Long-term comparison between index selection and optimal independent culling in plant breeding programs with genomic prediction

Lorena G Batista; Robert Chris Gaynor; Gabriel R A Margarido; Tim Byrne; Peter Amer; Gregor Gorjanc; John M Hickey

doi:10.1371/journal.pone.0235554

. 2021 May 10;16(5):e0235554. doi: 10.1371/journal.pone.0235554

Long-term comparison between index selection and optimal independent culling in plant breeding programs with genomic prediction

Lorena G Batista ^1,^*, Robert Chris Gaynor ², Gabriel R A Margarido ¹, Tim Byrne ³, Peter Amer ⁴, Gregor Gorjanc ², John M Hickey ²

Editor: James C Nelson⁵

PMCID: PMC8109766 PMID: 33970915

Abstract

In the context of genomic selection, we evaluated and compared breeding programs using either index selection or independent culling for recurrent selection of parents. We simulated a clonally propagated crop breeding program for 20 cycles using either independent culling or an economic index with two unfavourably correlated traits under selection. Cycle time from crossing to selection of parents was kept the same for both strategies. Both methods led to increasingly unfavourable genetic correlations between traits and, compared to independent culling, index selection led to larger changes in the genetic correlation between the two traits. When linkage disequilibrium was not considered, the two methods had similar losses of genetic diversity. Two independent culling approaches were evaluated, one using optimal culling levels and one using the same selection intensity for both traits. Optimal culling levels outperformed the same selection intensity even when traits had the same economic importance. Therefore, accurately estimating optimal culling levels is essential for maximizing gains when independent culling is performed. Once optimal culling levels are achieved, independent culling and index selection lead to comparable genetic gains.

Introduction

Crop breeding seeks to develop improved cultivars. Besides high yield levels, a successful cultivar in many crops must meet minimal standards for several other traits that are economically important, such as pest and disease resistance and product quality. Traits are often unfavourably correlated with each other [e.g., 1–5]. When traits are antagonistically correlated, selection for one trait causes an undesired economic response in the other trait [6, 7]. This makes breeding to simultaneously improve multiple traits complicated.

Independent culling and the use of a selection index are two commonly used methods in plant breeding programs for selecting for multiple traits [7]. Independent culling involves establishing minimum standards (i.e., culling levels) for each trait and selecting only individuals that meet these minimum standards. The thresholds can be set according to a specific selection intensity or a specific value, such as a value relative to an agronomic check. The application of independent culling can be to multiple traits simultaneously or to individual traits sequentially. The selection index method involves selection for all traits simultaneously based on a linear or nonlinear combination of individual traits weighted by their importance for the breeding objective [8].

Theoretically, the selection index is the most effective method of selection for multiple traits [8–10]. Independent culling is less effective than index selection because, when strictly applied, it will not select individuals below the threshold for only one trait despite being exceptional for all other traits, while the use of a selection index makes it possible to retain those individuals [7]. However, independent culling can achieve nearly equal effectiveness using optimised thresholds [11].

When cost is considered, independent culling can be more efficient than a selection index [11]. This is because independent culling does not require phenotypes for all traits at one time, whereas strict application of a selection index requires phenotypes for all traits. This benefit is particularly valuable to plant breeders, because early stages of the breeding program often have a very large number of individuals. Phenotyping all individuals for all traits is likely to be logistically and financially infeasible. For example, some traits have a high measurement cost, such as bread quality in wheat, so that they cannot be measured on a large number of individuals. Furthermore, some traits can be measured only on older plants, such as lifetime production in sugarcane, or on a plot or group basis. Delaying selection until these traits become available would be effectively equal to random selection, because the breeder would have to reduce the overall size of the early stage. Thus, practical constraints require at least some use of independent culling on traits that can be phenotyped simply/quickly and at a lower cost in breeding programs utilising phenotypic selection.

Genomic selection in plant breeding may render the cost efficiency benefit of independent culling irrelevant if all early generation individuals are genotyped. This is because genomic selection allows accurate prediction of all traits at once [12]. While genotyping all early generation individuals is not standard in most current breeding programs, it may become so in the future. This is likely to be the case if breeding programs adopt a two-part strategy to breeding that explicitly splits breeding programs into a rapid cycling, genomic selection guided, population improvement part tasked with developing new germplasm and a product development part focused on developing new varieties. Simulations of these breeding programs suggest they can deliver considerably more genetic gain than more conventional breeding programs [13].

Another reason why independent culling is often preferred over index selection is the need to correctly define the economic model for selection indices to be successful. However, what breeders often overlook is the fact that the accurate estimation of economic weights is required to maximize gains even under independent culling. This is because there is a combination of selection intensities for the traits that maximizes the genetic gain (optimal culling levels) and economic weights need to be accounted for when estimating optimal culling levels [11, 14, 15]. Therefore, regardless of the method of selection, plant breeders would benefit greatly from an increased emphasis on understanding and quantifying the economics of their species and using more analytical approaches when selecting for multiple traits.

Several studies have already shown the benefits of incorporating genomic selection strategies into crop breeding programs [13, 16–18]. Other studies have demonstrated that combining index selection and genomic prediction can increase genetic gain in breeding programs [19, 20] and, in the long term, even higher genetic gains can be obtained when multi-trait optimization strategies that also control for the loss of genetic diversity are used [21]. However, differences in how multi-trait selection methods can affect not only genetic gain but other population parameters such as genetic diversity and genetic correlations over several cycles of recurrent selection have not yet been thoroughly investigated. In order to provide a more detailed account of population dynamics in the genomic selection framework, we used simulations of recurrent breeding programs to evaluate and compare both index selection and the independent culling method for 20 cycles of selection. The purpose of these simulations was to quantify the difference between optimally set independent culling levels and an optimal selection index. The simulations also investigated the sensitivity of independent culling using a sub-optimal culling level.

Material and methods

Stochastic simulations of entire breeding programs for multiple traits were used to compare the genetic gains in a breeding program using independent culling levels and a breeding program using an economic selection index for selection of parents. In the independent culling approach, selection was performed for one trait at a time at each stage of selection. A clonally propagated crop species was considered. Generally, in breeding programs for clonally propagated species, several crosses are performed between highly heterozygous hybrids, and all the genotypes in the resulting F₁ progenies are candidate clones to be released as cultivars or used as parents in the next breeding cycle [22]. The methods were compared using the average of fifty replicates, each replicate consisting of: i) a burn-in phase shared by both strategies so that each strategy had an identical, realistic starting point; and ii) an evaluation phase that simulated future breeding with different breeding strategies. The burn-in phase consisted of 20 years of breeding using independent culling for the selection of parents and the evaluation phase consisted of 20 cycles of selection using either independent culling or index selection.

Genome sequence

For each replicate, a genome consisting of 10 chromosome pairs was simulated for the hypothetical plant species. In order to assign realistic values of simulation parameters for a crop species, we chose AlphaSimR [23] default values for wheat. The chromosomes were assigned a genetic length of 1.43 Morgans and a physical length of 8x10⁸ base pairs. Sequences for each chromosome were generated using the Markovian Coalescent Simulator [24] and AlphaSimR. Recombination rate was inferred from genome size (i.e. 1.43 Morgans / 8x10⁸ base pairs = 1.8x10^-9 per base pair), and mutation rate was set to 2x10^-9 per base pair. Effective population size was set to 50, with linear piecewise increases to 1,000 at 100 generations ago, 6,000 at 1,000 generations ago, 12,000 at 10,000 generations ago, and 32,000 at 100,000 generations ago [25].

Founder genotypes

Simulated genome sequences were used to produce 50 founder genotypes. These founder genotypes served as the initial parents in the burn-in phase. This was accomplished by randomly sampling gametes from the simulated genome to assign as sequences for the founders. Sites that were segregating in the founders’ sequences were randomly selected to serve as 1,000 causal loci per chromosome (10,000 across the genome in total). To simulate genetic correlations between traits, the traits were treated as pleiotropic and the additive effects of the causal loci alleles were sampled from a multivariate normal distribution with mean $μ = [\begin{matrix} 0 \\ 0 \end{matrix}]$ and desired values of correlation.

Estimated breeding values

The true genetic value of each simulated trait was determined by the summing of its causal loci allele effects. The matrix E with the estimated breeding values of the traits for each individual in the population was obtained according to the formula:

E = Y P^{- 1} G

where Y is the matrix of phenotypes simulated by adding random error to the true genetic values of the traits, where rows correspond to individuals in the population and columns correspond to traits. The random error was sampled from a multivariate normal distribution with mean $μ = [\begin{matrix} 0 \\ 0 \end{matrix}]$ and zero covariance, with variance values tuned to achieve a target level of accuracy (r). In this study we define accuracy as the correlation between true and estimated breeding values. P is the phenotypic variance-covariance matrix of the traits, and G is the genetic variance-covariance matrix for the traits.

Breeding methods

The simulations modelled breeding for two component traits (T1 and T2) that were improved using either independent culling or an economic selection index. With both strategies, an F₁ population of 5,000 individuals was generated in each cycle by randomly crossing the individuals in the crossing block (parents). With independent culling, selection was applied in two stages: a proportion of individuals was selected first based on T1 and then, from this proportion, the parents of the next breeding cycle were selected based on T2. With the selection index approach, the F₁ individuals with the highest values for the index trait were selected as parents of the next breeding cycle. The index trait (I) was the sum of the estimated breeding values for each trait weighted by their economic importance:

I = E w

where E is, as previously described, the matrix of estimated breeding values and w is the column vector of economic weights of the traits.

The number of selected parents (50 parents) and the cycle time from crossing to selection of new parents was kept the same for both strategies, so the comparisons between them reflect only differences due to the method of selection. The overall selection scheme used for each method of selection is shown in S1 Fig in S1 File. For simulation of breeding programs, we used the R package AlphaSimR. All codes used for the simulations are shown in S2 File.

Simulated scenarios

The selection index and independent culling methods were compared in a set of scenarios that aimed to assess the relative performance of the methods under different levels of accuracy of selection, and relative economic importance of T2. We were interested in investigating only the relative performance of selection methods under challenging conditions for multi-trait selection. For this reason, only an unfavourable genetic correlation between traits was simulated. We used a value of -0.50 for the genetic correlation. A summary of all simulated scenarios we used in this study is shown in Table 1.

Table 1. Summary of parameters simulated in all comparison scenarios of recurrent selection breeding programs using either independent culling or selection index with two traits.

Scenario	Selected Proportion		Relative economic importance of Trait 2	Accuracy
Scenario	Trait 1	Trait 2	Relative economic importance of Trait 2	Accuracy
1	Optimum	Optimum	1.0	0.3
2	Optimum	Optimum	1.0	0.5
3	Optimum	Optimum	1.0	0.99
4	Optimum	Optimum	1.0	0.7
5	Optimum	Optimum	2.5	0.7
6	Optimum	Optimum	5.0	0.7
7	10%	10%	1.0	0.7
8	10%	10%	2.5	0.7
9	10%	10%	5.0	0.7

Open in a new tab

For one set of scenarios we simulated four levels of accuracy (0.3, 0.5, 0.7, and 0.99) and assigned the same economic importance for both traits. In another set of scenarios, we varied the relative economic importance of T2, but fixed selection accuracy at 0.7. Three levels of relative economic importance were simulated. T1 was given an economic importance of 1.0 and T2 an economic importance of either 1.0, 2.5 or 5.0. For each level of relative economic importance, we simulated: i) scenarios where the proportion selected was the same (10%) for both traits, and ii) scenarios where the proportions selected were set to achieve optimal culling levels (i.e., optimal independent culling). To find the optimal proportions at each cycle, we fixed the number of parents selected (50 parents) and found the number of individuals to be selected in the first culling stage that maximized parents’ economic value (measured as the index trait)., which was obtained based on the estimated breeding values. Thus, over the cycles of selection, when using optimal culling levels, instead of a fixed proportion selected of 10%, the proportion selected for each trait varied between cycles.

Comparison

The comparisons were made in terms of: i) genetic gain ii) genetic diversity, iii) the efficiency of converting genetic diversity into genetic gain for the index; and iv) genetic correlation between traits. For genetic gain and genetic diversity, we report values based on the individuals in the crossing block (parents) at each cycle of selection. We measured genetic gain as the increment in genetic mean (average of true genetic values) compared to the genetic mean in year 20. We measured genetic diversity with genetic standard deviation and genic standard deviation. We calculated genetic standard deviation as standard deviation of true genetic values. We calculated genic standard deviation as $σ_{a} = \sqrt{2 \sum_{i = 1}^{n_{q}} p_{i} (1 - p_{i}) α_{i}^{2}}$ , where n_q is the number of causal loci and p_i and α_i are, respectively, allele frequency and allele substitution effect at the i-th causal locus.

To measure efficiency, genetic mean and genic standard deviation were standardized to mean zero and unit standard deviation in year 20. We measured efficiency of converting genetic diversity into genetic gain by regressing the achieved genetic mean ( $y_{t} = (μ_{a_{t}} - μ_{a_{20}}) / σ_{a_{20}}^{2}$ ) on lost genetic diversity ( $x_{t} = 1 - σ_{a_{t}} / σ_{a_{20}}$ ), i.e., y_t = α+bx_t+e_t, where b is efficiency [26]. We estimated efficiency with robust regression using function rlm() in R [27].

For genetic correlation, we report the correlation between the true genetic values of T1 and T2. We calculated this metric on the individuals in the F₁ population at each cycle of selection.

Results

Index selection provided consistent genetic gains and was equivalent to independent culling in terms of genetic gains and efficiency when optimal culling levels were used. Index selection performed better than independent culling in scenarios where independent culling was performed using the same selection intensity for each trait.

We have structured the description of the results in two parts, corresponding to how the relative performance of the selection methods was affected by: i) the accuracy of selection, and ii) the relative economic importance of traits.

Accuracy of selection

Increases in accuracy accentuated the differences in the genotypes being selected by either independent culling or index selection. This is shown in Fig 1, where the genotypes selected as parents by each selection method are highlighted. Lower levels of accuracy led to a more diffuse cluster of selected genotypes and, with increasing selection accuracy, the cluster of selected genotypes approached what was expected for each method of selection [7].

Fig 1 — Scatterplots of true genetic values for Trait 1 (T1) and Trait 2 (T2) of the genotypes in the F1 population (grey) and genotypes selected as parents (orange) in the third cycle of selection using either independent culling (a) or a selection index (b) with different levels of accuracy.

Fig 2 shows the change in the genetic correlation between the component traits for both independent culling and index selection over 20 cycles of selection at different levels of accuracy. Both selection methods resulted in the correlation between traits becoming increasingly unfavourable over the cycles of selection. For both methods, the change in the genetic correlation increased with higher values of accuracy. Compared to independent culling, index selection led to larger changes in the genetic correlation between the two traits. After 20 cycles of selection with accuracy of 0.3, independent culling led to a genetic correlation that was 9% more unfavourable than the genetic correlation in cycle 0, while index selection led to a genetic correlation that was 17% more unfavourable than the genetic correlation in cycle 0. After 20 cycles of selection with accuracy of 0.99, independent culling led to a genetic correlation that was 29% more unfavourable than the genetic correlation in cycle 0, while index selection led to a genetic correlation that was 64% more unfavourable than the genetic correlation in cycle 0.

The change of genetic mean in parents for the component traits and the index trait over the cycles of selection using each method is shown in Fig 3. For both methods, the genetic gains for the component traits and the index trait increased with higher values of accuracy. In general, the selection index method and independent culling with optimal culling levels led to equivalent genetic gains for the component traits and the index trait. Only in the scenario with 0.99 accuracy did index selection lead to a slightly higher genetic gain than that achieved with optimal independent culling. For the index trait, after 20 cycles of selection with accuracy of 0.99, index selection had a genetic gain 4% higher than the genetic gain achieved with independent culling.

Table 2 shows the genetic standard deviation of parents in cycle 20 and the loss in genetic standard deviation in cycle 20 compared to the genetic standard deviation in cycle 0 for the component traits and the index trait. The change of genetic diversity in parents for the component traits and the index trait over the cycles of selection using each method is shown in S2 Fig in S1 File. For the component traits, under index selection, the genetic standard deviation showed an initial increase in the first few cycles of selection followed by a gradual decrease in the subsequent cycles. Under independent culling, the decrease in the genetic standard deviation of the component traits was continual over the cycles of selection. Both of these trends were more obvious with increasing values of accuracy. For all values of accuracy, independent culling led to a higher loss in the genetic standard deviation of the component traits compared to the index selection. For T1 and T2, independent culling with accuracy of 0.3 led to losses of genetic standard deviation that were respectively 6% and 5% higher than the loss of genetic standard deviation observed for index selection. With accuracy of 0.99, for T1 and T2 independent culling led to losses of genetic standard deviation that were respectively 65% and 51% higher than the losses of genetic standard deviation observed for index selection. For the index trait, both methods led to equivalent values of genetic standard deviation. With accuracies of 0.3 and 0.99, index selection led to a loss in the genetic standard deviation of the index trait that was 3% higher than the loss of genetic standard deviation observed using independent culling.

Table 2. Mean genetic standard deviation (Genetic SD) of parents in cycle 20 and loss in genetic standard deviation in cycle 20 in comparison to the genetic standard deviation in cycle 0 (Loss over cycle 0) for trait 1 (T1), trait 2 (T2) and the index trait using either optimal independent culling or index selection with different levels of accuracy, unfavourably correlated traits, and T2 relative economic importance of 1.0.

	Independent culling
	T1		T2		Index trait
Accuracy	Genetic SD (cycle 20)	Loss over cycle 0	Genetic SD (cycle 20)	Loss over cycle 0	Genetic SD (cycle 20)	Loss over cycle 0
0.3	3.51 (0.08)^*	-17%	3.68 (0.08)	-16%	3.57 (0.06)	-22%
0.5	2.56 (0.06)	-30%	2.45 (0.04)	-28%	2.69 (0.05)	-32%
0.7	1.65 (0.04)	-42%	1.64 (0.03)	-37%	1.88 (0.04)	-45%
0.99	0.45 (0.01)	-68%	0.45 (0.01)	-55%	0.74 (0.02)	-62%
	Index Selection
	T1		T2		Index trait
Accuracy	Genetic SD (cycle 20)	Loss over cycle 0	Genetic SD (cycle 20)	Loss over cycle 0	Genetic SD (cycle 20)	Loss over cycle 0
0.3	3.80 (0.09)	-11%	4.00 (0.09)	-11%	3.66 (0.08)	-19%
0.5	3.19 (0.08)	-17%	3.19 (0.07)	-14%	2.57 (0.06)	-33%
0.7	2.69 (0.06)	-16%	2.60 (0.06)	-18%	1.86 (0.04)	-41%
0.99	1.93 (0.4)	-3%	1.91 (0.04)	-4%	0.51 (0.01)	-59%

Open in a new tab

* standard errors of the estimates are presented in parenthesis.

Table 3 shows the genic standard deviation of parents in cycle 20 and the loss in genic standard deviation in cycle 20 compared to the genic standard deviation in cycle 0 for the component traits and the index trait. The values of genic standard deviation of T1, T2, and the index trait were similar. The highest difference between methods in the loss in genic standard deviation was 1% for all values of accuracy, except with accuracy of 0.99. With 0.99 accuracy, for T1, T2 and the index trait, index selection led to a loss in the genic standard deviation that was 3% higher than the loss of genic standard deviation observed using independent culling.

Table 3. Genic standard deviation (Genic SD) of parents in cycle 20 and loss in genic standard deviation in cycle 20 in comparison to the genic standard deviation in cycle 0 (Loss over cycle 0) for trait 1 (T1), trait 2 (T2) and the index trait using either optimal independent culling or index selection with different levels of accuracy, unfavourably correlated traits, and T2 relative economic importance of 1.0.

	Independent culling
	T1		T2		Index trait
Accuracy	Genic SD (cycle 20)	Loss over cycle 0	Genic SD (cycle 20)	Loss over cycle 0	Genic SD (cycle 20)	Loss over cycle 0
0.3	3.94 (0.06)^*	-15%	4.11 (0.07)	-15%	4.04 (0.05)	-16%
0.5	3.48 (0.06)	-24%	3.41 (0.05)	-24%	3.44 (0.04)	-25%
0.7	2.94 (0.04)	-34%	2.89 (0.04)	-34%	2.89 (0.04)	-34%
0.99	2.35 (0.04)	-42%	2.35 (0.04)	-42%	2.33 (0.04)	-43%
	Index Selection
	T1		T2		Index trait
Accuracy	Genic SD (cycle 20)	Loss over cycle 0	Genic SD (cycle 20)	Loss over cycle 0	Genic SD (cycle 20)	Loss over cycle 0
0.3	3.92 (0.06)	-16%	4.08 (0.07)	-16%	4.02 (0.05)	-16%
0.5	3.44 (0.06)	-25%	3.37 (0.05)	-25%	3.39 (0.05)	-26%
0.7	2.92 (0.05)	-34%	2.88 (0.05)	-34%	2.87 (0.04)	-35%
0.99	2.21 (0.04)	-45%	2.22 (0.04)	-45%	2.17 (0.03)	-46%

Open in a new tab

* standard errors of the estimates are presented in parenthesis.

Relative economic importance of traits

Fig 4 shows the efficiency of converting genetic diversity into genetic gain for the index trait when the relative economic importance of T2 varies. Independent culling was compared to index selection using either optimal culling levels or selection with the same proportion of plants selected (10%) for each trait. Index selection had the highest efficiency and most gain for all levels of economic importance. The efficiency and gain for optimal independent culling levels were nearly equal to those of index selection. The efficiency and gain for selecting the same proportion of plants for both traits were lower than those of index selection for all levels of relative economic importances. Index selection was 10%, 128% and 310% more efficient than independent culling using the same proportion of selected plants for relative economic importance of 1.0, 2.5 and 5.0, respectively.

Fig 4 also shows the proportion of plants selected for T1 under optimal independent culling over the different levels of economic importance for T2. The mean proportion selected for T1 varied only slightly over the cycles of selection. The means were 29%, 93%, and 99% for relative economic importances of 1.0, 2.5, and 5.0, respectively. The variation about those means was largest with relative economic importance of 1.0 and smallest with relative economic importance of 5.0.

Discussion

This study evaluated and compared breeding programs that use either index selection or independent culling for the recurrent selection of parents by genomic prediction. Index selection was either better than or equivalent to independent culling in this context. Index selection outperformed independent culling when a sub-optimal culling level was used.

The main difference between index selection and independent culling is that, under index selection, genotypes that are exceptional for one of the traits under selection are more likely to be selected even though their performance for other traits is average. This can be seen in Fig 1, with the cluster of individuals selected as parents with the index method including individuals that are more contrasting for the two traits under selection than the individuals selected with independent culling. The main implications of this are in the way each method affects the correlation between traits and the genetic diversity over cycles of recurrent selection. We discuss each of these aspects in the following two sections. Lastly, we discuss how the relative economic importance of the traits can affect the relative performance of the methods.

Methods of selection and genetic correlation between traits

After only a few cycles of selection, index selection generates F₁ populations with a more unfavourable genetic correlation between traits than the F₁ populations generated by independent culling (Fig 2). An explanation for the faster decrease of the genetic correlation observed with index selection is that the index is a linear combination of component traits. As shown by Bulmer [28], selection on a linear combination leads to negative covariances between components (the Bulmer effect). Consequently, the same principle applies to the component traits and index selection, with index selection leading to an unfavourable genetic correlation between the component traits [29, 30].

In general, genetic gains in multi-trait selection, regardless of the method of selection, are expected to be higher when the correlation between traits is favourable and lower when this correlation is unfavourable [9]. As index selection generated F₁ populations with more unfavourable genetic correlation between traits than independent culling, the genetic gains for index selection were potentially lower than for independent culling. Nevertheless, despite index selection being carried out under increasingly unfavourable genetic correlations over the cycles, the genetic gains obtained for the index trait were equivalent to the gains obtained using independent culling (Fig 3).

Over the cycles of selection, both independent culling and index selection resulted in increasingly unfavourable genetic correlations between traits. Generally, it is assumed that unfavourable genetic correlations that cannot be broken after repeated cycles of recombination are likely due to pleiotropy. This is assumed to be the case in several crops, e.g., grain yield and protein content in cereal crops [31–33], quality and disease resistance in forage crops [34], and yield and disease resistance in barley [35]. However, the extent of the genetic correlation due to pleiotropy in these examples is unknown because, as our study demonstrates, unfavourable genetic correlations between the traits could also be, at least partly, induced by selection.

Methods of selection and genetic diversity over cycles of selection

According to Bulmer [28], reduction in the genetic variance due to selection stems mostly from the build-up of negative linkage disequilibrium between causal loci when selection is performed. This can be seen by comparing genetic and genic variation (Tables 2 and 3, respectively). Genic variation is a function of the allele frequencies and the allele substitution effect only, and thus is not affected by changes in linkage disequilibrium. The results in Table 3 show that the losses of genic standard deviation of the component traits and index trait were not greatly affected by the method of selection. Also, the method of selection did not greatly affect the trait means, as shown in Fig 3. This indicates that, in terms of allele frequencies, there was little difference in the parents selected by either independent culling or selection index in situations similar to our simulation. Therefore, the difference between the selection methods derives from how they induce and exploit linkage disequilibrium between the causal variants of the component traits. Specifically, as shown in Table 2, independent culling induced a greater degree of negative linkage disequilibrium between the causal variants of the component traits resulting in those traits having less genetic variation. A deviation from this result is expected with more intense selection schemes and more component traits selected in successive stages, which would induce larger changes in allele frequencies due to drift. As a consequence, differences between index selection and independent culling would be accentuated. In a previous study [36], the authors simulated and compared wheat breeding programs using different selection strategies under high and low selection intensities. They observed that index selection resulted in higher population coancestry over cycles of selection than independent culling, and the difference between methods increased in scenarios with high selection intensity. Their results indicate that index selection leads to a higher loss of genic standard deviation.

Somewhat surprisingly, it is possible to make an argument for the superiority of independent culling relative to a selection index on the basis of the differences observed in linkage disequilibrium. This is because independent culling produced populations with nearly equal mean performance, but with more consistent performance between individuals, as demonstrated by the lower variation observed for the component traits. This property could be beneficial from a management perspective if differences in the component traits require variations in management of individuals. Breeding for plant-architecture traits in outbreeding cultivars is a good example where this property might be valuable, as having more uniform plants in the field favours mechanical harvest. However, we believe this property is more of an academic curiosity than something that will have practical application.

For simplicity and ease of implementation, our simulations considered the same genetic architecture for both traits, with both traits being controlled by a high number (10,000) of causal loci with small additive effects. Under different circumstances, such as at least one of the traits being controlled by few causal loci with higher allele substitution effects, different results could be expected. The results for the two-locus model in [37] show that independent culling tends to eliminate genotypes that are homozygous for alleles with low effect for one of the traits. For one pleiotropic causal locus, when both alleles are favourable for one trait and unfavourable for the other trait, both homozygous genotypes tend to be culled, and independent culling would select the heterozygous genotypes. If heterozygous genotypes were preferred, the fixation of alleles would be slower and, therefore, the loss in genic standard deviation would be lower. Our results indicate that, for highly polygenic traits, differences between methods of selection in the loss of genetic diversity are mostly due to changes in linkage disequilibrium as opposed to distinct changes in allele frequencies. Therefore, in terms of conserving genetic diversity there was no obvious advantage for either method. Other strategies such as optimal-cross selection [26, 36, 38, 39] or the multi-objective optimized approach [21] should be considered in order to optimize gains while also controlling the loss of genetic diversity over cycles of selection.

Economic importance of the traits

In general, when the same selection intensity is applied to both traits, index selection will perform better than independent culling as the difference in the economic importance of the traits increases (Fig 4). Optimal independent culling performed better than independent culling using the same selection intensity for both traits for all levels of relative economic importance, including the scenario where traits had the same economic importance. The results in Fig 4 show that, when traits had the same economic importance, independent culling approached its maximal gain when a higher selection intensity was used for T1 and a lower selection intensity was used for T2. This indicates that the economic importance of the traits is not the only factor affecting the estimates of optimal culling levels and that accurately estimating them is essential for maximizing gains when independent culling is performed. The results also show that the effect of the economic importance of the traits in the estimates of optimal culling levels becomes more pronounced with increasing differences in the economic importance of the traits. In fact, when one trait had 5 times the economic importance of the other trait, the optimum was achieved when almost no selection was applied for the less important trait.

Our results show that the two ways of incorporating the true economic weights of the traits in the selection process, either by optimal culling levels or a selection index, lead to nearly equal genetic gains. However, it is worth noting that optimal independent culling would require the complex estimation of optimal culling levels for each trait [11, 14, 15]. When parents are selected based on an index, optimal gain is achieved by simply summing the values of the traits weighted by their economic importance, a much simpler way of maximizing genetic gains in a breeding program.

There is little to no evidence suggesting that plant breeders use analytical techniques to determine optimal independent culling thresholds and/or constructing selection indices in most plant breeding programs. More likely, the majority of breeders rely on their intuition for setting thresholds and constructing indices. Their decisions are likely guided by the performance of agronomic checks and are prone to fluctuations between seasons and individual breeders. This model has clearly been successful, because plant breeding programs have continued to deliver genetic gain. However, it is likely sub-optimal, and the value of a more analytical approach becomes greater as genomic selection is more widely used.

Conclusions

We evaluated and compared breeding programs using either independent culling or index selection for recurrent parent selection with genomic prediction. Even in the presence of unfavourable genetic correlations, index selection achieved genetic gains equal to or greater than those achieved with independent culling in all simulated scenarios. In terms of genetic diversity, the differences between methods in the studied system were driven mostly by differences in the generation of linkage disequilibrium between causal loci induced and not by differences in allele frequencies. When linkage disequilibrium was not considered, the two methods had similar losses of genetic diversity, and the differences in efficiency of converting genetic diversity into genetic gains between the methods mostly reflected the differences in the genetic gains obtained with each method. To obtain higher genetic gains, accurately estimating optimal culling levels is essential for maximizing gains when independent culling is performed. Once optimal culling levels are estimated, independent culling and index selection lead to nearly equal genetic gains.

Supporting information

S1 File

(DOCX)

Click here for additional data file.^{(783.1KB, docx)}

S2 File

(PDF)

Click here for additional data file.^{(142.2KB, pdf)}

Data Availability

All relevant data are within the manuscript and its Supporting Information files.

Funding Statement

LGB was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Computational Biology Programme, Grant No. BEX 0043/17-6, Finance Code 001). JMH, RCG and GG acknowledge the financial support from BBSRC and KWS UK, RAGT Seeds Ltd., Elsoms Wheat Ltd and Limagrain UK for the project “GplusE: Genomic selection and Environment modelling for next generation wheat breeding” (grants BB/L022141/1 and BB/L020467/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The funder Abacusbio provided support in the form of salaries for authors TB and PA but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.

References

1.Kwon SH, Torrie JH. Heritability of and interrekationships among traits of two soybean population. 1964. [Google Scholar]
2.Meredith WR, Bridge RR. Breakup of Linkage Blocks in Cotton, Gossypium hirsutum L.1. Crop Science. 1971;11:695–8. [Google Scholar]
3.Erskine W, Williams PC, Nakkoul H. Genetic and environmental variation in seed yield, seed size and cooking quality of lentil. Field Crops Research. 1985;12:153–61. [Google Scholar]
4.Kato T, Takeda K. Associations among Characters Related to Yield Sink Capacity in Space-Planted Rice. Crop Science. 1996;36:1135–9. [Google Scholar]
5.Triboi E, Martre P, Girousse C, Ravel C, Triboi-Blondel AM. Unravelling environmental and genetic relationships between grain yield and nitrogen concentration for wheat. European Journal of Agronomy. 2006;25(2):108–18. [Google Scholar]
6.Falconer DS, Mackay TF, Frankham R. Introduction to Quantitative Genetics (4th edn). Trends in Genetics. 1996;12(7):280. [Google Scholar]
7.Bernardo R. Breeding for quantitative traits in plants. 1st ed. Woodbury: Stemma Press; 2010. 390 p. [Google Scholar]
8.Hazel LN, Lush JL. The Efficiency of Three Methods of Selection. Journal of Heredity. 1942;33(11):393–9. [Google Scholar]
9.Young S. A further examination of the relative efficiency of three methods of selection for genetic gains under less-restricted conditions. Genetical Research Cambridge. 1961;2(1961):106–21. [Google Scholar]
10.Pesek J, Baker RJ. Comparison of tandem and index selection in the modified pedigree method of breeding self-pollinated species. Canadian Journal of Plant Science. 1969. November;49(6):773–81. [Google Scholar]
11.Xu S, Muir WM. Multistage Selection for Genetic Gain by Orthogonal Transformation. Genetics. 1991. November;129(3):963–74. [DOI] [PMC free article] [PubMed] [Google Scholar]
12.Meuwissen THE, Hayes BJ, Goddard ME. Prediction of total genetic value using genome-wide dense marker maps. Genetics. 2001;157(4):1819–29. [DOI] [PMC free article] [PubMed] [Google Scholar]
13.Gaynor RC, Gorjanc G, Bentley AR, Ober ES, Howell P, Jackson R, et al. A Two-Part Strategy for Using Genomic Selection to Develop Inbred Lines. Crop Science. 2017;57:2372–86. [Google Scholar]
14.Saxton AM. INDCULL Version 3.0: Independent Culling for Two or More Traits. Journal of Heredity. 1989. March 1;80(2):166–7. [Google Scholar]
15.Ducrocq V, Colleau JJ. Optimum truncation points for independent culling level selection on a multivariate normal distribution, with an application to dairy cattle selection. Genetics Selection Evolution. 1989. June 15;21(2):185. [Google Scholar]
16.Bernardo R, Yu J (2007) Prospects for Genomewide Selection for Quantitative Traits in Maize. Crop Science 47:1082–1090. 10.2135/cropsci2006.11.0690 [DOI] [Google Scholar]
17.Heffner EL, Sorrells ME, Jannink J-L (2009) Genomic Selection for Crop Improvement. Crop Science 49:1–12. 10.2135/cropsci2008.08.0512 [DOI] [Google Scholar]
18.Hickey JM, Chiurugwi T, Mackay I, Powell W, Participants IGS in CBPW. Genomic prediction unifies animal and plant breeding programs to form platforms for biological discovery. Nature Genetics. 2017. August 30;49:1297. 10.1038/ng.3920 [DOI] [PubMed] [Google Scholar]
19.Slavov GT, Davey CL, Bosch M, Robson PRH, Donnison IS, Mackay IJ. Genomic index selection provides a pragmatic framework for setting and refining multi-objective breeding targets in Miscanthus. Annals of Botany [Internet]. 2018. October 23 [cited 2019 Jun 9]; Available from: https://academic.oup.com/aob/advance-article/doi/10.1093/aob/mcy187/5142550 [DOI] [PMC free article] [PubMed] [Google Scholar]
20.Michel S, Löschenberger F, Ametz C, Pachler B, Sparry E, Bürstmayr H. Simultaneous selection for grain yield and protein content in genomics-assisted wheat breeding. Theoretical and Applied Genetics. 2019. June;132(6):1745–60. 10.1007/s00122-019-03312-5 [DOI] [PMC free article] [PubMed] [Google Scholar]
21.Akdemir D, Beavis W, Fritsche-Neto R, Singh AK, Isidro-Sánchez J. Multi-objective optimized genomic breeding strategies for sustainable food improvement. Heredity. 2019. May;122(5):672–83. 10.1038/s41437-018-0147-1 [DOI] [PMC free article] [PubMed] [Google Scholar]
22.Grüneberg W, Mwanga R, Andrade M, Espinoza J. Selection methods. Part 5: Breeding clonally propagated crops. Plant Breeding and Farmer Participation. 2009;(April):275–322. [Google Scholar]
23.Gaynor RC, Gorjanc G, Wilson DL. AlphaSimR: An R Package for Breeding Program Simulations. Manuscr Prep. [DOI] [PMC free article] [PubMed] [Google Scholar]
24.Chen GK, Marjoram P, Wall JD. Fast and flexible simulation of DNA sequence data. Genome research. 2009;19(1):136–42. 10.1101/gr.083634.108 [DOI] [PMC free article] [PubMed] [Google Scholar]
25.Thuillet A-C, Bataillon T, Poirier S, Santoni S, David JL. Estimation of long-term effective population sizes through the history of durum wheat using microsatellite data. Genetics. 2005;169(3):1589–99. 10.1534/genetics.104.029553 [DOI] [PMC free article] [PubMed] [Google Scholar]
26.Gorjanc G, Gaynor RC, Hickey JM. Optimal cross selection for long-term genetic gain in two- part programs with rapid recurrent genomic selection. bioRxiv. 2017; [DOI] [PMC free article] [PubMed] [Google Scholar]
27.Venables WN, Ripley BD. Modern Applied Statistics with S. Fourth Edi. New York: Springer; 2002. [Google Scholar]
28.Bulmer MG (1971) The effect of selection on genetic variability. 105:1–88 [Google Scholar]
29.Tallis GM. Ancestral covariance and the Bulmer effect. Theoretical and Applied Genetics. 1987;73(6):815–20. 10.1007/BF00289384 [DOI] [PubMed] [Google Scholar]
30.Itoh Y. Changes in genetic correlations by index selection. Genetics selection evolution GSE. 1991;23(4):301–8. [Google Scholar]
31.Duvick DN, Cassman KG. Post–Green Revolution Trends in Yield Potential of Temperate Maize in the North-Central United States. Crop Science. 1999;39:1622–30. [Google Scholar]
32.Rharrabti Y, Elhani S, Martos-Núñez V, García del Moral LF. Protein and Lysine Content, Grain Yield, and Other Technological Traits in Durum Wheat under Mediterranean Conditions. Journal of Agricultural and Food Chemistry. 2001. August 1;49(8):3802–7. 10.1021/jf001139w [DOI] [PubMed] [Google Scholar]
33.Rotundo JL, Borrás L, Westgate ME, Orf JH. Relationship between assimilate supply per seed during seed filling and soybean seed composition. Field Crops Research. 2009;112(1):90–6. [Google Scholar]
34.Casler MD, Vogel KP. Accomplishments and Impact from Breeding for Increased Forage Nutritional Value. Crop Science. 1999;39:12–20. [Google Scholar]
35.Smedegaard-Petersen V, Tolstrup K. The Limiting Effect of Disease Resistance on Yield. Annual Review of Phytopathology. 1985;23(1):475–90. [Google Scholar]
36.Cowling W, Li L. Turning the heat up on independent culling in crop breeding. 2018. 119–134 p. [Google Scholar]
37.Bennett G, Swiger L. Genetic variance and correlation after selection for two traits by index, independent culling levels and extreme selection. Genetics. 1980;94(3):763–75. [DOI] [PMC free article] [PubMed] [Google Scholar]
38.Clark SA, Kinghorn BP, Hickey JM, Van Der Werf JHJ. The effect of genomic information on optimal contribution selection in livestock breeding programs. Genetics Selection Evolution. 2013;45(1):1–8. 10.1186/1297-9686-45-44 [DOI] [PMC free article] [PubMed] [Google Scholar]
39.Woolliams JA, Berg P, Dagnachew BS, Meuwissen THE. Genetic contributions and their optimization. Journal of Animal Breeding and Genetics. 2015. April;132(2):89–99. 10.1111/jbg.12148 [DOI] [PubMed] [Google Scholar]

PLoS One. doi: 10.1371/journal.pone.0235554.r001

Decision Letter 0

Roberto Fritsche-Neto

2 Apr 2020

PONE-D-20-04603

An economic selection index should be used instead of independent culling in plant breeding programs with genomic selection

PLOS ONE

Dear Dr. Batista,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

We would appreciate receiving your revised manuscript by May 17 2020 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.
A marked-up copy of your manuscript that highlights changes made to the original version. This file should be uploaded as separate file and labeled 'Revised Manuscript with Track Changes'.
An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

We look forward to receiving your revised manuscript.

Kind regards,

Roberto Fritsche-Neto, Ph.D.

Academic Editor

PLOS ONE

Journal requirements:

When submitting your revision, we need you to address these additional requirements:

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at http://www.plosone.org/attachments/PLOSOne_formatting_sample_main_body.pdf and http://www.plosone.org/attachments/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. Thank you for stating the following in the Competing Interests section:

"The authors have declared that no competing interests exist."

We note that one or more of the authors are employed by a commercial company: Abacusbio.

1. Please provide an amended Funding Statement declaring this commercial affiliation, as well as a statement regarding the Role of Funders in your study. If the funding organization did not play a role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript and only provided financial support in the form of authors' salaries and/or research materials, please review your statements relating to the author contributions, and ensure you have specifically and accurately indicated the role(s) that these authors had in your study. You can update author roles in the Author Contributions section of the online submission form.

Please also include the following statement within your amended Funding Statement.

“The funder provided support in the form of salaries for authors [insert relevant initials], but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.”

If your commercial affiliation did play a role in your study, please state and explain this role within your updated Funding Statement.

2. Please also provide an updated Competing Interests Statement declaring this commercial affiliation along with any other relevant declarations relating to employment, consultancy, patents, products in development, or marketed products, etc.

Within your Competing Interests Statement, please confirm that this commercial affiliation does not alter your adherence to all PLOS ONE policies on sharing data and materials by including the following statement: "This does not alter our adherence to PLOS ONE policies on sharing data and materials.” (as detailed online in our guide for authors http://journals.plos.org/plosone/s/competing-interests) . If this adherence statement is not accurate and there are restrictions on sharing of data and/or materials, please state these. Please note that we cannot proceed with consideration of your article until this information has been declared.

Please include both an updated Funding Statement and Competing Interests Statement in your cover letter. We will change the online submission form on your behalf.

Please know it is PLOS ONE policy for corresponding authors to declare, on behalf of all authors, all potential competing interests for the purposes of transparency. PLOS defines a competing interest as anything that interferes with, or could reasonably be perceived as interfering with, the full and objective presentation, peer review, editorial decision-making, or publication of research or non-research articles submitted to one of the journals. Competing interests can be financial or non-financial, professional, or personal. Competing interests can arise in relationship to an organization or another person. Please follow this link to our website for more details on competing interests: http://journals.plos.org/plosone/s/competing-interests

3. Thank you for stating the following financial disclosure:

"LGB was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Computational Biology Programme, Grant No. BEX 0043/17-6). JMH, RCG and GG acknowledge the financial support from BBSRC and KWS UK, RAGT Seeds Ltd., Elsoms Wheat Ltd and Limagrain UK for the project “GplusE: Genomic selection and Environment modelling for next generation wheat breeding” (grants BB/L022141/1 and BB/L020467/1)."

Please state what role the funders took in the study. If the funders had no role, please state: "The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript."

If this statement is not correct you must amend it as needed.

Please include this amended Role of Funder statement in your cover letter; we will change the online submission form on your behalf.

4. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The study idea is good. However, there are some points in the text that should be better described or explained. They are all highlighted in the text. My main objection to the study is to have considered/simulated a very specific selection condition for such a broad objective. In my opinion, the simulated condition responds only to one condition, which involves negatively correlated traits. The correlation between traits is not always negative, nor is it caused by pleiotropy. Thus, it cannot be extrapolated to the whole as the study intends. I suggest that the title, objective and discussion be adjusted to a more restricted selection situation and not as wide as the study contemplated.

Reviewer #2: Review for: An economic selection index should be used instead of independent culling in plant breeding programs with genomic selection

This paper compares two different selection strategies, namely, independent culling and index selection in the context of multi-trait genomic selection. Simulations have been performed for two negatively correlated traits over 20 cycles of breeding for 9 different scenarios with varying selection accuracy and relative economic importance. Results demonstrate, given the economic importance of each trait, maximum genetic gains are more easily achieved with index selection. This study does not provide any new approach or methodology in terms of multi-trait selection and assumes the accurate knowledge of economic importance of traits. However, the reviewer believes it can be useful to the practitioners of genomic selection.

The manuscript is generally well written, and the discussions seem sound. There are some typos throughout the paper which would benefit from proofreading. The figures are not very clear, the authors should provide figures with a higher resolution.

Here are a few specific comments, suggestions and discussion points:

L93-94: What if we select for both traits simultaneously?

L142: It would be worthwhile to consider nonlinear selection indices as well.

L143-147: How are the selected parents mated? Does AlphaSimR have any strategies for mating?

L153: Report the correlation value between two traits.

L155, Table 1: What are the optimum values? These values should be reported. Figure 4 has demonstrated the proportion selected for different relative economic importance, but it would be better to report these variables earlier when showing the results in Table 1.

L203, Figure 1: This Figure demonstrates the genetic values for the selected parents and the F1 population for both traits in the 3rd cycle. It will be interesting to see the same Figure for the final generation (the 20th cycle).

L220, Figure 2: For 0.99 accuracy, the correlation has decreased in the first cycle when using independent culling. How do you describe/interpret that?

L299: The proportion of selected parents for REI=5 is 99%. I wonder what happens if we have a large REI, say 20.

Data availability: Is the simulated data available? I couldn’t find any source links to that.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

Attachment

Submitted filename: PONE-D-20-04603_reviewer.pdf

Click here for additional data file.^{(1.6MB, pdf)}

PLoS One. 2021 May 10;16(5):e0235554. doi: 10.1371/journal.pone.0235554.r002

Author response to Decision Letter 0

16 May 2020

Thank you for these comments. We feel that they have improved the manuscript.

We have dealt with each of the comments. In what follows we describe our response and give a line number to each change made in the manuscript. For ease of review these changes are also highlighted in yellow in the resubmitted manuscript.

Response: The reviewer has a fair point. In the beginning of the development of the study we also simulated scenarios with favourably correlated traits. However, the results showed the same patterns observed for unfavourably correlated traits, only less pronounced, as there were more coincidences in the individuals being selected by the two methods (which is expected when traits are favourably correlated). We chose to keep the results that made more evident the differences between methods. Besides that, unfavourable genetic correlations are ubiquitous in breeding programs and are the main challenge faced by breeders deploying multi-trait selection. Both in our introduction (L36) and discussion (L385-387) we provide evidence of unfavourable genetic correlations between traits occurring in several economically important crops.

Given that the scenarios investigated in this study are relevant to the great majority of breeding programs, we consider our title to be appropriate even if we do not show results for other specific scenarios. We have however added clarifications to the introduction (L93) and to the discussion (L379-382) and also added a figure with results from a scenario with favourably correlated traits to our supplementary material.

L55 - Reviewer comment:

“But in traditional breeding, individuals without information are penalized and may not be selected, correct?

Is your claim in the context of genomic selection? I suggest detailing more!”

Response: This claim was made in the context of phenotypic selection. The purpose of the sentence is to compare independent culling to index selection. Index selection requires phenotypes for all traits to be available, whereas with independent culling selection can be made one trait at a time. To make this distinction clearer, we have removed “for all individuals” from the sentence (L55)

L67: Reviewer comment (highlighted the word “render”):“to better?”

Response: We have changed the word “render” to “result in” (L67)

L110-112: Reviewer comment: “Measures with based on any study?”

Response: The reviewer has a fair point.

These are AlphaSimR default values for the species “wheat”. Given that our goal was to simulate a hypothetical crop species, we considered realistic to use values already observed for a commercial crop such as wheat. We made that explicit and also included the reference:

L111-118

L119-120: Reviewer comment

“It was not clear to me why the traits were treated as pleiotropic.

This may have generated negative correlations between traits over the generations. But it is not a situation that can be generalized.

Needs explanations!”

Response: The reviewer has a valid point. AlphaSimR only simulates pleiotropic traits, but we believe our results can still be generalized for quantitative traits.

In our simulations we have 10,000 causal loci, each with a specific additive allele effect for each simulated trait. These allele effects are randomly assigned, resulting in loci having many possible combinations of additive effects for each trait. The loci can be assigned additive effects with the same sign (positive or negative) for both traits, they can be assigned additive effects with opposite signs for the traits, and they can be assigned additive effects with varying absolute values for each trait (i.e. a high effect for one trait and a low effect for the other trait). These are all realistic assumptions under the infinitesimal model, where both traits are controlled by an infinite number of loci with different additive effects for each trait. It also means that although QTL are pleiotropic, they are implicitly acting as non-pleiotropic (i.e., genetic correlations will also be generated by negative linkage disequilibrium). Mechanistically this is the only way to our knowledge to simulate genetic correlations in a controlled way.

L143: Reviewer comment

“Were these F1s obtained from the 50 founder genotypes? To explain better! To account for this number of descendants, heterozygous parents were probably considered”

Response: The founder genotypes served as the initial parents in the burn-in phase and generated the first F1 population. Genotypes were then selected from the F1 population to be used as parents in the subsequent cycle. We have now modified the sentence to make this clearer.

L143-146

L154: Reviewer comment

“It was not clear to me why this correlation was considered negative. The simulation refers to a specific selection situation and not what occurs in general.”

Response: This is described in lines 165-167. Our intention was to simulate a challenging scenario for the breeder. Unfavourable genetic correlations can be either positive or negative, depending on the direction of the selection being carried for each trait. In our simulations we were selecting for higher genetic values for both traits, hence we used a negative genetic correlation as unfavourable. A positive genetic correlation would be unfavourable if the direction of selection was different between traits.

Moreover, for favourably correlated traits, both methods perform very similarly, because most of the individuals selected by index selection would also be selected by independent culling. We considered that scenarios with favourable genetic correlation would not be of much additional value to the manuscript and we decided to report and discuss only results from simulations which represent challenging scenarios for multi trait selection, and which would differentiate the two methods of selection being evaluated. We have added clarifications to the introduction (L93), results (L219-222 and 228-229) and to the discussion (L379-382) and also added a figure with results from a scenario with favourably correlated traits to our supplementary material.

L167-168: Reviewer comment:

“This has a consequence for genetic diversity. This does not reflect reality”

Response: The reviewer is right. Our goal in the paper was to compare index selection to the best possible results that can be obtained with independent culling, hence the optimal was chosen. Nevertheless, we also report and discuss the results (Fig. 4) for independent culling when a suboptimal proportion selected was used for each trait. The results are discussed in terms of efficiency in converting genetic diversity into genetic gain.

L240-243: Reviewer comment

“Probably linked to the maximization of genetic gains that promoted a more drastic reduction”

Response: As stated in lines 407-409 of our discussion, after comparing the genetic standard deviation with the genic standard deviation, we believe this difference between the selection methods stem from the how these methods are inducing and exploiting linkage disequilibrium between the causal variants.

L336-339: Reviewer comment

“It is a very specific situation. What if the correlation was positive? I would like to see this situation.”

Response: For favourably correlated traits, both methods would perform very similarly, because most of the individuals selected by index selection would also be selected by independent culling.

We have however added clarifications to the discussion (L379-382) and also added a figure with results from a scenario with favourably correlated traits to our supplementary material.

L394-396: Reviewer comment

“I agree. However, in practice I do not know of a breeding program for clonally propagated species conducted over many cycles. I believe it is impractical.”

Response: The reviewer has a point. Conventional breeding programs for clonally propagated crops take several years for development of cultivars, which are generally used as parents in the next breeding cycle.

As shown by Gaynor et al. (2017), genomic selection allows breeding programs to be restructured by decoupling their cultivar development component from their population improvement component. As the population improvement component operates independently, this enables rapid recurrent selection with potentially several cycles of selection per year to be carried. In this context, the loss of genetic diversity needs to be carefully managed.

L446-447: Reviewer comment

“economics weights of the traits?”

Response: The reviewer is correct. We have modified the sentence:

L511-512

Reviewer #2: Review for: An economic selection index should be used instead of independent culling in plant breeding programs with genomic selection

Response: We thank the reviewer for the comments. We have proofread the manuscript again and found a number of typos. We apologise for their presence in the earlier version. Regarding the submitted figures, we used the highest resolution allowed in the Journal submission guidelines.

Here are a few specific comments, suggestions and discussion points:

L93-94: What if we select for both traits simultaneously?

Response: Independent culling consists of selection for each trait being carried independently of the other traits, even if selection for multiple traits is carried simultaneously. The genotypes being selected would have been the same, although cycle time would be shorter.

L142: It would be worthwhile to consider nonlinear selection indices as well.

Response: The reviewer has a good point and our group is planning subsequent research using non-linear indexes as well. In this study, we decided to only consider linear selection indexes. We address this in L489-491 of our manuscript, in the discussion section.

L143-147: How are the selected parents mated? Does AlphaSimR have any strategies for mating?

Response: In this study the parents were randomly crossed. AlphaSimR also allows user-supplied crossing plans.

L153: Report the correlation value between two traits.

Response: The reviewer is correct. We have added this information in L167-168.

Response: Table 1 is not in the results section so for this reason we excluded the results there. The optimal values of proportion selected varied across different replicates of the simulations, which is shown by the confidence margins in Figure 4. We have now provided the mean values of proportion selected for each cycle in Table S1.1 of our supplementary material in addition to the figure.

Response: The purpose of this figure is to illustrate which individuals were being selected by each of the methods. The characteristic pattern of individuals being selected by each method does not change over the cycles of selection. We have added the figure for the 20th cycle to the supplementary results and included a sentence summary of the similarities and differences between the 1st and the 20th cycles on lines L219-223.

L220, Figure 2: For 0.99 accuracy, the correlation has decreased in the first cycle when using independent culling. How do you describe/interpret that?

Response: Very good question. In the burn-in phase we used independent culling as the selection method. Hence, for the independent culling scenarios the first cycle being reported is merely a continuation of the burn-in phase, i.e. there’s nothing specific to the first cycle which differentiates it from the other cycles of selection. Given that the observed change in genetic correlation was not significant, we believe the increase in genetic correlation was not a relevant occurrence. However, we have added a sentence to report this in our results:

Line 238-239

L299: The proportion of selected parents for REI=5 is 99%. I wonder what happens if we have a large REI, say 20.

Response: In this case, results reported in Hazel and Lush (1942) indicate that no selection at all would be carried for the trait with lower economic importance.

Data availability: Is the simulated data available? I couldn’t find any source links to that.

Response: The reviewer has a valid point. To address this, we decided to make the code we used for the simulations available as supplementary material.

Attachment

Submitted filename: Response to reviewers.docx

Click here for additional data file.^{(25.3KB, docx)}

PLoS One. doi: 10.1371/journal.pone.0235554.r003

Decision Letter 1

James C Nelson

5 Nov 2020

PONE-D-20-04603R1

An economic selection index should be used instead of independent culling in plant breeding programs with genomic selection

PLOS ONE

Dear Dr. Batista,

==============================

As you can see, both of the original reviewers were satisfied with your responses to their points. Your manuscript has been passed to me to handle, and I request some clarification and changes.

The main point made in this paper appears to be that independent culling (IC) faces the problem of determination of selection intensity according to the economic weighting of the traits under selection. However, for maximum efficiency of genetic gain, index selection (IS) also requires estimation of these economic weights. I have read and reread the MS and cannot find any admission that when these weights are accurately estimated, the only differences between IC and IS are that IC can be applied sequentially according to when traits are scorable, and that IS allows selection of genotypes with sub-threshold scores for some traits when the remaining traits have superior scores. The authors cite both advantages as having been well known before the study was undertaken.

On line 143 appears “The index trait was the sum of the estimated breeding values for each trait weighted by their economic importance.” It would be helpful to see the mathematical expression for this weighting.

But if we can develop an economic selection index based on known economic weights, why could we not perform IC based on the same weights? The authors say on line 195 “Index selection performed better than independent culling in scenarios where independent culling levels were suboptimal.” Well, sure. You could just as well say that IC performed better than IS in scenarios where IS economic weights were suboptimal. But if you know how to weight one method, you know how to weight the other.

I ask the authors to address this difficulty.

There are many writing and some organizational errors in the text; many of them are listed below with corrections.. The line numbers are those of the authors’ revised submission, PONE-D-20-04603_R1.pdf. The authors are not required to adopt the exact substitute wording shown with each item, but it is strongly recommended.

23 accordingly => according

24 efficiency => efficiencies

25 both => the two

26 proportion selected => selection proportion

27 a relative economic importance => relative economic importances

29 fact => finding

30 to index => to those from index

40 on => for

41 only selecting => selecting only

44 on => to [twice]

46 non-linear => nonlinear

52 equivalent => equal

61 only be measured => be measured only

63 equivalent => equal

69 allows for accurate => allows accurate

76 discussed => shown [studies cannot discuss]

77 In addition, other => Other

86 quantify the magnitude of the difference => quantify the difference

124 the simulated traits => each simulated trait

128 Where => where

139 Parents => parents

139 carried out => applied

144 [You mention economic importance here, but you have not described how economic importance was assigned.]

153 only interested in investigating => interested in investigating only

154 multi trait => multi-trait [correct this error throughout the MS]

155 Hence => For this reason

163 to => at

163 Here, three => Three

169 the proportion selected for each trait => for each trait the selection proportion [in most cases in the MS you can replace “proportion selected” with “selection proportion”]

174 (i.e. index trait) => (measured as the index trait)

193 Overall the results show that index => Index

201 The results show that increases => Increases

214 was higher with higher values of => increased with

217 compared to => than [please make the same correction throughout, when a comparative expression is used. A few other examples: 221, 256, 271]

243, 245, 314 when using => under

252 loss of genetic standard deviation that was => losses of genetic standard deviation that were respectively

253, 257 , respectively. => . [delete this word and preceding comma]

267 The values of genic standard deviation of T1, T2, and the index trait were equivalent. [Equivalent means having the same value. We don’t say that values have the same value. If you are using equivalent to mean similar, please don’t. Just write similar. If you are using it to mean equal, please write equal.]

286 equivalent to index => equal to that of

287 was worse than => were lower than those of

300 plant => plants

301 only varied => varied only

308 either use => use either

310 Overall the results show that using index selection is either better => Index selection was either better than

312 Our results demonstrate that accurately...is essential => Accurately...was essential

327 The results show that, after...generates => After...generated

332 (i.e. Bulmer => (the Bulmer

343 - 348 This material is not discussion. It is introduction and belongs only there, as part of the motivation for the study. In Discussion we discuss only the results of the present study and ideas that were first suggested by the results.

357 are => were

370 observed => observed that

372 indicate => indicate that

377 which is => as

384 consider = > considered

395 distinctive => distinct

401 using the same selection intensity for => the same selection intensity is applied to

404 when performing => under

412 carried out => applied

412 These results demonstrate that => Thus,

418 using these weights => these weights are used

421 suggesting => suggesting that

422 constructing => construct

430 show => show that

431 when using => in

433 Miscanthus => [italicize this genus name]

433 This [what is “this”?]

435 be => be on

436 paper => study

437 the the => the

437 and it is => and is

438 non-linear => nonlinear [two places]

443 that suggest selection weights should be => in which selection weights are

445 eigen selection => [Eigen is not a word by itself. Consider eigenselection or eigenvalue selection, whatever the original author used]

445 do => does

447 On => Under

447 carried => made

455 The results show that, despite selection being carried out under unfavourable genetic correlations when using the selection index instead of independent culling, equivalent or higher genetic gains were achieved with index selection in all simulated scenarios => Even in the presence of unfavourable genetic correlations, index selection achieved genetic gains equal to or greater than those achieved with independent culling.

460 not => not by

461 both => the two [it is meaningless to say that one method was equivalent and so was the other]

==============================

Please submit your revised manuscript by Dec 20 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

James C. Nelson, Ph.D.

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Reviewer #1: The authors answered or clarified all doubts and suggestions and, therefore, I recommend the publication of the paper.

Reviewer #2: The authors have addressed all comments raised in the last round. The reviewer does not have additional comments.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PLoS One. 2021 May 10;16(5):e0235554. doi: 10.1371/journal.pone.0235554.r004

Author response to Decision Letter 1

2 Dec 2020

Response to Academic Editor

Editor comment:

“As you can see, both of the original reviewers were satisfied with your responses to their points. Your manuscript has been passed to me to handle, and I request some clarification and changes.”

Response: We’d like to thank the Editor for taking over the review process of the manuscript. We appreciate that the review process is now moving forward in the fairest way possible.

Throughout this rebuttal letter we will use the line numbers in the “Manuscript.docx” file. Line numbers are indicated by the letter “L” followed by the line number.

Editor comment:

“The main point made in this paper appears to be that independent culling (IC) faces the problem of determination of selection intensity according to the economic weighting of the traits under selection. However, for maximum efficiency of genetic gain, index selection (IS) also requires estimation of these economic weights. I have read and reread the MS and cannot find any admission that when these weights are accurately estimated, the only differences between IC and IS are that IC can be applied sequentially according to when traits are scorable, and that IS allows selection of genotypes with sub-threshold scores for some traits when the remaining traits have superior scores. The authors cite both advantages as having been well known before the study was undertaken.

Response: We agree with the Editor and have included the formula in matrix notation in the manuscript (L142 – L146)

Editor comment:

“But if we can develop an economic selection index based on known economic weights, why could we not perform IC based on the same weights? The authors say on line 195 “Index selection performed better than independent culling in scenarios where independent culling levels were suboptimal.” Well, sure. You could just as well say that IC performed better than IS in scenarios where IS economic weights were suboptimal. But if you know how to weight one method, you know how to weight the other. I ask the authors to address this difficulty.”

Response: The Editor has a valid point and we modified the discussion in order to address his comments.

L414 – L419: we make more explicit in our discussion that both independent culling and index selection could lead to optimal genetic gain. However, we also considered important to emphasize that finding optimal culling levels is a much more complex task than using an index (see references 11,38,39,40,41,42 and 43). Therefore, index selection should be preferred.

Editor comment:

“There are many writing and some organizational errors in the text; many of them are listed below with corrections. The line numbers are those of the authors’ revised submission, PONE-D-20-04603_R1.pdf. The authors are not required to adopt the exact substitute wording shown with each item, but it is strongly recommended.”

Response:

We thank the Editor for his thorough review and for pointing out the many errors we have overlooked. We have modified the manuscript in accordance with all of the suggestions. Some of the suggestions are presented below followed by a response.

"144 [You mention economic importance here, but you have not described how economic importance was assigned.]"

Response: The description requested can be found in L166 – L168.

"343 - 348 This material is not discussion. It is introduction and belongs only there, as part of the motivation for the study. In Discussion we discuss only the results of the present study and ideas that were first suggested by the results."

Response: The Editor has a valid point and we modified the paragraph in order to keep only what is relevant for the discussion of the results (L344 – L351).

"433 This [what is “this”?]"

Response: The sentences were modified in order to be more specific (L433)

Attachment

Submitted filename: Response to reviewers.docx

Click here for additional data file.^{(15.8KB, docx)}

PLoS One. doi: 10.1371/journal.pone.0235554.r005

Decision Letter 2

James C Nelson

15 Dec 2020

PONE-D-20-04603R2

An economic selection index should be used instead of independent culling in plant breeding programs with genomic selection

PLOS ONE

Dear Dr. Batista,

Please submit your revised manuscript by Jan 29 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

We look forward to receiving your revised manuscript.

Kind regards,

James C. Nelson, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (if provided):

Rather than ask further reviewers to read a submission I find confusing, I have chosen to try to clarify it myself. I am sorry to keep pointing out things I consider problematic, but every time I read the revised MS I find more problems and less substance. I hope these remarks will help the authors in communicating what they did and in separating what this study really established from what they could have written without ever having done a study. I can’t yet distinguish a failure to communicate from a failure of experimental rigor, but both are fatal. PLoS One standards will not prevent publication of a study of light weight, so long as it was done with rigor, and I would add: that readers can tell what it actually contributes to the field, however little that may be.

In short: what did you find out that you didn’t already know, and couldn’t have predicted from prior knowledge? That most of your Discussion is just introduction and is independent of your experimental results is troublesome. I ask the authors to define “accuracy” as computed in their simulation study, and to remove from Discussion all material that was not first suggested by the results (details below). I ask them to clarify how selection was performed under independent culling (details below). I ask them to acknowledge, if they agree, that all they have shown about the non-optimality of independent culling is that a flat 10% selection intensity is not as effective (by their chosen criteria) as index selection.

164 and Table 1 Four levels of accuracy... => You have nowhere defined accuracy or explained how these levels were applied to the simulation. You could presumably show this mathematically or, failing that, algorithmically. Even up to line 201, citing “the accuracy of selection”, you have not defined accuracy. The paper simply makes no sense without such a definition.

171-172 Maximised the genetic gain [to establish culling levels]? The true genetic gain is not known to a breeder. If you are using that, the simulation is not realistic. This is important, because your conclusions cite “optimal” culling levels. Did you maximise the genetic gain estimated from the phenotype, a parameter that would be available to a breeder? But then in line 176-177 you write that you did not use genetic gain at all, but economic value, and applied index selection to determine culling levels. Supplementary figure S.1.1 shows that this paragraph mixes the two methods without distinction. But the main MS should not depend on the supplementary material for explanation.

198 independent culling levels were suboptimal => This is deceptive, because you did not simulate “suboptimal levels”. You simulated only one, a 10% selection proportion.

313 Accurately assessing the economic importance of the traits is essential => Where is the experimental evidence for this assertion, given that you have not defined accuracy or, as far as your M&M indicates, simulated any process by which a breeder might assess economic importance? Is the 10% selection variant the only test you are using to represent “inaccurate” estimation of economic importance?

412 Same as 313. How can you make this assertion?

358 loss => losses

402-407, 414-419; this was all known before the study and is not discussion of the results.

412-413. You did not test estimation errors; you compared only the flat 10% (which no sensible breeder would be likely to apply for traits with clear differences in economic importance) with projection of genetic gain.

421-428 This material is not discussion of your results and is not a conclusion from your results. You knew it from the literature before the study was performed. The same is true of 435-441; you could have written it without doing any experiment. Your simulation doesn’t include any test of estimation errors of culling levels.

429-434 All except the second sentence are introduction. They serve as background knowledge and motivation for the decision to perform this study. The second sentence just repeats a claimed finding; repetition doesn’t add evidence.

435-452 is pure introduction. It is not derived from any findings of this study.

463-466 is introduction. That optimal culling levels are complex to estimate was given, not shown in the study.

As a reminder: an Introduction poses the research problem and says what we know about it, what we wish to find out, and how we propose to find it out.

The M&M and Results section seem to be in order in this MS, except for the omission in explaining “accuracy” and how it was simulated.

A Discussion explains and draws inferences from the results. Unlike the Introduction, it’s concerned with presenting ideas that we didn’t already know and that were first suggested by the results. If there is little to discuss, the section should be short. Introductory material, such as composes much of the Discussion in this MS, should be moved to the Introduction, unless it is mere repetition of material that is already there.

[Note: HTML markup is below. Please do not edit.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PLoS One. 2021 May 10;16(5):e0235554. doi: 10.1371/journal.pone.0235554.r006

Author response to Decision Letter 2

13 Jan 2021

Editor Comment:

“Rather than ask further reviewers to read a submission I find confusing, I have chosen to try to clarify it myself. I am sorry to keep pointing out things I consider problematic, but every time I read the revised MS I find more problems and less substance. I hope these remarks will help the authors in communicating what they did and in separating what this study really established from what they could have written without ever having done a study. I can’t yet distinguish a failure to communicate from a failure of experimental rigor, but both are fatal. PLoS One standards will not prevent publication of a study of light weight, so long as it was done with rigor, and I would add: that readers can tell what it actually contributes to the field, however little that may be.”

Response: We appreciate and we are thankful for the provided input. We agree that a failure to communicate is aggravating, hence we modified the manuscript in order to address the issues pointed out in the revision.

Editor Comment:

“In short: what did you find out that you didn’t already know, and couldn’t have predicted from prior knowledge?”

Response: Our study has fully detailed the effect of different methods of selection in key population parameters such as genetic diversity, genetic correlation and genetic gain over several cycles of selection. No other study has compared index selection and independent culling for that many cycles of selection. Some of the results we observed were expected and consistent with previous literature, some of the results were somewhat surprising, like the increasingly unfavourable genetic correlation between traits (which the Bulmer effect eventually helped us understand).

Editor Comment:

“That most of your Discussion is just introduction and is independent of your experimental results is troublesome.”

Response: We thank the editor for pointing this out, and we have moved some of the paragraphs from the Discussion to the introduction.

These paragraphs arose as a result from many discussions with other researchers and plant breeders while presenting our results. We wrongly decided to include them as a part of our discussion. However, not with the intent of claiming these findings to our study, but as important takeaway messages to breeders.

Editor Comment:

“I ask the authors to define “accuracy” as computed in their simulation study, and to remove from Discussion all material that was not first suggested by the results (details below).I ask them to clarify how selection was performed under independent culling (details below). I ask them to acknowledge, if they agree, that all they have shown about the non-optimality of independent culling is that a flat 10% selection intensity is not as effective (by their chosen criteria) as index selection.

Response: We defined accuracy as the correlation between true and estimated breeding values. This definition is present in the manuscript. We now slightly modified the sentence to highlight it better (L138-L139)

Editor Comment:

“171-172 Maximised the genetic gain [to establish culling levels]? The true genetic gain is not known to a breeder. If you are using that, the simulation is not realistic. This is important, because your conclusions cite “optimal” culling levels. Did you maximise the genetic gain estimated from the phenotype, a parameter that would be available to a breeder? But then in line 176-177 you write that you did not use genetic gain at all, but economic value, and applied index selection to determine culling levels. Supplementary figure S.1.1 shows that this paragraph mixes the two methods without distinction. But the main MS should not depend on the supplementary material for explanation.”

Response: We have included in the manuscript that optimal independent culling aimed at maximizing the genetic gain for the index trait, but it does it by selecting on one trait at a time. We obtained the index trati from estimated breeding values of the traits (L180-L181). We thank the Editor for pointing that out.

The figure in S.1.1 only represents the selection methods graphically, it doesn’t add information that is not already included in the Material and Methods.

1) In the independent culling method selection is performed one trait at a time as is often done in plant breeding. Individuals are ranked based on one trait and the individuals with the highest values are kept while the other individuals are culled. The individuals that were kept are then ranked based on a second trait and then culled again. This process is repeated for each additional trait under selection.

2) In the selection index method individuals are selected for all traits at once, generally by using a linear combination of the traits, which is the index. Individuals are ranked based on the index and the ones with the highest values are kept.

Hence, in the optimal independent culling methodology we do not mix the two methods. The index trait is used as a reference for establishing which are the optimal selection intensities we need to use for each trait. Once we have these selection intensities (i.e. the number of individuals we need to cull in each stage) independent culling is carried as described in 1. We did not use the index trait to rank the individuals, selection was carried out for each trait at a time.

Editor Comment:

“198 independent culling levels were suboptimal => This is deceptive, because you did not simulate “suboptimal levels”. You simulated only one, a 10% selection proportion.”

Response: We agree with the Editor and we have modified the sentence accordingly (L207-208)

Editor Comment:

“313 Accurately assessing the economic importance of the traits is essential => Where is the experimental evidence for this assertion, given that you have not defined accuracy or, as far as your M&M indicates, simulated any process by which a breeder might assess economic importance? Is the 10% selection variant the only test you are using to represent “inaccurate” estimation of economic importance?

412 Same as 313. How can you make this assertion?”

Response: We agree with the Editor and we have removed the sentences from our manuscript

Editor Comment:

“402-407, 414-419; this was all known before the study and is not discussion of the results.

Response: Please see below.

435-452 is pure introduction. It is not derived from any findings of this study.

Response: Please see below.

463-466 is introduction. That optimal culling levels are complex to estimate was given, not shown in the study.

As a reminder: an Introduction poses the research problem and says what we know about it, what we wish to find out, and how we propose to find it out.

The M&M and Results section seem to be in order in this MS, except for the omission in explaining “accuracy” and how it was simulated.

Response: We agree with the Editor and we have considered all these comments carefully in order to modify the manuscript. Some of the paragraphs in our discussion were excluded from the manuscript and some were moved to the introduction, in accordance with the remarks.

We thank the Editor’s for these comments, and we belie this revision helped us improve our discussion. We also changed our title in accordance to the comments.

The flat 10% selection intensity for both traits would have been the breeder’s intuitive choice in scenarios with a relative economic importance of 1.0 (traits with equal economic importance). Even in that case, optimal culling levels performed better than the intuitive choice. We have decided to argue in our discussion that this result indicates that culling levels should not be chosen based on intuition and should be estimated accurately aiming at maximizing economic value.

We have kept the remark about the complexity of estimating optimal culling levels in the discussion, but we removed it from our conclusions. Since we showed that both optimal independent culling and index selection lead to equivalent genetic gains, the complexity is an important caveat when deciding between the two methods.

Attachment

Submitted filename: Response to reviewers.docx

Click here for additional data file.^{(19.7KB, docx)}

PLoS One. doi: 10.1371/journal.pone.0235554.r007

Decision Letter 3

James C Nelson

25 Jan 2021

Long-term comparison between index selection and optimal independent culling in plant breeding programs with genomic prediction

PONE-D-20-04603R3

Dear Dr. Batista,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

James C. Nelson, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Thanks to the authors for their patience — in fact they had explained accuracy and I had overlooked it.

I am recommending acceptance of the MS for publication, but I ask the authors to attend to the corrections and questions below before submitting their final version, which I do not need to see.

Abstract: had equivalent loss => had similar [equal, identical] losses

67 obsolete => irrelevant

77 the correct => accurate

79 for each trait [? Multiple selection intensities for a single trait? Do you mean “for the traits”?]

96 culling a sub-optimal culling level [? Doesn’t make sense. Do you mean “culling using suboptimal culling levels”?]

114 AlphaSimR [This must be defined or cited when first mentioned, not at a later mention. And once it has been cited, it should not be cited again.]

117 1.8x10-9 what? Giraffes?

177 (10%) when selecting for => (10%) for

183-186 Doesn’t this repeat 179-181?

199 mean => [don’t you mean “gain”?]

294-295 was nearly equal to that => were nearly equal to those

260-262 loss ... that was 6% and 5% higher... respectively => losses...that were respectively 6% and 5% higher...

298, 313 importance => importances

320 better or => better than or

383 equivalent => equal

423 both => the two

424 leads => lead

424 by using optimal culling levels or a => by optimal culling levels or by a

428 importance, therefore being a => importance, a

445 equivalent loss => similar losses

446 the efficiency => the differences in efficiency

Reviewers' comments:

PLoS One. doi: 10.1371/journal.pone.0235554.r008

Acceptance letter

James C Nelson

24 Jun 2020

PONE-D-20-04603R1

An economic selection index should be used instead of independent culling in plant breeding programs with genomic selection

Dear Dr. Batista:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Professor Roberto Fritsche-Neto

Academic Editor

PLOS ONE

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

S1 File

(DOCX)

Click here for additional data file.^{(783.1KB, docx)}

S2 File

(PDF)

Click here for additional data file.^{(142.2KB, pdf)}

Attachment

Submitted filename: PONE-D-20-04603_reviewer.pdf

Click here for additional data file.^{(1.6MB, pdf)}

Attachment

Submitted filename: Response to reviewers.docx

Click here for additional data file.^{(25.3KB, docx)}

Attachment

Submitted filename: Response to reviewers.docx

Click here for additional data file.^{(15.8KB, docx)}

Attachment

Submitted filename: Response to reviewers.docx

Click here for additional data file.^{(19.7KB, docx)}

Data Availability Statement

All relevant data are within the manuscript and its Supporting Information files.

[pone.0235554.ref001] 1.Kwon SH, Torrie JH. Heritability of and interrekationships among traits of two soybean population. 1964. [Google Scholar]

[pone.0235554.ref002] 2.Meredith WR, Bridge RR. Breakup of Linkage Blocks in Cotton, Gossypium hirsutum L.1. Crop Science. 1971;11:695–8. [Google Scholar]

[pone.0235554.ref003] 3.Erskine W, Williams PC, Nakkoul H. Genetic and environmental variation in seed yield, seed size and cooking quality of lentil. Field Crops Research. 1985;12:153–61. [Google Scholar]

[pone.0235554.ref004] 4.Kato T, Takeda K. Associations among Characters Related to Yield Sink Capacity in Space-Planted Rice. Crop Science. 1996;36:1135–9. [Google Scholar]

[pone.0235554.ref005] 5.Triboi E, Martre P, Girousse C, Ravel C, Triboi-Blondel AM. Unravelling environmental and genetic relationships between grain yield and nitrogen concentration for wheat. European Journal of Agronomy. 2006;25(2):108–18. [Google Scholar]

[pone.0235554.ref006] 6.Falconer DS, Mackay TF, Frankham R. Introduction to Quantitative Genetics (4th edn). Trends in Genetics. 1996;12(7):280. [Google Scholar]

[pone.0235554.ref007] 7.Bernardo R. Breeding for quantitative traits in plants. 1st ed. Woodbury: Stemma Press; 2010. 390 p. [Google Scholar]

[pone.0235554.ref008] 8.Hazel LN, Lush JL. The Efficiency of Three Methods of Selection. Journal of Heredity. 1942;33(11):393–9. [Google Scholar]

[pone.0235554.ref009] 9.Young S. A further examination of the relative efficiency of three methods of selection for genetic gains under less-restricted conditions. Genetical Research Cambridge. 1961;2(1961):106–21. [Google Scholar]

[pone.0235554.ref010] 10.Pesek J, Baker RJ. Comparison of tandem and index selection in the modified pedigree method of breeding self-pollinated species. Canadian Journal of Plant Science. 1969. November;49(6):773–81. [Google Scholar]

[pone.0235554.ref011] 11.Xu S, Muir WM. Multistage Selection for Genetic Gain by Orthogonal Transformation. Genetics. 1991. November;129(3):963–74. [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref012] 12.Meuwissen THE, Hayes BJ, Goddard ME. Prediction of total genetic value using genome-wide dense marker maps. Genetics. 2001;157(4):1819–29. [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref013] 13.Gaynor RC, Gorjanc G, Bentley AR, Ober ES, Howell P, Jackson R, et al. A Two-Part Strategy for Using Genomic Selection to Develop Inbred Lines. Crop Science. 2017;57:2372–86. [Google Scholar]

[pone.0235554.ref014] 14.Saxton AM. INDCULL Version 3.0: Independent Culling for Two or More Traits. Journal of Heredity. 1989. March 1;80(2):166–7. [Google Scholar]

[pone.0235554.ref015] 15.Ducrocq V, Colleau JJ. Optimum truncation points for independent culling level selection on a multivariate normal distribution, with an application to dairy cattle selection. Genetics Selection Evolution. 1989. June 15;21(2):185. [Google Scholar]

[pone.0235554.ref016] 16.Bernardo R, Yu J (2007) Prospects for Genomewide Selection for Quantitative Traits in Maize. Crop Science 47:1082–1090. 10.2135/cropsci2006.11.0690 [DOI] [Google Scholar]

[pone.0235554.ref017] 17.Heffner EL, Sorrells ME, Jannink J-L (2009) Genomic Selection for Crop Improvement. Crop Science 49:1–12. 10.2135/cropsci2008.08.0512 [DOI] [Google Scholar]

[pone.0235554.ref018] 18.Hickey JM, Chiurugwi T, Mackay I, Powell W, Participants IGS in CBPW. Genomic prediction unifies animal and plant breeding programs to form platforms for biological discovery. Nature Genetics. 2017. August 30;49:1297. 10.1038/ng.3920 [DOI] [PubMed] [Google Scholar]

[pone.0235554.ref019] 19.Slavov GT, Davey CL, Bosch M, Robson PRH, Donnison IS, Mackay IJ. Genomic index selection provides a pragmatic framework for setting and refining multi-objective breeding targets in Miscanthus. Annals of Botany [Internet]. 2018. October 23 [cited 2019 Jun 9]; Available from: https://academic.oup.com/aob/advance-article/doi/10.1093/aob/mcy187/5142550 [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref020] 20.Michel S, Löschenberger F, Ametz C, Pachler B, Sparry E, Bürstmayr H. Simultaneous selection for grain yield and protein content in genomics-assisted wheat breeding. Theoretical and Applied Genetics. 2019. June;132(6):1745–60. 10.1007/s00122-019-03312-5 [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref021] 21.Akdemir D, Beavis W, Fritsche-Neto R, Singh AK, Isidro-Sánchez J. Multi-objective optimized genomic breeding strategies for sustainable food improvement. Heredity. 2019. May;122(5):672–83. 10.1038/s41437-018-0147-1 [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref022] 22.Grüneberg W, Mwanga R, Andrade M, Espinoza J. Selection methods. Part 5: Breeding clonally propagated crops. Plant Breeding and Farmer Participation. 2009;(April):275–322. [Google Scholar]

[pone.0235554.ref023] 23.Gaynor RC, Gorjanc G, Wilson DL. AlphaSimR: An R Package for Breeding Program Simulations. Manuscr Prep. [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref024] 24.Chen GK, Marjoram P, Wall JD. Fast and flexible simulation of DNA sequence data. Genome research. 2009;19(1):136–42. 10.1101/gr.083634.108 [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref025] 25.Thuillet A-C, Bataillon T, Poirier S, Santoni S, David JL. Estimation of long-term effective population sizes through the history of durum wheat using microsatellite data. Genetics. 2005;169(3):1589–99. 10.1534/genetics.104.029553 [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref026] 26.Gorjanc G, Gaynor RC, Hickey JM. Optimal cross selection for long-term genetic gain in two- part programs with rapid recurrent genomic selection. bioRxiv. 2017; [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref027] 27.Venables WN, Ripley BD. Modern Applied Statistics with S. Fourth Edi. New York: Springer; 2002. [Google Scholar]

[pone.0235554.ref028] 28.Bulmer MG (1971) The effect of selection on genetic variability. 105:1–88 [Google Scholar]

[pone.0235554.ref029] 29.Tallis GM. Ancestral covariance and the Bulmer effect. Theoretical and Applied Genetics. 1987;73(6):815–20. 10.1007/BF00289384 [DOI] [PubMed] [Google Scholar]

[pone.0235554.ref030] 30.Itoh Y. Changes in genetic correlations by index selection. Genetics selection evolution GSE. 1991;23(4):301–8. [Google Scholar]

[pone.0235554.ref031] 31.Duvick DN, Cassman KG. Post–Green Revolution Trends in Yield Potential of Temperate Maize in the North-Central United States. Crop Science. 1999;39:1622–30. [Google Scholar]

[pone.0235554.ref032] 32.Rharrabti Y, Elhani S, Martos-Núñez V, García del Moral LF. Protein and Lysine Content, Grain Yield, and Other Technological Traits in Durum Wheat under Mediterranean Conditions. Journal of Agricultural and Food Chemistry. 2001. August 1;49(8):3802–7. 10.1021/jf001139w [DOI] [PubMed] [Google Scholar]

[pone.0235554.ref033] 33.Rotundo JL, Borrás L, Westgate ME, Orf JH. Relationship between assimilate supply per seed during seed filling and soybean seed composition. Field Crops Research. 2009;112(1):90–6. [Google Scholar]

[pone.0235554.ref034] 34.Casler MD, Vogel KP. Accomplishments and Impact from Breeding for Increased Forage Nutritional Value. Crop Science. 1999;39:12–20. [Google Scholar]

[pone.0235554.ref035] 35.Smedegaard-Petersen V, Tolstrup K. The Limiting Effect of Disease Resistance on Yield. Annual Review of Phytopathology. 1985;23(1):475–90. [Google Scholar]

[pone.0235554.ref036] 36.Cowling W, Li L. Turning the heat up on independent culling in crop breeding. 2018. 119–134 p. [Google Scholar]

[pone.0235554.ref037] 37.Bennett G, Swiger L. Genetic variance and correlation after selection for two traits by index, independent culling levels and extreme selection. Genetics. 1980;94(3):763–75. [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref038] 38.Clark SA, Kinghorn BP, Hickey JM, Van Der Werf JHJ. The effect of genomic information on optimal contribution selection in livestock breeding programs. Genetics Selection Evolution. 2013;45(1):1–8. 10.1186/1297-9686-45-44 [DOI] [PMC free article] [PubMed] [Google Scholar]

[pone.0235554.ref039] 39.Woolliams JA, Berg P, Dagnachew BS, Meuwissen THE. Genetic contributions and their optimization. Journal of Animal Breeding and Genetics. 2015. April;132(2):89–99. 10.1111/jbg.12148 [DOI] [PubMed] [Google Scholar]

PERMALINK

Long-term comparison between index selection and optimal independent culling in plant breeding programs with genomic prediction

Lorena G Batista

Robert Chris Gaynor

Gabriel R A Margarido

Tim Byrne

Peter Amer

Gregor Gorjanc

John M Hickey

Roles

Abstract

Introduction

Material and methods

Genome sequence

Founder genotypes

Estimated breeding values

Breeding methods

Simulated scenarios

Table 1. Summary of parameters simulated in all comparison scenarios of recurrent selection breeding programs using either independent culling or selection index with two traits.

Comparison

Results

Accuracy of selection

Fig 1.

Fig 2. Change in genetic correlation (mean and 95% confidence interval) between traits in the F1 population over 20 cycles of selection using either optimal independent culling (IC) or a selection index (SI) with different levels of accuracy, and Trait 2 relative economic importance of 1.0.

Fig 3. Change in genetic mean for Trait 1 (T1), Trait 2 (T2) and Index Trait (Index) over 20 cycles of selection using either optimal independent culling (IC) or a selection index (SI) with different levels of accuracy, unfavourably correlated traits, and T2 relative economic importance of 1.0.

Relative economic importance of traits

Fig 4.

Discussion

Methods of selection and genetic correlation between traits

Methods of selection and genetic diversity over cycles of selection

Economic importance of the traits

Conclusions

Supporting information

Data Availability

Funding Statement

References

Decision Letter 0

Roberto Fritsche-Neto

Roles

Author response to Decision Letter 0

Decision Letter 1

James C Nelson

Roles

Author response to Decision Letter 1

Decision Letter 2

James C Nelson

Roles

Author response to Decision Letter 2

Decision Letter 3

James C Nelson

Roles

Acceptance letter

James C Nelson

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

Similar articles

Cited by other articles

Links to NCBI Databases