Optimizing simultaneous selection in long-term breeding: a stochastic simulation study for a tropical corn haploid inducer population

doi:10.21203/rs.3.rs-1952851/v1

Download PDF

Research Article

Optimizing simultaneous selection in long-term breeding: a stochastic simulation study for a tropical corn haploid inducer population

https://doi.org/10.21203/rs.3.rs-1952851/v1

This work is licensed under a CC BY 4.0 License

Version 1

posted

You are reading this older preprint version

Read the latest preprint version →

Plant breeders widely use recurrent selection schemes to increase the frequency of favorable alleles for quantitative traits in a population. Although simultaneous selection is complex because it involves several traits combined with selection cycles, the use of selection indexes (SI) is applied to increase the chance of success of the breeding program. Moreover, many indices are available in the literature; therefore, simulations can help breeders determine which selection index can be adjusted better considering the selection goals, intensity, and genetic correlation among traits over breeding cycles. In this context, we aimed to optimize the simultaneous selection in long-term breeding programs via stochastic simulations using as an example a tropical maize inducer breeding. Furthermore, we proposed a new approach to optimize the initial weights for the Smith-Hazel method to maximize the genetic gains for all traits in a balanced way. Finally, our results confirm that the traditional Smith and Hazel approach outperformed other methods for the total and balanced response to selection for important traits in a tropical corn haploid inducer breeding population.

We proposed a new approach to optimize the initial weights for the Smith-Hazel method.
Stochastic simulations are useful for establishing specific selection indices according to the target traits.
The traditional Smith and Hazel method, when well defined, outperformed others.

The selection based on only one trait may be useful to improve it but can lead to undesirable performance for other essential traits (Viana et al. 2010; Lyra et al. 2017). This situation can be even more complex when the breeding scheme adopted by the program involves several selective cycles, such as recurrent selection schemes (Hallauer et al. 2010). Thus, a way to increase the chance of success is by simultaneously selecting a set of important traits using selection indexes (SI) described by (Henderson 1963).

The concept of SI was first addressed by Smith(1936) for plant breeding and subsequently adapted for animal breeding by Hazel(1943) to predict the genetic merit of a target trait given a set of correlated phenotypes. The classic SI proposed by these authors consists of a weighted sum of the measured phenotypes with weights derived to maximize the correlation between the genetic merit for the selected target and the SI (Lopez-Cruz and de Los Campos, 2021). Therefore, the classical theory presented in these two aforementioned papers has the SI as the best linear predictor of the net genetic merit as an additional trait that, when used for selection, makes it possible to maximize gains simultaneously in all evaluated traits. However, a major limitation of this SI is that the genetic improvement for a given trait cannot be particularized since the maximization function is derived without any restrictions.

Consequently, several alternatives for selecting multiple traits emerge, such as independent culling. In this method, a certain level of merit is established for each trait, and all individuals below that level are discarded, regardless of their superiority or inferiority to other traits (Hazel and Lush 1942). Furthermore, the thresholds can be set according to a specific selection intensity or a specific value, such as a value relative to an agronomic check (Batista et al. 2021). For the same overall selected proportion, the expected genetic gain from SI is never smaller than that from independent culling (Hazel and Lush 1942; Muir and Xu 1991). However, when traits are measured at different stages, or there is a large difference in the costs of measuring various traits, selection by independent culling levels may give a higher aggregate economic return because not all traits need to be measured on all individuals (Young 1964; Xu and Muir 1992). However, a practical problem with independent culling is the difficulty of choosing appropriate truncation points for traits to obtain the desired genetic gains or maximize aggregate breeding value (Muir and Xu 1991).

Another approach addressed by Pešek and Baker (1969) is based on the desired gains, where the coefficients (b's) are calculated according to the importance established by the breeder for each trait. Thus, its construction involves the knowledge of the expression of the expected gain of the various traits under study. Finally, Henderson and Quaas (1976) proposed the multi-trait best linear unbiased prediction (MT-BLUP), which presents greater accuracy because it simultaneously considers more data and uses the genetic and residual correlations among traits.

Plant and animal breeders often employ SI during selection, especially when considering several traits to progress genotypes to the next breeding stage(Gibson and Kennedy 1990; Hazel et al. 1994). However, choosing the best SI and determining weights for each characteristic is crucial and challenging for breeders. There are several ways to determine weights for each trait that compounds the SI, but a common strategy is to assign economic weights derived from a profit function for each trait that impacts the monetary gain reached by the final product (Brascamp et al. 1985), mainly when the traits considered for selection are genetically correlated (Hidalgo-Contreras et al. 2021). Usually, selecting a SI and choosing the weights for each trait is made empirically, since static datasets do not contemplate long-term effects. However, when we consider long-term breeding programs, the selection changes the allelic frequencies throughout breeding stages and recurrent cycles, which may cause alteration in the genetic correlation between characteristics (Hidalgo-Contreras et al. 2021). Also, this fluctuation in genetic correlation can impact index values and, hence, influence the selection. Therefore, an important strategy will be to consider this genetic correlation between traits and their fluctuation to maximize all features simultaneously. Nevertheless, planning all these points is practically impossible since future data are unavailable in a real scenario. Hence, a simulation process is a helpful tool for breeders to determine which selection index might be adjusted better considering genetic correlation fluctuation throughout all selection processes.

One example of the simultaneous selection can be shown in tropical haploid maize inducer breeding. The doubled haploid (DH) technique has been applied in maize breeding to fasten maize line development. It is based on obtaining haploid individuals, identifying them, and artificial chromosomal doubling of haploid seedlings (Prigge et al. 2011; Melchinger et al. 2014). Haploids are obtained by crossing haploid inducers with a source of germplasm (Prasanna et al. 2012). Aiming to identify haploids, researchers use the marker R1-Navajo, a gene that works as a morphological marker due to its ability to produce anthocyanin in the endosperm and embryo tissues (Nanda and Chase 1966). Thus, haploid induction rate (HIR) and R1-Navajo expressiveness (EXP) are essential for the technique's success. Furthermore, this technique has been employed in maize temperate breeding programs for quite some time. In contrast, it is not commonly applied in tropical breeding programs because tropical inducers are scarce, and those available are under patent. Hence, it is crucial to develop more tropical haploid inducers available to the scientific community.

Our study aimed to optimize the simultaneous selection in long-term breeding programs via stochastic simulations. For that, we used a case study of a tropical corn haploid inducer breeding population and compared eight different methods of simultaneous selection. Furthermore, we proposed a new approach to optimize the initial weights for the Smith-Hazel method to maximize the genetic gains for all traits in a balanced way.

Breeding method for a haploid inducer population

The method presented here used an intra-populational recurrent selection to develop an improved, stable, and easy-to-maintain maize inducer population. At the beginning of each breeding cycle, we sampled 50 plants from the population and crossed them with two different testers (two single-crosses – one flint and one dent germplasm) (Fig. 1). Testers were from different germplasm to avoid bias because different genetic backgrounds can modify the R1-Navajo expressiveness (Kebede et al. 2011; Chaikam et al. 2015). This variation makes it hard to identify the haploid individuals and results in high false positive rates (Melchinger et al. 2014; Chaikam et al. 2015). Thus, each cross's two replicates (ears) were evaluated, totaling four ears per sampled plant from the breeding population. After individually collecting pollen from each of the 50 inducer plants, the crosses were performed by silking four hybrid plants (female parent) on the same day. The 50 plants were also self-fertilized, producing S1 progenies to be used in the recombination step.

At the physiological maturity stage, the four hybridized ears were harvested. Their kernels were counted (total number of seeds – TNS) and visually evaluated for their possible ploidy level based on the R1-navajo expression. Putative haploid kernels presented white embryos and purple endosperm (PHK). Seeds that presented purple embryos and purple endosperm were counted and considered diploids. Seeds without any purple marker were called inhibited (INH). HIRp was calculated as HIRp = PHK/TNS. In addition, expressiveness (EXP) was used to account for the ability to observe a putative haploid seed [EXP = 1 - (INH / TNS)], hence, the higher the expressiveness value, the lower the rate of inhibition in the seed.

The putative and inhibited seed fractions were sown in the field, following a completely randomized design with four replicates to evaluate the real haploid inducing rate (HIRr). The haploid plants were, in general, downgraded, small, and showed erect, short leaves in the field. Conversely, the diploid plants were vigorous and developed normally. Usually, after evaluating the real breeding program, we have used an "empirical" index to rank all the genotypes: I = 0.50 HIRr + 0.25 HIRp + 0.25 EXP. This index was built with the standardized values of the observations. Finally, the five best parents were selected to compose the recombination step. For that, 40 S1 plants of each superior progeny were planted under greenhouse conditions and randomly crossed.

Long-term breeding schemes employing selection index

Our study compared different strategies for multi-trait simultaneous selection in a long-term breeding program. We used maize (Zea mays L.) as a model crop and stochastic simulations performed by the AlphaSimR package (Gaynor et al. 2021). Furthermore, we evaluated different strategies for updating the SI weights and how they influenced genetic parameters over breeding cycles.

Historical population and genetic parameters

The historical double-haploid inducer maize founder population was simulated as 100 unique diploid inbred individuals, with 10 chromosome pairs each, using a Markovian Coalescent Simulator (MaCS) (Chen et al. 2009). Two thousand biallelic segregating sites were considered uniformly distributed across chromosomes, and for each target inducer trait, 100 segregating loci were randomly sampled as quantitative trait nucleotides (QTN). The aim of the simulation was the three quantitative traits described in the previous section (HIRp, HIRr, and EXP). In addition, the following genetic parameters were considered (Table 1), based on empirical data of our real population in the breeding characterization (Couto et al. 2019).

Table 1

Narrow-sense heritability (ha), genetic correlations (rg), economic weights (w), and desired genetic gain (d) in genetic standard deviations for the target traits.
rg	HIRp	HIRr	EXP
HIRp		0.35	-0.15
HIRr			0.05
ha	0.11	0.91	0.14

For each QTN, we randomly allocated an additive effect. The Additive effects ($a$) were sampled of a gamma distribution with scale and shape parameters equal to 1 and randomly assigned for each QTN. No dominance effects were considered in this study. Therefore, the breeding values for each genotype were obtained by summing the additive effects of all QTN. The phenotypic values were obtained by adding a random error sampled of a Gaussian distribution with a mean equal to 0 and variance ${\sigma }_{e}^{2}$ equal to 1, defined by narrow-sense (ha) heritability.

Base population and burn-in phase

A base population was obtained from the historical population to perform the recurrent selection scheme (Fig. 1). Initially, we selected the 49 best plants based on HIRr. Then, among these 49 genotypes, we selected the best and worst as testers in our recurrent selection breeding scheme with external testers. Finally, we randomly crossed them, obtaining the first inducer population (C0).

Once the base populations were created, a burn-in stage followed. Then, we used the three cycles of the recurrent phenotypic selection, according to the method described earlier (Fig. 1), selecting individuals based on HIRr.

Selection index schemes simulations

Simulations were based on the breeding program structure described above. Considering that, seven schemes of multi-trait simultaneous selection were compared. Below we described details about each selection index (SI) scheme applied:

Truncated (Trunc): the selection was made based on one trait, independent of the consequences on the others. Therefore, this approach has three nested variations, one for each trait.
Independent Culling (Culling) (Hazel and Lush 1942; Bernardo 2010): this method selects those parents that present performance better than a pre-determined threshold for all traits simultaneously, regardless of the correlation among the traits. In this case, we consider the population average as the culling point for the three traits.
Multi-trait (MT) (Henderson 1963): in this approach, we used the multi-trait mixed model equations to obtain the breeding values for each parent, then select the best ones. We used the method described by Mendonça et al. (2017).
Pešek-Baker (PB) (Pešek and Baker 1969): select parents based on desired gains. Hence, in each cycle, to estimate the b's of the SI, we used the following equation, $b={G}^{-}d$, where G is the genetic correlation among traits and d is the vector of desired gains in terms of standard deviation (HIRp = 1, HIRr = 2, EXP = 1).
Smith-Hazel (SH) (Smith 1936; Hazel 1943): based on this method, we selected parents based on maximum genetic gains for all traits, weighted by each trait's empirical/economic importance $\left(w\right)$. Thus, in each cycle, to estimate the b's of the SI, we used the following equation, $b={P}^{-}Gw$, where P and G are phenotypic and genetic correlation among traits, respectively, and $w$was(HIRp = 0.25, HIRr = 0.50, EXP = 0.25).
SI_Emp: in this method, we select parents based on the direct multiplication of the breeding values by each trait's empirical/economic importance $\left(w\right)$. Thus, over the cycles, $b=w$, where $w$ = (HIRp = 0.25, HIRr = 0.50, EXP = 0.25).
Smith-Hazel + optim() (SH_Optim): in this variation of the SH, we optimized the $w$ to maximize the genetic gains for all traits in a most balanced way. We applied the optim() R function in the breeder's equation for multi-trait selection (supplementary material). Then, similarly to the classical SH, in each breeding cycle, to estimate the b's of the SI, we used the following equation, $b={P}^{-}Gw$, where P and G are phenotypic and genetic correlation among traits, respectively. However, for this study the optimized $w$ is (HIRp = 0.83, HIRr = 1.00, EXP = 0.15).

Each scheme was run independently and simulated over 20 breeding cycles, and 100 replicates, totaling 2,000 estimates. The average genetic value, weights, and genetic correlation among traits were calculated for each breeding cycle and method. The response to selection was calculated following the equation:

$$RS=\frac{{X}_{i}-{X}_{0}}{t}$$

where $RS$ is the relative response to selection to the previous cycle; ${X}_{i}$ is the genetic value mean of the parental group in the $i$ cycle; ${X}_{0}$ is the genetic value mean of the previous parental group;, and$t$ is the breeding cycle time.

All the scripts used to perform the simulations are available in the supplementary material.

The usefulness of different approaches for simultaneous or indirect selection has been investigated in many crops. In this context, the response to selection and the genetic variability, weights, and correlations among traits over breeding cycles must be investigated (Bernardo 1991). With this aim, our study brings the optimization of the simultaneous selection in long-term breeding programs via stochastic simulations. For that, we compared eight different methods of simultaneous selection. Moreover, we proposed a new approach to optimize the initial weights for the Smith-Hazel method to maximize the genetic gains for all traits in a balanced way.

Not surprisingly, the traits achieved their highest response to selection (genetic additive standard deviations) if selected on the traits per se rather than based on indices. Conversely, the negatively correlated traits were penalized due to the indirect negative selection based on the truncated selection (Figs. 1a, 1b, and 1c). Overall, all indices provided positive gains for all traits. However, it is clear the presence of a crossover interaction between trait and index concerning the response to selection (RS) (Fig. 2). For instance, for the Putative Haploid Inducer Rate (HIRp), the best methods were SH_Optim, (µ = 4.88) followed by MT (µ = 4.84) and SI_Emp (µ = 4.63). On the other hand, for the Real Haploid Inducer Rate (HIRr), higher genetic gains were obtained using SI_Emp (µ = 8.72), followed by SH_Optim (µ = 8.65) and PB (µ = 8.12), respectively. Nevertheless, the RS for expressiveness (EXP) was smaller in contrast to HIR, with better estimates achieved using the SH method (µ = 3.95), followed by Culling (µ = 3.76) and MT (µ = 2.67).

As expected, each selection index works differently in the selection process. For example, it can identify the "best recombinant combinations" or change the allele frequencies over cycles. Therefore, it has significant consequences regarding the weight for each trait and the correlations among traits. Concerning the weights for HIRp, HIRr, and EXP, all methodologies have not changed over the cycles, except for PB (Fig. 1d, 1e, and 1f). Regarding HIRp, after 17 cycles, there was a huge increase in weight and maintained until cycle 17th, and after, it decreased until it reached negative (19th ) and increased again at 20th (Fig. 1d). For HIRr and EXP, the weights were increasing slowly, and after 17 cycles, they increased, reaching a maximum rate at the 20th cycle (Figs. 1e and 1f). Overall, over the breeding cycles, the selection and recombination processes tend to reduce the differences among the weights for each trait, converging then to the same point.

All simulation methods fluctuated through cycles considering the genetic correlations among traits (Figs. 1g, 1h, and 1i). The highest genetic correlation between HIRp and HIRr was achieved after 6 cycles using the Trunc_EXP approach, while the other methods oscillated around 0.1–0.3 over cycles (Fig. 1g). SH_Optim and SI_Emp, after the 13th and MT after the 17th cycle, turned the correlations negative (Fig. 1g). Considering the genetic correlation between HIRp and EXP, PB showed a decreasing pattern while the Trunc_HIRp showed an increase in the genetic correlation (Fig. 1h). A similar negative pattern was observed for genetic correlation between HIRr and EXP, constant over cycles, whose peaks were founded after 18 breeding cycles (Figs. 1 and 1i).

Overall SI aims to improve several traits concomitantly and, besides the interaction between trait x index, it is necessary to define a method that provides the maximum or the desired genetic gains for all traits, at least in this targeted case. Hence, we sum up the response to selection per method across all traits. There were significant differences among the method, where the SH outperformed the others in terms of total genetic gains across all traits (µ = 15.76), followed by MT (µ = 15.34), and PB (µ = 15.15) (Fig. 3). Furthermore, SH also outperformed others in the total balanced gain (µ = 9.88), followed by Culling (µ = 7.69), and MT (µ = 5.72) (Fig. 4). Conversely, our proposed method, SH_optim, was the worst concerning the total genetic gain (µ = 14.22) and total balanced gain (µ = 3.63). The “super” optimized weights might create this inferiority for traits based on the dataset of the first breeding cycle, which shows not work in long-term breeding.

Theoretically, SI methods are more effective than the Independent Culling (Hazel and Lush 1942), and this has been confirmed based on our results, other authors working with simulated experiments (Batista et al. 2021), and empirical data (Elgin et al. 1970). In literature, it has been described that the Pešek and Baker index, when defined in terms of the genetic covariances among traits and the desired gain based on genetic standard deviations, outperformed other methods. It was not the case in the present study but was in others such as the Smith-Hazel selecting energy cane clones with good fiber, sucrose, and cane yield in tons per hectare (de Azeredo et al. 2017) or the independent Culling for protein content among families with above-average oil concentration levels (Openshaw and Hadley 1984). The lack of consistency in the PB across different studies is probably due to defining the desired genetic gains and matching them with the genetic variability available in the population and the constraints generated by the genetic correlations among the target traits. Therefore, more stable methods such as SH are prone to provide better genetic gains (total and balanced) in a wide range of scenarios. The main reason is that it maximizes the genetic gains for all traits, balancing the weight of each trait by their heritability (Smith 1936; Hazel 1943), which is closely related to the accuracy and the genetic variability available for selection.

Finally, it is possible to conclude that SI is a key factor in the multi-trait response to selection in long-term breeding programs. Among the options, our results showed that the traditional Smith and Hazel approach outperformed other methods for the total and balanced response to selection for important traits in a tropical corn haploid inducer breeding population.

Funding: CNPq (400029/2016-2).

Conflicts of Interest: The authors declare no conflict of interest.

Data Availability Statement: all the data is available as supplementary information.

Code availability: all the scripts are available as supplementary information.

Ethical standards: Not applicable

Author Contributions: RFN elaborated on the hypothesis, conducted the analyses, interpreted the results, and contributed to the writing. FS, JCD, PHS, JC, and KLRB contributed to the writing and discussion. All authors read and approved the final manuscript.

ACKNOWLEDGMENTS

We are thankful to Excellence in Breeding - CGIAR platform and Allogamous Breeding lab-USP members for their comments and suggestions.

Batista LG, Gaynor RC, Margarido GRA, et al (2021) Long-term comparison between index selection and optimal independent culling in plant breeding programs with genomic prediction. PLOS ONE 16:e0235554. https://doi.org/10.1371/journal.pone.0235554
Bernardo R (2010) Selection for multiple traits. In: Breeding for Quantitative Traits in Plants, 1st edn. Stemma Press, Woodbury, pp 323–336
Bernardo R (1991) Retrospective Index Weights Used in Multiple Trait Selection in a Maize Breeding Program. Crop Science 31:1174–1179. https://doi.org/10.2135/cropsci1991.0011183X003100050020x
Brascamp EW, Smith C, Guy DR (1985) Derivation of economic weights from profit equations. Animal Science 40:175–179. https://doi.org/10.1017/S0003356100031986
Chaikam V, Nair SK, Babu R, et al (2015) Analysis of effectiveness of R1-nj anthocyanin marker for in vivo haploid identification in maize and molecular markers for predicting the inhibition of R1-nj expression. Theoretical and Applied Genetics 128:159–171. https://doi.org/10.1007/s00122-014-2419-3
Chen GK, Marjoram P, Wall JD (2009) Fast and flexible simulation of DNA sequence data. Genome Research 19:136–142. https://doi.org/10.1101/gr.083634.108
Couto EG de O, Cury MN, Bandeira e Souza M, et al (2019) Effect of F1 and F2 generations on genetic variability and working steps of doubled haploid production in maize. PLOS ONE 14:e0224631. https://doi.org/10.1371/journal.pone.0224631
de Azeredo AAC, Bhering LL, Brasileiro BP, et al (2017) Comparison between different selection indices in energy cane breeding. Genetics and Molecular Research 16:. https://doi.org/10.4238/gmr16019535
Elgin JH, Hill RR, Zeiders KE (1970) Comparison of Four Methods of Multiple Trait Selection for Five Traits in Alfalfa ¹. Crop Science 10:190–193. https://doi.org/10.2135/cropsci1970.0011183X001000020023x
Gaynor RC, Gorjanc G, Hickey JM (2021) AlphaSimR: an R package for breeding program simulations. G3 Genes|Genomes|Genetics 11:. https://doi.org/10.1093/g3journal/jkaa017
Gibson JP, Kennedy BW (1990) The use of constrained selection indexes in breeding for economic merit. Theoretical and Applied Genetics 80:801–805. https://doi.org/10.1007/BF00224195
Hallauer AR, Filho JBM, Carena MJ (2010) Breeding Plants. In: Quantitative Genetics in Maize Breeding. Springer New York, New York, NY
Hazel LN (1943) The genetic basis for constructing selection indexes. Genetics 28:476–490
Hazel LN, Dickerson GE, Freeman AE (1994) The Selection Index—Then, Now, and for the Future. Journal of Dairy Science 77:3236–3251. https://doi.org/10.3168/jds.S0022-0302(94)77265-9
Hazel LN, Lush JL (1942) The efficiency of three methods of selection. Journal of Heredity 33:393–399. https://doi.org/10.1093/oxfordjournals.jhered.a105102
Henderson CR (1963) Selection Index and Expected Genetic Advance. In: Statistical Genetics and Plant Breeding. National Academy of Sciences, National Research Council Publication, Washington DC, pp 141–163
Henderson CR, Quaas RL (1976) Multiple Trait Evaluation Using Relatives’ Records. Journal of Animal Science 43:1188–1197. https://doi.org/10.2527/jas1976.4361188x
Hidalgo-Contreras JV, Salinas-Ruiz J, Eskridge KM, Baenziger SP (2021) Incorporating Molecular Markers and Causal Structure among Traits Using a Smith-Hazel Index and Structural Equation Models. Agronomy 11:1953. https://doi.org/10.3390/agronomy11101953
Kebede AZ, Dhillon BS, Schipprack W, et al (2011) Effect of source germplasm and season on the in vivo haploid induction rate in tropical maize. Euphytica 180:219–226. https://doi.org/10.1007/s10681-011-0376-3
Lopez-Cruz M, de los Campos G (2021) Optimal breeding-value prediction using a sparse selection index. Genetics 218:. https://doi.org/10.1093/genetics/iyab030
Lyra DH, de Freitas Mendonça L, Galli G, et al (2017) Multi-trait genomic prediction for nitrogen response indices in tropical maize hybrids. Molecular Breeding 37:80. https://doi.org/10.1007/s11032-017-0681-1
Melchinger AE, Schipprack W, Friedrich Utz H, Mirdita V (2014) In Vivo Haploid Induction in Maize: Identification of Haploid Seeds by Their Oil Content. Crop Science 54:1497–1504. https://doi.org/10.2135/cropsci2013.12.0851
Mendonça L de F, Granato ÍSC, Alves FC, et al (2017) Accuracy and simultaneous selection gains for N-stress tolerance and N-use efficiency in maize tropical lines. Scientia Agricola 74:481–488. https://doi.org/10.1590/1678-992x-2016-0313
Muir WM, Xu S (1991) An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions. Theoretical and Applied Genetics 82:457–465. https://doi.org/10.1007/BF00588599
Nanda DK, Chase SS (1966) An Embryo Marker for Detecting Monoploids Of Maize ( Zea Mays L.) ¹. Crop Science 6:213–215. https://doi.org/10.2135/cropsci1966.0011183X000600020036x
Openshaw SJ, Hadley HH (1984) Selection Indexes to Modify Protein Concentration of Soybean Seeds ¹. Crop Science 24:1–4. https://doi.org/10.2135/cropsci1984.0011183X002400010001x
Pešek J, Baker RJ (1969) DESIRED IMPROVEMENT IN RELATION TO SELECTION INDICES. Canadian Journal of Plant Science 49:803–804. https://doi.org/10.4141/cjps69-137
Prasanna BM, Chaikam V, Mahuku G (2012) Doubled haploid technology in maize breeding: theory and practice. CIMMYT, Mexico
Prigge V, Sánchez C, Dhillon BS, et al (2011) Doubled Haploids in Tropical Maize: I. Effects of Inducers and Source Germplasm on in vivo Haploid Induction Rates. Crop Science 51:1498–1506. https://doi.org/10.2135/cropsci2010.10.0568
Smith HF (1936) A discriminant function for plant selection. Annals of Eugenics 7:240–250. https://doi.org/10.1111/j.1469-1809.1936.tb02143.x
Viana JMS, Sobreira FM, de Resende MD v., Faria VR (2010) Multi-trait BLUP in half-sib selection of annual crops. Plant Breeding 129:599–604. https://doi.org/10.1111/j.1439-0523.2009.01745.x
Xu S, Muir WM (1992) Selection index updating. Theoretical and Applied Genetics 83:451–458. https://doi.org/10.1007/BF00226533
Young SSY (1964) Multi-stage selection for genetic gain. Heredity (Edinb) 19:131–145. https://doi.org/10.1038/hdy.1964.11

Download PDF

Version 1

posted

You are reading this older preprint version

Read the latest preprint version →

Optimizing simultaneous selection in long-term breeding: a stochastic simulation study for a tropical corn haploid inducer population

Status:

Version 1

Abstract

Figures

Core Ideas

Introduction

Materials And Methods

Breeding method for a haploid inducer population

Long-term breeding schemes employing selection index

Historical population and genetic parameters

Base population and burn-in phase

Selection index schemes simulations

Results And Discussion

Declarations

References

Status:

Version 1