hybrid cereals by Marulanda et al. In their case, achieving more benefits from GS required adopting a genomic breeding scheme with fewer stages of phenotypic selection in order to reduce the duration of the breeding cycle. Developing an efficient breeding scheme with a reduced generation interval thanks to GS is also desirable in oil palm.

Indeed, the genomic preselection suggested here is not the optimal use of the possibilities offered by GS for this species, i. We conclude that for now, the use of GS should be limited to preselection for some traits before progeny tests because GS did not perform sufficiently well for all the traits evaluated during the progeny tests. Indeed, the fact that a control model using pedigrees instead of marker data PBLUP gave prediction accuracies equal or even higher than GS for some traits indicated that, for these traits, GS was not able to take the Mendelian segregation into account.

Hence, it does not enable selection within full-sib families of parents, while this is the core of oil palm breeding. Other studies are therefore required to increase GS prediction accuracies for all yield components, which would enable its optimal use. In particular, this could be done by increasing the size of the training set.

One efficient way to reach this goal would be to use a training set aggregating data from multiple breeding cycles, as demonstrated empirically in hybrid rye by Auinger et al. Also, because the parents of the oil palm hybrid crosses are heterozygotes, another tempting approach would be to genotype hybrid individuals in addition to their parents, as suggested by Cros et al. In addition to increasing the size of the training set, optimizing its design is a further way to achieve higher GS accuracy. Several approaches have been developed [ 53 , 54 , 55 ], in particular for hybrid crops [ 56 ], which should now be investigated in detail in oil palm.

This indicated that, for these traits, the available dataset was not optimal for GS validation. Indeed, it is easier to show the GBLUP ability to account for the Mendelian segregation term when the phenotypic variability is not structured by differences between families. With such a structure, the ability of GBLUP to account for the Mendelian segregation term would be better evaluated by measuring prediction accuracy in large full-sib families of A and B parents.

To this end, suitable experiments should be conducted by progeny testing a significant number of A or B individuals of several full-sib families. Here we considered rather similar environments, while in real situations the marketing area of the best crosses could possibly involve more contrasted environments. In that case, particularly if genotype by environment interactions exist, it would be necessary to use models combining phenotypic data from various environments, genomic data and environmental covariables see for instance Bustos-Korts et al.

However, this is an area that requires further methodological investigation, as well as access to multi-environment oil palm data that are currently not available. However, with a larger or more diverse training set, it might be necessary to use a larger number of SNPs than the number that corresponded to plateaus in our study.

This would likely not be a problem with GBS, as it would yield more markers if applied to a larger or more diverse population. In oil palm, GBS appears to be an efficient genotyping approach for genetics studies in general, as it has already been successfully used for mapping and QTL detection [ 25 ].

Indeed, the SSRs used by Marchal et al. Second, Marchal et al. As a consequence, in Marchal et al. We found that using the pedigrees when imputing the missing SNP data enabled an increase in prediction accuracy. The observed variation in GBLUP predictive ability between SNP samples led us to apply several filtering strategies, in addition to the method minimizing the percentage of missing data presented here: We do not present the results here because these methods had inconsistent or detrimental effects on prediction accuracy.

One possible explanation is that our population was more complex, with a more unbalanced contribution of the population founders, which could have led to the existence of low frequency alleles but that were representative of some families or individuals, and therefore that were useful to keep in the dataset. The fact that filtering SNPs based on the percentage of missing data was only efficient for PF suggested a problem with the imputation of markers located in genome regions of importance for this trait and that had a high percentage of missing data. An alternative solution to these imputation and filtering problems would be to use a SNP array instead of GBS, as the percentage of missing data in SNP arrays is very low.

This could be done with already available arrays [ 19 , 60 , 61 ], or by developing a new array more specific to the populations used here. In addition to these SNP filtering strategies, we also used several methods to compute the genomic coancestry matrices G , to check whether they could improve GS accuracies: These results are not presented here as, with our data, they did not improve prediction accuracies. According to their pedigrees, the individuals used for validation were more related to the training individuals in Group B than in Group A, but the SNPs showed they were actually related to the same degree.

This likely resulted from the fact that the pedigree of Group A did not go back to the founders, whereas it did or almost did for Group B, and because SNPs are able to capture these relationships even when they do not appear in the pedigrees due to their incompleteness. This was already observed in our previous study [ 17 ] using SSR markers. Our results show that the phenotypic distribution of the traits affected GS accuracy.

Both studies therefore are partly in agreement, because in our study, GS accuracy only appeared to be related to phenotypic variation and not to the skewness of the distribution. Indeed, the two traits with the lowest GS cross value prediction accuracies, FB and PF, also had low phenotypic variation. Regarding skewness, FB had the least skewed distribution, and ABW had the most skewed distribution but high GS accuracy for cross value.

Therefore, other factors, such as the genetic architecture of the traits number of genes, distribution of their effects, etc. As a consequence, the main driver of the prediction accuracy of cross values was the prediction accuracy of GCA in Group B. Likewise, increasing the number of B candidates was a more efficient way to increase the FFB of hybrid crosses than increasing the number of A candidates.

The fact that adding an SCA term to the parental GCAs when calculating the prediction accuracies of cross values did not improve the results was likely the consequence of an insufficient proportion of dominance variance in total genetic variance. Indeed, some traits e. For the other traits, even if the proportion of SCA variance in the total variance could be much higher, it might still not be high enough to increase prediction accuracy when SCA terms are predicted in addition to GCAs.

Indeed, Denis and Bouvet [ 66 ] showed in simulations that including dominance effects in the GS model was only advantageous when dominance effects were preponderant dominance to additive variance ratio of 1. Similar results were obtained empirically in apple [ 67 ] and rice [ 68 ], where dominance effects did not improve prediction accuracies. GS prediction accuracies reached intermediate to high values for some key yield components 0. This enabled genomic preselection in the parental populations prior to progeny tests, which increased selection intensity. Preselection for key yield components using GBS is the first possible application of GS in oil palm for which empirical evidence of efficiency is available.

However, more benefits are expected from GS in this species. Indeed, the genomic preselection suggested here would not make it possible to increase selection intensity for all traits, and progeny tests would still be required, making it impossible to reduce the generation interval. Further research is therefore needed to enhance GS prediction accuracies for all yield components. In particular, further studies are necessary to enlarge and optimize the training set and to model genotype by environment interactions.

This would enable the optimal use of GS, which would revolutionize oil palm breeding. GS clearly has a major role to play in meeting the huge increase in the demand for palm oil expected in the coming decades, in a sustainable way, i. Characteristics of the experimental designs used in the two sites. Distribution of progeny tested individuals among parental groups and breeding populations. The figures below the chromosomes indicate their number of SNPs.

The funding body took part in planning and installing the field trials and in the collection of the phenotypic data. It did not execute any influence on the genomic selection analyzes described in this manuscript. The datasets used during the current study are available from the corresponding author on reasonable request and with permission of PalmElit.

DC analyzed the data and wrote the paper. VP participated in the genotyping work. All authors read and approved the final manuscript. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. National Center for Biotechnology Information , U. Published online Nov 2. This distribution was defined assuming a correlation of The breeding additive value for each individual and the additive variance were defined according to the quantitative genetic model of Falconer and Mackay [ 4 ].

As we assumed purely additive genetic determinism, they were equal to twice the interpopulation additive variances. The residual correlation between BW and BN was assumed to be zero. The phenotype was assumed to be the sum of the breeding value, environmental effects and mean value of the population. Initially, the mean values of the population for BW kg and BN traits were set at 15 in order to avoid negative values for bunch production and to obtain realistic phenotypic values for BW and BN in the simulated initial breeding populations.

We proceeded by trial and error to set the simulation parameters that were not known from the literature or from real data e. The equilibrium base population was randomly divided into two populations A and B of individuals each. For generations, A and B populations evolved independently and their sizes remained constant. Mating was random without selfing. Each population had a different selection regime so they had divergent evolution for the two traits: The parents of individuals in a given generation were sampled in the previous generation, where the probability for each individual to be chosen as parent was proportional to its phenotypic value.

After these first generations, four individuals were taken at random in population A to simulate the bottleneck event at the origin of the actual Deli population, which originated from four oil palms planted in Indonesia in This was followed by three generations of random mating without selfing with 25 individuals per generation, and by six generations with an increasing number of individuals 50, 50, 60, 75, and individuals per generation. Mass selection was applied on bunch production during these last six generations.

For mass selection, bunch production of each individual was computed as the product between BN and BW phenotypes. This was followed by two generations with an increasing number of individuals 75, and mass selection on bunch production. Here, EBV were simulated as values correlated with the true breeding values, with a correlation of 0.

In each parental population, we selected the top 20 individuals giving crosses with highest expected bunch production. In the last generation generation 0 in Fig. They are hereafter referred to as initial breeding populations. The simulation process was repeated several times from the allocation of QTL to the generation of initial breeding populations. This calibration was done on: The real values of the F st , interpopulation additive variances and genetic correlations were obtained from the dataset described in Cros et al.

They were genotyped with SSR markers. The Weir and Cockerham estimate of F st was computed using the Hierfstat R package [ 18 ] in the simulated data, and with the diveRsity R package [ 19 ] in the real data. The actual genetic correlation between BN and BW and additive variances for BN and BW in the parental populations were computed from the hybrid phenotypic values using a mixed model analysis.

For LD, the absolute values were affected by the marker type, so we only used the profile of LD curves to compare the simulated and real populations. The mating design for progeny tests was an incomplete factorial design with crosses i. The chosen numbers of progeny-tested individuals and crosses corresponded to what is done in actual oil palm breeding programs.

The model was of the following form:. The number of crosses was the same for all individuals. In the simulations, we studied the effects of reducing the generation interval and increasing the selection intensity on the RRGS performance. First, a reduction in the generation interval was obtained when applying RRGS in the generation s following the progeny-tested individuals.

In this case, the selection candidates were not progeny tested but only genotyped; and they were selected based on their sole genotype and reproduced once they were sexually mature. We varied the progeny-test frequency to assess the potential of RRGS when used to reduce the generation interval. 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.

As different within-population crosses could be made, the individuals were obtained by simulating one or two individuals per possible cross, up to a total of In the generations with progeny tests and when using candidates, individuals were randomly chosen to be progeny tested among the and the selection was made among them and their non-progeny-tested sibs. From these molecular data, G was computed according to Van Raden [ 2 ] and Habier et al. The genotyped hybrid individuals were randomly sampled among the 13, existing hybrids, taking the same number of individuals per cross i.

As the progeny tests included 13, phenotyped hybrids, the non-genotyped hybrids were also included in the model, as their phenotypic values contributed to estimate the GEBV of their parents. For this purpose, we used the single-step approach of Legarra et al. We did not consider genotyping more than hybrid individuals or using more than candidate individuals per population for computational reasons. We distinguished between two types of factors: The effects of biological factors and the interaction between biological and technical factors are crucial, because the genetic architecture is unknown in actual situations.

The breeder has to design a breeding program where technical factors will give the highest annual selection response, regardless of the unknown genetic architecture of the traits. Each of these combinations had five replicates, which had different simulated initial breeding populations. At the end of the simulation i. Analyses of variance ANOVA were performed to study the effect of the different technical and biological factors and their interactions on the selection response, as well as on the genetic parameters in the parental populations selection accuracy and additive variance for BW and BN, genetic correlation between BW and BN, inbreeding.

The annual response is expressed in percentage of hybrid production in the initial generation generation 0 per year. Breeding scheme includes the breeding strategy RRS: The selection accuracy with RRS was very high and remained constant over generations, i. For RRGS, we first considered its simplest implementation i. Secondly, we assessed how the selection accuracy was affected by the absence of progeny tests. The accuracy of the progeny-tested individuals was much higher than that of non-progeny-tested individuals of the following s generation s , which fell to 0. The accuracy of the progeny-tested individuals was also higher than that of their non-progeny-tested sibs, which was 0.

This can be seen when comparing levels of equivalent combinations between Fig. Accuracy of reciprocal recurrent genomic selection RRGS for bunch number in the Deli population according to years and the RRGS breeding scheme with a and b selection candidates. Means are calculated over 45 values. The additive variance decreased with generations, which is a well-known effect of selection and genetic drift. The major factor affecting the cumulative decrease in additive variance was the number of candidates, with resulting in a more rapid decrease in variance than with candidates see Fig.

A similar result was obtained for both populations and traits. This occurred as the number of selected individuals was kept constant, so increasing the number of candidates led to the selection of individuals with a higher average value but lower genetic variability. This indicated that the number of candidates was the major factor affecting the decrease in variation. Additive variance for bunch number according to years and the reciprocal recurrent genomic selection RRGS breeding scheme in Deli with a and b selection candidates. The number of QTL that were assumed in the model also had a role regarding the decrease in additive variance.

This occurred as the simulation was designed to have the same additive variances in generation 0 regardless of the number of QTL. Consequently, when the QTL were fewer they also had stronger effects and were correspondingly under higher selection pressure up to their fixation. Therefore, the fewer the number of QTL, the stronger the effect of selection was in depleting the additive variance. The percentage of pleiotropic QTL was the most important factor of the study. The number of QTL also had a strong effect. The selection response increased when the percentage of pleiotropic QTL decreased and when the number of QTL increased.

The cumulative response was This resulted from the fact that the genetic progress potential depended mostly on the fixation of favorable alleles at QTL controlling either BN or BW, rather than at the pleiotropic QTL, as they had antagonistic effects on both traits. Similarly, the genetic progress potential was higher when the total number of QTL controlling each trait increased.

Their effects are detailed in the following paragraphs. Therefore, obtaining a higher selection response with RRGS compared to RRS could not be achieved without modifying the breeding scheme in order to reduce the generation interval or to increase the selection intensity. In this case, decreasing the progeny-test frequency led to a lower cumulative selection response, i. With generations without progeny tests, the selection accuracy was reduced and consequently the cumulative selection response decreased.

An opposite effect was noted in the annual response, i. With progeny tests performed every four generations, the generation interval decreased by Thirdly, regarding the RRGS gain, we studied the effect of an increase in selection intensity, which was obtained by increasing the number of candidates, as the number of selected individuals was constant.

With candidates, the best We also found that the number of candidates significantly interacted with the percentage of pleiotropic QTL and the number of QTL on the selection response, although these interactions had less impact than the previously mentioned factors. This was not surprising as, with the largest numbers of non-pleiotropic QTL per trait either due to a high number of QTL or to a low percentage of pleiotropic QTL , selection candidates were not enough to capture all of the existing additive variation.

In this case, using candidates led to a higher selection response. By contrast, with a smaller number of non-pleiotropic QTL, candidates were enough to capture all of the additive variation and an increase in the number of candidates did not markedly increase the selection response. The coefficient of variation CV for the annual selection response of that best scheme reached 0.

The three following breeding schemes in the ranking of gain had similar levels of performance and CV for the annual response: Variation in annual selection response associated with each breeding scheme. The breeding scheme includes the breeding strategy RRS: The filled dots represent the means, calculated over 45 values. As expected, inbreeding increased with the generation turnover see Fig. With candidates, they all belonged to different full-sib families due to the method used to mate the selected individuals.

However, the sets of candidates mostly consisted of pairs of full-sibs, which increased the probability of having full-sib individuals among the selected individuals. Inbreeding according to years and the reciprocal recurrent genomic selection RRGS breeding scheme in the Deli population using a and b candidates.

Inbreeding is expressed as a percentage of inbreeding in the parental populations in the initial generation generation 0 per year. Bars indicate standard deviations. The magnitude of the genetic correlation between BW and BN increased markedly in the generations in which progeny tests were conducted Fig. In absolute value, the increase in the generations with progeny tests was greater than the decrease in the generations without progeny tests, so the correlation thus tended to increase over the four generations, except in the case where progeny tests were only performed in the first generation.

Genetic correlation between BN and BW in the Deli population according to years and the reciprocal recurrent genomic selection RRGS breeding scheme with a selection candidates and b candidates. 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.

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. 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.

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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.

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. 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 ]. 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. 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.

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