Hybrid maize breeding with doubled haploids: III. Efficiency of early testing prior to doubled haploid production in two-stage selection for testcross performance

Early testing prior to doubled haploid (DH) production is a promising approach in hybrid maize breeding. We (1) determined the optimum allocation of the number of S₁ families, DH lines, and test locations for two different breeding schemes, (2) compared the maximum selection gain achievable under both breeding schemes, and (3) investigated limitations in the current method of DH production. Selection gain was calculated by numerical integration in two-stage breeding schemes with evaluation of testcross progenies of (1) DH lines in both stages (DHTC), or (2) S₁ families in the first and DH lines within S₁ families in the second stage (S₁TC-DHTC). Different assumptions were made regarding the budget, variance components, and time of DH production within S₁ families. Maximum selection gain in S₁TC-DHTC was about 10% larger than in DHTC, indicating the large potential of early testing prior to DH production. The optimum allocation of test resources in S₁TC-DHTC involved similar numbers of test locations and test candidates in both stages resulting in a large optimum number of S₁ families in the first stage and DH lines within the best two S₁ families in the second stage. The longer cycle length of S₁TC-DHTC can be compensated by haploid induction of individual S₁ plants instead of S₁ families. However, this reduces selection gain largely due to the current limitations in the DH technique. Substantial increases in haploid induction and chromosome doubling rates as well as reduction in costs of DH production would allow early testing of S₁ lines and subsequent production and testing of DH lines in a breeding scheme that combines high selection gain with a short cycle length. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Hybrid maize breeding with doubled haploids. IV. Number versus size of crosses and importance of parental selection in two-stage selection for testcross performance

Parental selection influences the gain from selection and the optimum allocation of test resources in breeding programs. We compared two hybrid maize (Zea mays L.) breeding schemes with evaluation of testcross progenies: (a) doubled haploid (DH) lines in both stages (DHTC) and (b) S₁ families in the first stage and DH lines within S₁ families in the second stage (S₁TC-DHTC). Our objectives were to (1) determine the optimum allocation regarding the number of crosses, S₁ families, DH lines, and test locations, (2) investigate the impact of parental selection on the optimum allocation and selection gain (ΔG), and (3) compare the maximum ΔG achievable with each breeding scheme. Selection gain was calculated by numerical integration. Different assumptions were made regarding the budget, variance components, correlation between the mean phenotypic performance of the parents and the mean genotypic value of the testcross performance of their progenies (ρ _P ), and the composition of the finally selected test candidates. In comparison with randomly chosen crosses, maximum ΔG was largely increased with parental selection in both breeding schemes. With an increasing correlation ρ _P , this superiority increased strongly, while the optimum number of crosses decreased in favor of an increased number of test candidates within crosses. Thus, concentration on few crosses among the best parental lines might be a promising approach for short-term success in advanced cycle breeding. Breeding scheme S₁TC-DHTC led to a larger ΔG but had a longer cycle length than DHTC. However, with further improvements in the DH technique and the realization of more than two generations per year, early testing of S₁ families prior to production of DH lines would become very attractive in hybrid maize breeding. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. T. Wegenast and C. F. H. Longin contributed equally to this work.     

Hybrid maize breeding with doubled haploids: V. Selection strategies for testcross performance with variable sizes of crosses and S1 families

In hybrid maize (Zea mays L.) breeding, doubled haploids (DH) are increasingly replacing inbreds developed by recurrent selfing. Doubled haploids may be developed directly from S₀ plants in the parental cross or via S₁ families. In both these breeding schemes, we examined 2 two-stage selecting strategies, i.e., considering or ignoring cross and family structure while selection among and within parental crosses and S₁ families. We examined the optimum allocation of resources to maximize the selection gain ΔG and the probability P(q) of identifying the q% best genotypes. Our specific objectives were to (1) determine the optimum number and size of crosses and S₁ families, as well as the optimum number of test environments and (2) identify the superior selection strategy. Selection was based on the evaluation of testcross progenies of (1) DH lines in both stages (DHTC) and (2) S₁ families in the first stage and of DH lines within S₁ families in the second stage (S₁TC-DHTC) with uniform and variable sizes of crosses and S₁ families. We developed and employed simulation programs for selection with variable sizes of crosses and S₁ families within crosses. The breeding schemes and selection strategies showed similar relative efficiency for both optimization criteria ΔG and P (0.1%). As compared with DHTC, S₁TC-DHTC had larger ΔG and P (0.1%), but a higher standard deviation of ΔG. The superiority of S₁TC-DHTC was increased when the selection was done among all DH lines ignoring their cross and family structure and using variable sizes of crosses and S₁ families. In DHTC, the best selection strategy was to ignore cross structures and use uniform size of crosses.     

Comparison of bread wheat lines selected by doubled haploid, single-seed descent and pedigree selection methods

 Yield performance of each group of ten spring bread wheat lines selected by doubled haploid (DH), single-seed descent (SSD) and pedigree selection (PS) methods from three F₁ crosses was compared with the aim of evaluating the DH method in breeding programs. Populations of 65–97 DH lines and 110 SSD lines per cross were used for selection. PS lines were developed by repeated selections from 1500 F₂ plants. Yield evaluation was performed at the F₆ generation of SSD and PS lines along with DH lines in a 2-year field experiment. It took only 2 years from the planting of wheat materials for DH production to the planting of selected DH lines for yield evaluation. There was no significant difference in grain yield between DH lines and PS lines selected from an F₁ cross whose parental varieties were closely related in their pedigrees. In two crosses with low coefficients of parentage and a large variation in their progenies, grain yield of selected DH lines was significantly lower than those of selected SSD and PS lines. These results confirm that the DH method can save time in obtaining recombinant inbred lines ready for yield evaluation. However, a larger DH population is required to achieve the same level of genetic advance with the PS method in crosses containing greater genetic variation. Received: 23 December 1997 / Accepted: 12 March 1998     

A combination of walk-back and optimum contribution selection in fish: a simulation study

The aim of this paper was to study the performance of a novel fish breeding scheme, which is a combination of walk-back and optimum contribution selection using stochastic simulation. In this walk-back selection scheme, batches of different sizes (50, 100, 1000, 5000 and 10 000) with the phenotypically superior fish from one tank with mixed families were genotyped to set up the pedigree. BLUP estimated breeding values were calculated. The optimum contribution selection method was used with the rate of inbreeding (ΔF) constrained to 0.005 or 0.01 per generation. If the constraint on ΔF could not be held, a second batch of fish was genotyped etc. Compared with the genotyping of all selection candidates (1000, 5000 or 10 000), the use of batches saves genotyping costs. The results show that two batches of 50 fish were often necessary. With a batch size of 100, genetic level was 76–92% of the genetic level achieved for schemes with all fish being genotyped and thus candidates for the optimum contribution selection step. More parents were selected for schemes with larger batches, resulting in a higher genetic gain, especially when all selection candidates were genotyped. There was little extra genetic gain in genotyping of 1000 fish instead of 100 for the larger schemes of 5000 and 10 000 candidates. The accuracy of breeding values was similar for all batch sizes (~0.30), but higher (~0.5) when all candidates were included. Since only the phenotypically most superior fish were genotyped, BLUP-EBV were biased. Compared with genotyping of all selection candidates, the use of batches saves genotyping costs, while simultaneously maintaining high genetic gains.     

Efficiency of including first-generation information in second-generation ranking and selection: results of computer simulation

Using computer simulation, we evaluated the impact of using first-generation information to increase selection efficiency in a second-generation breeding program. Selection efficiency was compared in terms of increase in rank correlation between estimated and true breeding values (i.e., ranking accuracy), reduction in coefficient of variation of correlation coefficients (i.e., ranking reliability), and increase in realized gain, with best linear unbiased prediction (BLUP). The test populations were generated with varying parameters: selection strategy (forward vs backward selection of parents); number of parents (24∼96); number of crosses per parent (1∼8); heritability (0.05∼0.35); ratio of dominance to additive variance (0∼3); ratio of additive-by-site to additive variance (0∼3); and ratio of dominance-by-site to additive variance (0∼3). The two selection strategies gave distinct results. When parents of the second-generation crosses had been selected via backward selection, adding first-generation information markedly increased selection efficiency. Conversely, when parents had been selected via forward selection, first-generation information provided little increase in efficiency. The amount of increase depended more on heritabilities in both generations and less on dominance and genotype–by–environment effects. Including first-generation information helped more when there were many parents and few crosses per parent in the second generation. Only in the case of extremely low first-generation heritabilities was there no benefit to adding first-generation information in terms of improved ranking reliability and accuracy.     

Hybrid maize breeding with doubled haploids: I. One-stage versus two-stage selection for testcross performance

Optimum allocation of resources is of fundamental importance for the efficiency of breeding programs. The objectives of our study were to (1) determine the optimum allocation for the number of lines and test locations in hybrid maize breeding with doubled haploids (DHs) regarding two optimization criteria, the selection gain ΔG _k and the probability P _k of identifying superior genotypes, (2) compare both optimization criteria including their standard deviations (SDs), and (3) investigate the influence of production costs of DHs on the optimum allocation. For different budgets, number of finally selected lines, ratios of variance components, and production costs of DHs, the optimum allocation of test resources under one- and two-stage selection for testcross performance with a given tester was determined by using Monte Carlo simulations. In one-stage selection, lines are tested in field trials in a single year. In two-stage selection, optimum allocation of resources involves evaluation of (1) a large number of lines in a small number of test locations in the first year and (2) a small number of the selected superior lines in a large number of test locations in the second year, thereby maximizing both optimization criteria. Furthermore, to have a realistic chance of identifying a superior genotype, the probability P _k of identifying superior genotypes should be greater than 75%. For budgets between 200 and 5,000 field plot equivalents, P _k > 75% was reached only for genotypes belonging to the best 5% of the population. As the optimum allocation for P _k (5%) was similar to that for ΔG _k , the choice of the optimization criterion was not crucial. The production costs of DHs had only a minor effect on the optimum number of locations and on values of the optimization criteria. C. Friedrich H. Longin and H. Friedrich Utz contributed equally to this work.     

Within-family marker-assisted selection for aquaculture species

A within-family marker-assisted selection scheme was designed for typical aquaculture breeding schemes, where most traits are recorded on sibs of the candidates. Here, sibs of candidates were tested for the trait and genotyped to establish genetic marker effects on the trait. BLUP breeding values were calculated, including information of the markers (MAS) or not (NONMAS). These breeding values were identical for all family members in the NONMAS schemes, but differed between family members in the MAS schemes, making within-family selection possible. MAS had up to twice the total genetic gain of the corresponding NONMAS scheme. MAS was somewhat less effective when heritability increased from 0.06 to 0.12 or when the frequency of the positive allele was < 0.5. The relative efficiency of MAS was higher for schemes with more candidates, because of larger fullsib family sizes. MAS was also more efficient when male:female mating ratio changed from 1:1 to 1:5 or when the QTL explained more of the total genetic variation. Four instead of two markers linked to the QTL increased genetic gain somewhat. There was no significant difference in polygenic genetic gain between MAS and NONMAS for most schemes. The rates of inbreeding were lower for MAS than NON-MAS schemes, because fewer full-sibs were selected by MAS.     

Selection against genetic defects in conservation schemes while controlling inbreeding

We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding (ΔF) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1–2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on ΔF needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained ΔF at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of ΔF is very important.     

Economic aspects of implementing genomic evaluations in a pig sire line breeding scheme

Background

Replacing pedigree-based BLUP evaluations by genomic evaluations in pig breeding schemes can result in greater selection accuracy and genetic gains, especially for traits with limited phenotypes. However, this methodological change would generate additional costs. The objective of this study was to determine whether additional expenditures would be more profitably devoted to implementing genomic evaluations or to increasing phenotyping capacity while retaining traditional evaluations.

Methods

Stochastic simulation was used to simulate a population with 1050 breeding females and 50 boars that was selected for 10 years for a breeding goal with two uncorrelated traits with heritabilities of 0.4. The reference breeding scheme was based on phenotyping 13 770 candidates per year for trait 1 and 270 sibs of candidates per year for trait 2, with selection based on pedigree-based BLUP estimated breeding values. Increased expenditures were allocated to either increasing the phenotyping capacity for trait 2 while maintaining traditional evaluations, or to implementing genomic selection. The genomic scheme was based on two training populations: one for trait 2, consisting of phenotyped sibs of the candidates whose number increased from 1000 to 3430 over time, and one for trait 1, consisting of the selection candidates. Several genomic scenarios were tested, where the size of the training population for trait 1, and the number of genotyped candidates pre-selected based on their parental estimated breeding value, varied.

Results

Both approaches resulted in higher genetic trends for the population breeding goal and lower rates of inbreeding compared to the reference scheme. However, even a very marked increase in phenotyping capacity for trait 2 could not match improvements achieved with genomic selection when the number of genotyped candidates was large. Genotyping just a limited number of pre-selected candidates significantly reduced the extra costs, while preserving most of the benefits in terms of genetic trends and inbreeding. Implementing genomic evaluations was the most efficient approach when major expenditure was possible, whereas increasing phenotypes was preferable when limited resources were available.

Conclusions

Economic decisions on implementing genomic evaluations in a pig nucleus population must take account of population characteristics, phenotyping and genotyping costs, and available funds.     

Determination of self-locompatibility genotypes of Korean apple cultivars based on S-RNase PCR

To prevent self-fertilization, apple has a gametophytic self-incompatibility mechanism, part of a widespread intraspecific system, that is controlled by a multi-allelic locus. This attribute has been exploited in breeding programs for new cultivars. Likewise, many apple orchards depend on artificial pollination. Therefore, molecular analysis and early identification of the self-incompatibility (S) genotype could greatly improve breeding schemes and pollen donors selection. Here, we PCR-amplified the S-RNase PCR fragments from a total of 14 cultivars and parents, using new primers (ASPF3+ASPR3) common to 23 S-alleles in apple. The S-genotypes were determined for the following: ‘Hongro’ (S₁S₃), ‘Gamhong’ (S₁S₉), ‘Saenara’ (S₁S₃), ‘Chukwang’ (S₃S₉), ‘Hwahong’ (S₃S₉), ‘Seokwang’ (S₃S₃), ‘Hwarang’ (S₁S₉), ‘Sunhong’ (S₃S₉), ‘S.E.B.’ (S₁S₁₉), ‘S.G.D.’ (S₂S₃), and ‘Mollie’s Delicious’ (S₃S₇). We also confirmed the characteristics of the S-genotypes for eight Korean apple cultivars by PCR-Southern blot analysis, using seven S-RNases as probes.     

Hybrid maize breeding with doubled haploids: II. Optimum type and number of testers in two-stage selection for general combining ability

Optimum allocation of test resources is of crucial importance for the efficiency of breeding programs. Our objectives were to (1) determine the optimum allocation of the number of lines, test locations, as well as number and type of testers in hybrid maize breeding using doubled haploids with two breeding strategies for improvement of general combining ability (GCA), (2) compare the maximum selection gain (ΔG) achievable under both strategies, and (3) give recommendations for the optimum implementation of doubled haploids in commercial hybrid maize breeding. We calculated ΔG by numerical integration for two two-stage selection strategies with evaluation of (1) testcross performance in both stages (BS1) or (2) line per se performance in the first stage followed by testcross performance in the second stage (BS2). Different assumptions were made regarding the budget, variance components (VCs), and the correlation between line per se performance and GCA. Selection gain for GCA increased with a broader genetic base of the tester. Hence, testers combining a large number of divergent lines are advantageous. However, in applied breeding programs, the use of single- or double-cross testers in the first and inbred testers in the second selection stage may be a good compromise between theoretical and practical requirements. With a correlation between line per se performance and GCA of 0.50, ΔG for BS1 is about 5% higher than for BS2, if an economic weight of line per se performance is neglected. With increasing economic weight of line per se performance, relative efficiency of BS2 increased rapidly resulting in a superiority of BS2 over BS1 already for an economic weight for line per se performance larger than 0.1. Considering the importance of an economic seed production, an economic weight larger than 0.1 seems realistic indicating the necessity of separate breeding strategies for seed and pollen parent heterotic groups. C. Friedrich H. Longin and H. Friedrich Utz have contributed equally to this work.     

Genomic selection in forest tree breeding

Genomic selection (GS) involves selection decisions based on genomic breeding values estimated as the sum of the effects of genome-wide markers capturing most quantitative trait loci (QTL) for the target trait(s). GS is revolutionizing breeding practice in domestic animals. The same approach and concepts can be readily applied to forest tree breeding where long generation times and late expressing complex traits are also a challenge. GS in forest trees would have additional advantages: large training populations can be easily assembled and accurately phenotyped for several traits, and the extent of linkage disequilibrium (LD) can be high in elite populations with small effective population size (N _e) frequently used in advanced forest tree breeding programs. Deterministic equations were used to assess the impact of LD (modeled by N _e and intermarker distance), the size of the training set, trait heritability, and the number of QTL on the predicted accuracy of GS. Results indicate that GS has the potential to radically improve the efficiency of tree breeding. The benchmark accuracy of conventional BLUP selection is reached by GS even at a marker density ~2 markers/cM when N _e ≤ 30, while up to 20 markers/cM are necessary for larger N _e. Shortening the breeding cycle by 50% with GS provides an increase ≥100% in selection efficiency. With the rapid technological advances and declining costs of genotyping, our cautiously optimistic outlook is that GS has great potential to accelerate tree breeding. However, further simulation studies and proof-of-concept experiments of GS are needed before recommending it for operational implementation.     

Molecular breeding for grain yield in barley: an evaluation of QTL effects in a spring barley cross

 We report results from a breeding strategy designed to accumulate favorable QTL alleles for grain yield identified in the SteptoeבMorex’ (SM) barley germplasm. Two map lines (SM73 and SM145) from the original mapping population were selected based on their marker genotype and QTL structure. When crossed, these lines would be expected to produce progeny with most favorable QTL alleles. One hundred doubled haploid (DH) lines from the F₁ hybrid of this cross were genotyped with ten RFLP markers and one morphological marker defining grain yield to monitor QTL segregation. A subset of 24 lines representing various combinations of putatively favorable and unfavorable QTL alleles, together with Steptoe, ‘Morex’, SM73, and SM145, were phenotyped for grain yield in five environments. Multiple regression procedures were used to explore phenotype and genotype relationships. Most target QTLs showed significant effects. However, significance and magnitude of QTL effects and favorable QTL allele phase varied across environments. All target QTLs showed significant QTL-by-environment interaction (QTL×E), and the QTL on chromosome 2 expressed alternative favorable QTL alleles in different environments. Digenic epistatic effects were also detected between some QTL loci. For traits such as grain yield, marker-assisted selection efforts may be better targeted at determining optimum combinations of QTL alleles rather than pyramiding alleles detected in a reference mapping population. Received: 2 June 1998 / Accepted: 17 September 1998     

Enhanced recovery of doubled haploid lines from parthenogenetic plants of melon (<Emphasis Type="Italic">Cucumis melo</Emphasis> L.)

Recovery of doubled haploid (DH) progeny from haploid melon plants for use in breeding programs requires efficient chromosome doubling procedures. We describe improved procedures for recovery of fruits and viable seeds from parthenogenetic melon plants. Plant regeneration from nodal explants treated with 500 mg/L colchicine for 12 h was increased from 40 to 88% by transferring the treated explants to medium supplemented with a combination of growth regulators [5 μM IAA; 5 μM BA; 1 μM ABA; 30 μM AgNO₃). Prolonged exposure (2–7 days) to colchicine inhibited regeneration from nodal explants but had less effect on shoot tip explants. Many colchicine-treated plantlets flowered in vitro, allowing early assessment of their male fertility. Production of stained pollen in plants from nodal explants was highest after 0.5–2 days of colchicine treatment and on plants from shoot tips after 1–2 days. In vitro pollen counts correlated well with counts from greenhouse grown plants and with fruit set. The fruit set rate for colchicine-treated plants with a high pollen number was 47%. Appropriate colchicine treatment and culture of nodal explants as well as tip explants can substantially increase the number of fertile plants and DH lines recovered from parthenogenetic melons.     

Response to genomic selection: The Bulmer effect and the potential of genomic selection when the number of phenotypic records is limiting

Background

Over the last ten years, genomic selection has developed enormously. Simulations and results on real data suggest that breeding values can be predicted with high accuracy using genetic markers alone. However, to reach high accuracies, large reference populations are needed. In many livestock populations or even species, such populations cannot be established when traits are difficult or expensive to record, or when the population size is small. The value of genomic selection is then questionable.

Methods

In this study, we compare traditional breeding schemes based on own performance or progeny information to genomic selection schemes, for which the number of phenotypic records is limiting. Deterministic simulations were performed using selection index theory. Our focus was on the equilibrium response obtained after a few generations of selection. Therefore, we first investigated the magnitude of the Bulmer effect with genomic selection.

Results

Results showed that the reduction in response due to the Bulmer effect is the same for genomic selection as for selection based on traditional BLUP estimated breeding values, and is independent of the accuracy of selection. The reduction in response with genomic selection is greater than with selection based directly on phenotypes without the use of pedigree information, such as mass selection. To maximize the accuracy of genomic estimated breeding values when the number of phenotypic records is limiting, the same individuals should be phenotyped and genotyped, rather than genotyping parents and phenotyping their progeny. When the generation interval cannot be reduced with genomic selection, large reference populations are required to obtain a similar response to that with selection based on BLUP estimated breeding values based on own performance or progeny information. However, when a genomic selection scheme has a moderate decrease in generation interval, relatively small reference population sizes are needed to obtain a similar response to that with selection on traditional BLUP estimated breeding values.

Conclusions

When the trait of interest cannot be recorded on the selection candidate, genomic selection schemes are very attractive even when the number of phenotypic records is limited, because traditional breeding requires progeny testing schemes with long generation intervals in those cases.     

Genomic selection requires genomic control of inbreeding

Background

In the past, pedigree relationships were used to control and monitor inbreeding because genomic relationships among selection candidates were not available until recently. The aim of this study was to understand the consequences for genetic variability across the genome when genomic information is used to estimate breeding values and in managing the inbreeding generated in the course of selection on genome-enhanced estimated breeding values.

Methods

These consequences were measured by genetic gain, pedigree- and genome-based rates of inbreeding, and local inbreeding across the genome. Breeding schemes were compared by simulating truncation selection or optimum contribution selection with a restriction on pedigree- or genome-based inbreeding, and with selection using estimated breeding values based on genome- or pedigree-based BLUP. Trait information was recorded on full-sibs of the candidates.

Results

When the information used to estimate breeding values and to constrain rates of inbreeding were either both pedigree-based or both genome-based, rates of genomic inbreeding were close to the desired values and the identical-by-descent profiles were reasonably uniform across the genome. However, with a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding were much higher than expected. With pedigree-instead of genome-based estimated breeding values, the impact of the largest QTL on the breeding values was much smaller, resulting in a more uniform genome-wide identical-by-descent profile but genomic rates of inbreeding were still higher than expected based on pedigree relationships, because they measure the inbreeding at a neutral locus not linked to any QTL. Neutral loci did not exist here, where there were 100 QTL on each chromosome. With a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding substantially exceeded the value of its constraint. In contrast, with a genome-based inbreeding constraint and genome-based estimated breeding values, marker frequencies changed, but this change was limited by the inbreeding constraint at the marker position.

Conclusions

To control inbreeding, it is necessary to account for it on the same basis as what is used to estimate breeding values, i.e. pedigree-based inbreeding control with traditional pedigree-based BLUP estimated breeding values and genome-based inbreeding control with genome-based estimated breeding values.     

Asymptotic rates of response from forest tree breeding strategies using best linear unbiased prediction

 Genetic gain equations are developed for selection on multiple traits using either multi- or univariate best linear unbiased predictors (BLUP) and for selection under controlled and open pollination and polymix mating schemes. The equations assume an infinite population and account for the effects of selection. A comparison with simulated populations under the same mating schemes show that the gain equations predict selection response well, with the predictions having some upward bias. The gain equations are used to compare across mating schemes, to compare univariate to multivariate analyses, and to measure the reduction in the rate of genetic gain due to selection disequilibrium. Results show controlled pollination schemes can offer as much as a 56% advantage in genetic gain relative to open pollination. The reduction in the rate of genetic gain due to selection disequilibrium is approximately 27% under controlled pollination for the breeding goals studied. The results show a limited benefit in using multivariate analyses for predicting breeding values. Received: 20 April 1997 / Accepted: 8 October 1997     

A low-marker density implementation of genomic selection in aquaculture using within-family genomic breeding values

Background

Genomic selection can increase genetic gain within aquaculture breeding programs, but the high costs related to high-density genotyping of a large number of individuals would make the breeding program expensive. In this study, a low-cost method using low-density genotyping of pre-selected candidates and their sibs was evaluated by stochastic simulation.

Methods

A breeding scheme with selection for two traits, one measured on candidates and one on sibs was simulated. Genomic breeding values were estimated within families and combined with conventional family breeding values for candidates that were pre-selected based on conventional BLUP breeding values. This strategy was compared with a conventional breeding scheme and a full genomic selection program for which genomic breeding values were estimated across the whole population. The effects of marker density, level of pre-selection and number of sibs tested and genotyped for the sib-trait were studied.

Results

Within-family genomic breeding values increased genetic gain by 15% and reduced rate of inbreeding by 15%. Genetic gain was robust to a reduction in marker density, with only moderate reductions, even for very low densities. Pre-selection of candidates down to approximately 10% of the candidates before genotyping also had minor effects on genetic gain, but depended somewhat on marker density. The number of test-individuals, i.e. individuals tested for the sib-trait, affected genetic gain, but the fraction of the test-individuals genotyped only affected the relative contribution of each trait to genetic gain.

Conclusions

A combination of genomic within-family breeding values, based on low-density genotyping, and conventional BLUP family breeding values was shown to be a possible low marker density implementation of genomic selection for species with large full-sib families for which the costs of genotyping must be kept low without compromising the effect of genomic selection on genetic gain.     

Gene stacking strategies with doubled haploids derived from biparental crosses: theory and simulations assuming a finite number of loci

Recent progress in genotyping and doubled haploid (DH) techniques has created new opportunities for development of improved selection methods in numerous crops. Assuming a finite number of unlinked loci (ℓ) and a given total number (n) of individuals to be genotyped, we compared, by theory and simulations, three methods of marker-assisted selection (MAS) for gene stacking in DH lines derived from biparental crosses: (1) MAS for high values of the marker score (T, corresponding to the total number of target alleles) in the F₂ generation and subsequently among DH lines derived from the selected F₂ individual (Method 1), (2) MAS for augmented F₂ enrichment and subsequently for T among DH lines from the best carrier F₂ individual (Method 2), and (3) MAS for T among DH lines derived from the F₁ generation (Method 3). Our objectives were to (a) determine the optimum allocation of resources to the F₂ ( n₁^* \, n_{1}^{*} ) and DH generations (n - n₁^* ) (n - n_{1}^{*} ) for Methods 1 and 2 by simulations, (b) compare the efficiency of all three methods for gene stacking by simulations, and (c) develop theory to explain the general effect of selection on the segregation variance and interpret our simulation results. By theory, we proved that for smaller values of ℓ, the segregation variance of T among DH lines derived from F₂ individuals, selected for high values of T, can be much smaller than expected in the absence of selection. This explained our simulation results, showing that for Method 1, it is best to genotype more F₂ individuals than DH lines ($ n_{1}^{*} :n > 0.5 $ n_{1}^{*} :n > 0.5 ), whereas under Method 2, the optimal ratio n₁^* :n n_{1}^{*} :n was close to 0.5. However, for ratios deviating moderately from the optimum, the mean [`(X)] \overline{X} of T in the finally selected DH line ( T<sub>\textDH</sub><sup>*</sup> T_{\text{DH}}^{*} ) was hardly reduced. Method 3 had always the lowest mean [`(X)] \overline{X} of T_\textDH^* T_{\text{DH}}^{*} except for small numbers of loci (ℓ = 4) and is favorable only if a small number of loci are to be stacked in one genotype and/or saving one generation is of crucial importance in cultivar development. Method 2 is under most circumstances the superior method, because it generally showed the highest mean [`(X)] \overline{X} and lowest SD of T_\textDH^* T_{\text{DH}}^{*} for the finally selected DH.