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Background Recurrent selection is a foundational breeding method for quantitative trait improvement. It typically features rapid breeding cycles that can lead to high rates of genetic gain. Usually, generations are discrete in recurrent selection, which means that breeding candidates are evaluated and considered for selection for only one cycle. Alternately, generations can overlap, with breeding candidates considered for selection as parents for multiple cycles. With recurrent genomic selection but not phenotypic selection, candidates can be re-evaluated by using genomic estimated breeding values without additional phenotyping of the candidates themselves. Therefore, it may be that candidates with true high breeding values discarded in one cycle due to underestimation of breeding value could be identified and selected in subsequent cycles. The consequences of allowing generations to overlap in recurrent selection are unknown. We assessed whether maintaining overlapping and discrete generations led to differences in genetic gain for phenotypic, genomic truncation, and genomic optimum contribution recurrent selection by stochastic simulation. Results With phenotypic selection, overlapping generations led to decreased genetic gain compared to discrete generations due to increased selection error bias. Selected individuals, which were in the upper tail of the distribution of phenotypic values, tended to also have high absolute error relative to their true breeding value compared to the overall population. Without repeated phenotyping, these individuals erroneously believed to have high value were repeatedly selected across cycles, leading to decreased genetic gain. With genomic truncation selection, overlapping and discrete generations performed similarly as updating breeding values precluded repeatedly selecting individuals with inaccurately high estimates of breeding values in subsequent cycles. Overlapping generations did not outperform discrete generations in the presence of a positive genetic trend with genomic truncation selection, as individuals from previous breeding cycles typically had truly lower breeding values than candidates from the current generation. With genomic optimum contribution selection, overlapping and discrete generations performed similarly, but overlapping generations slightly outperformed discrete generations in the long term if the targeted inbreeding rate was extremely low. Conclusion Maintaining discrete generations in recurrent phenotypic selection leads to increased genetic gain, especially at low heritabilities, by preventing selection error bias. With genomic truncation selection and genomic optimum contribution selection, genetic gain does not differ between discrete and overlapping generations assuming non-genetic effects are not present. Overlapping generations may increase genetic gain in the long term with very low targeted rates of inbreeding in genomic optimum contribution selection.

Key messageReciprocal recurrent selection sometimes increases genetic gain per unit cost in clonal diploids with heterosis due to dominance, but it typically does not benefit autopolyploids.Breeding can change the dominance as well as additive genetic value of populations, thus utilizing heterosis. A common hybrid breeding strategy is reciprocal recurrent selection (RRS), in which parents of hybrids are typically recycled within pools based on general combining ability. However, the relative performances of RRS and other breeding strategies have not been thoroughly compared. RRS can have relatively increased costs and longer cycle lengths, but these are sometimes outweighed by its ability to harness heterosis due to dominance. Here, we used stochastic simulation to compare genetic gain per unit cost of RRS, terminal crossing, recurrent selection on breeding value, and recurrent selection on cross performance considering different amounts of population heterosis due to dominance, relative cycle lengths, time horizons, estimation methods, selection intensities, and ploidy levels. In diploids with phenotypic selection at high intensity, whether RRS was the optimal breeding strategy depended on the initial population heterosis. However, in diploids with rapid-cycling genomic selection at high intensity, RRS was the optimal breeding strategy after 50 years over almost all amounts of initial population heterosis under the study assumptions. Diploid RRS required more population heterosis to outperform other strategies as its relative cycle length increased and as selection intensity and time horizon decreased. The optimal strategy depended on selection intensity, a proxy for inbreeding rate. Use of diploid fully inbred parents vs. outbred parents with RRS typically did not affect genetic gain. In autopolyploids, RRS typically did not outperform one-pool strategies regardless of the initial population heterosis.

The undomesticated rice relative Oryza longistaminata is a valuable genetic resource for the improvement of the domesticated Asian rice, Oryza sativa . To facilitate the conservation, management, and use of O. longistaminata germplasm, we sought to quantify the population structure and diversity of this species across its geographic range, which includes most of sub-Saharan Africa, and to determine phylogenetic relationships to other AA-genome species of rice present in Africa, including the prevalence of interspecific hybridization between O. longistaminata and O. sativa . Though past plant breeding efforts to introgress genes from O. longistaminata have improved biotic stress resistance, ratooning ability, and yield in O. sativa , progress has been limited by substantial breeding barriers. Nevertheless, despite the strong breeding barriers observed by plant breeders who have attempted this interspecific cross, there have been multiple reports of spontaneous hybrids of O. sativa and O. longistaminata (aka “Obake”) obtained from natural populations in Africa. However, the frequency and extent of such natural introgressions and their effect on the evolution of O. longistaminata had not been previously investigated. We studied 190 O. longistaminata accessions, primarily from the International Rice Research Institute genebank collection, along with 309 O. sativa , 25 Oryza barthii , and 83 Oryza glaberrima control outgroups, and 17 control interspecific O. sativa / O. longistaminata hybrids. We analyzed the materials using 178,651 single-nucleotide polymorphisms (SNPs) and seven plastid microsatellite markers. This study identified three genetic subpopulations of O. longistaminata , which correspond geographically to Northwestern Africa, Pan-Africa, and Southern Africa. We confirmed that O. longistaminata is, perhaps counterintuitively, more closely related to the Asian species, O. sativa , than the African species O. barthii and O. glaberrima . We identified 19 recent spontaneous interspecific hybrid individuals between O. sativa and O. longistaminata in the germplasm sampled. Notably, the recent introgression between O. sativa and O. longistaminata has been bidirectional. Moreover, low levels of O. sativa alleles admixed in many predominantly O. longistaminata accessions suggest that introgression also occurred in the distant past, but only in Southern Africa.

Background: Recurrent selection is a foundational breeding method for quantitative trait improvement. It typically features rapid breeding cycles that can lead to high rates of genetic gain. In recurrent phenotypic selection, generations do not overlap, which means that breeding candidates are evaluated and considered for selection for only one cycle. With recurrent genomic selection, candidates can be evaluated based on genomic estimated breeding values indefinitely, therefore facilitating overlapping generations. Candidates with true high breeding values that were discarded in one cycle due to underestimation of breeding value could be identified and selected in subsequent cycles. The consequences of allowing generations to overlap in recurrent selection are unknown. We assessed whether maintaining overlapping and discrete generations led to differences in genetic gain for phenotypic, genomic truncation, and genomic optimum contribution recurrent selection by simulation of traits with various heritabilities and genetic architectures across fifty breeding cycles. We also assessed differences of overlapping and discrete generations in a conventional breeding scheme with multiple stages and cohorts. Results: With phenotypic selection, overlapping generations led to decreased genetic gain compared to discrete generations due to increased selection error bias. Selected individuals, which were in the upper tail of the distribution of phenotypic values, tended to also have high absolute error relative to their true breeding value compared to the overall population. Without repeated phenotyping, these erroneously outlying individuals were repeatedly selected across cycles, leading to decreased genetic gain. With genomic truncation selection, overlapping and discrete generations performed similarly as updating breeding values precluded repeatedly selecting individuals with inaccurately high estimates of breeding values in subsequent cycles. Overlapping generations did not outperform discrete generations in the presence of a positive genetic trend with genomic truncation selection, as past generations had lower mean genetic values than the current generation of selection candidates. With genomic optimum contribution selection, overlapping and discrete generations performed similarly, but overlapping generations slightly outperformed discrete generations in the long term if the targeted inbreeding rate was extremely low. Conclusions: Maintaining discrete generations in recurrent phenotypic mass selection leads to increased genetic gain, especially at low heritabilities, by preventing selection error bias. With genomic truncation selection and genomic optimum contribution selection, genetic gain does not differ between discrete and overlapping generations assuming non-genetic effects are not present. Overlapping generations may increase genetic gain in the long term with very low targeted rates of inbreeding in genomic optimum contribution selection. Competing Interest Statement The authors have declared no competing interest.

To produce genetic gain, hybrid crop breeding can change the additive as well as dominance genetic value of populations, which can lead to utilization of heterosis. A common hybrid breeding strategy is reciprocal recurrent selection (RRS), in which parents of hybrids are typically recycled within pools based on general combining ability (GCA). However, the relative performance of RRS and other possible breeding strategies have not been thoroughly compared. RRS can have relatively increased costs and longer cycle lengths which reduce genetic gain, but these are sometimes outweighed by its ability to harness heterosis due to dominance and increase genetic gain. Here, we used stochastic simulation to compare gain per unit cost of various breeding strategies with different amounts of population inbreeding depression and heterosis due to dominance, relative cycle lengths, time horizons, estimation methods, selection intensities, and ploidy levels. In diploids with phenotypic selection at high intensity, whether RRS was the optimal breeding strategy depended on the initial population heterosis. However, in diploids with rapid cycling genomic selection at high intensity, RRS was the optimal breeding strategy after 50 years over almost all amounts of initial population heterosis under the study assumptions. RRS required more population heterosis to outperform other strategies as its relative cycle length increased and as selection intensity decreased. Use of diploid fully inbred parents vs. outbred parents with RRS typically did not affect genetic gain. In autopolyploids, RRS typically was not beneficial regardless of the amount of population inbreeding depression. Competing Interest Statement The authors have declared no competing interest.