# Estimation of Breeding Parameters from Phenotypic Data of F4:5 RIL in Ethiopian Malt Barley (Hordeum distichum L.) Breeding Population

Authors: Endeshaw Tadesse; Peer Wilde; Kassahun Tesfaye; Yohannes Fekadu; Tesfahun Alemu; Rebeka Gebretsadik
Journal: International Journal of Agronomy
 (2022)

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## Abstract

The critical stage for any breeder is the selection of crossing parents to drive improved inbred for subsequent breeding cycles. In our study, we estimate breeding parameters such as mid-parent value (MPV), variances among and within crosses, the heritability of relevant traits and their correlations, the usefulness of crosses, and regression of cross means on MPV. 900 F4:5 Recombinant inbred lines (RILs) derived from 30 crosses were tested together with their parental lines in a modified split-plot p-rep design at two locations. The analysis revealed significant genetic variation among parents, crosses, and RIL for almost all traits. Heritability for parents ranged from 49.50% (malt extract) to 93.60% (plant height) and heritability for crosses ranged from 29.52% (grain protein concentration) to 87.0% (days to maturity), whereas heritability for RIL was the lowest with 27.40% for beta-glucan and the highest to 73.60% for thousand kernel weight, respectively. Significant (P<0.01) genotypic correlations with high impact for practical breeding were found between malting traits. Accordingly, the genotypic correlation ranged from −0.73 to 0.78 whereas the phenotypic correlation ranged from −0.60 to 0.65, respectively. Significant (P<0.01) regression of cross-mean on MPV where R2 ranges from 0.27 to 0.70 and is higher than 0.5 for most of the traits demonstrates that cross means can accurately be predicted from MPV and selection among crosses at an early stage is highly effective. Based on the usefulness criterion, 16 superior crosses were identified compared to the planet as the actual leading malt variety. Starting from a simple additive genetic model with random mating, we discuss deviations from the initial model and their impact on the actual estimates implying how to design a state-of-the-art cereal breeding program.


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## Body

## 1. Introduction

Plant breeding programs are based on the effective maintaining and reuse/shuffling of genetic variation aimed at generating new and improved combinations of alleles and assembling them in a single superior genetic background[1, 2]. Genetic variation can be obtained from germplasm sources such as landraces or exotic lines from foreign countries that could be directly used to exploit the inherent genetic variance. Alternatively, elite lines are combined in crosses to form a base population from which new and improved lines are developed (“second cycle breeding”) [3–6]. Hence, the genetic variance can be structured into variance between crosses and within crosses. The variance between crosses is the variation observed between crosses generated from different parental lines [6]. This should be distinguished from the variance within crosses which is the variation between recombinant inbred lines (RILs) generated from a given cross through subsequent selfing.Thus, breeding can be regarded as a two-step selection process [6]. The first step is the selection between crosses and the corresponding selection gain depends on the genetic variance among cross means (σc2). The second step is the selection among RIL within crosses and the corresponding selection gain depends on segregation variance (σgij2) among lines within a given cross of parent i and parent j which has been selected in the first step. Therefore, information about σc2 and σgij2 is important to the breeder to optimize the allocation of resources with regard to the number of crosses exploited and the number of RIL evaluated per individual cross [7]. For example, if σc2 is large and σgij2 is small, the breeder will invest more into crosses and less into the number of lines per cross. Also, the choice of crosses decides on which genes will be (re)combined to obtain superior progenies [8–10].In cross formation, parental selections play a major role which in turn depends on heritability which is an important parameter in practical plant breeding, because it determines the genetic gain. Breeders evaluate cultivars of interests across multiple locations and several years which are known as multienvironmental trials (METs) [11].Heritability can be estimated in different ways. For instance, the standard heritability estimate as the ratio ofσg2 to σp2 assumes that the trial design is completely balanced, genotype effects are independent, and variance and covariance are homogeneous [12–14]. However, when considering segregating populations, the RILs of a given cross share the same parental lines and RILs from two crosses might be related to each other as half-sibs because one of the parental lines is identical. In the case of testing the entries in different environments, the respective variances and covariances are not necessarily homogeneous. Under such circumstances, heritability should be based on BLUP (Best Linear Unbiased Predictor). Hence, [11] suggested fitting the genetic term as a random effect (BLUP) and explained heritability as a function of the ratio: mean-variance of a difference of two BLUPs for the genotypic effect divided by twice the genotypic variance.Correlations between traits can be caused by phenotypic, genotypic, and environmental effects. Phenotypic correlation (rp) occurs when phenotypic values of the two traits are correlated due to genetic and/or nongenetic effects. Genetic correlation (rg) can arise from pleiotropy caused by the same genes influencing two different traits and/or linkage disequilibrium between genes controlling different characters [15, 16]. Environmental correlation is the correlation of environmental effects [15]. For example, drought might affect plant height and thousand-grain weight in the same direction. Trait correlations are important phenomena in crop improvement because enhancement in one trait may have a negative impact on another trait which is also important [17, 18].Regression of cross-mean (CM) on mid-parent (MPV) values is relevant for practical breeding because MPV could be used as a predictor of the offspring or CM for the traits of interest. In our experimental context, the offspring mean is identical to the mean of all RIL derived from a cross between the parents P1 and P2. The association between MPV and offspring can be explained [15] through the regression of offspring on mid-parent values bOMPV:(1)bOMPV=covOMPVσMPV2,where COVOMPV is the covariance of the offspring with the mid-parent and σMP2 is the variance of the phenotypic means of P1 and P2. For the denominator, we can derive assuming that the two parents have the same variance:(2)σ2MP=12σ2P1+σ2P2.Under the assumptions of an idealized population, the variance of the phenotypic means of the individual parents can be dissected into(3)σP2=σG2+σE2,σG2=σA2+σI2.σG2 is the variance of genetic effects, σA2 is the variance of additive effects, σI2 is the variance of epistatic effects, and σE2 is the variance of environmental (e.g., genotype × environment-interaction) effects.The potential of a cross for a given quantitative trait can be quantified by the usefulness criterion [19]. U is determined by the cross-mean (μ) and the genetic gain (ihσ) from exploiting the segregation variance within the cross: U = μ + iℎσ, where σ is the genetic standard deviation within the cross. i (α) is the selection intensity depending on the selection rate. α(h) is the selection accuracy as defined above.In summary, our objectives were to (i) estimate and compare mid-parent value and cross-mean, (ii) estimate and compare the variance between means of crosses (σc2) and segregation variance of recombinant inbred line within crosses (σg2), (iii) estimate the heritability of the traits under selection and correlation among them, and (iv) estimate the usefulness of crosses.


## 2. Materials and Methods

### 2.1. Germplasm

Thirty (30) crosses derived from 17 parents were conducted at Holeta Agricultural Research Center in the year 2018 (Table1), and 30 RIL per cross had been developed in an SSD procedure in the following growing seasons. RILs used for testing descend from F4 single plants and were tested in F5-generation (F4:5-L). Thus, RIL populations comprising 900 entries were used in this study. The 17 parental lines and 13 well-known malt barley varieties were included as checks. The parental lines used in the crossing program were organized from released malt barley varieties and elite germplasm selected from national variety trials based on their good line per se performance. The parental selection and combination were based on criteria such as high yield, adaptiveness to the Ethiopian environment, and good malt quality. The origin of the parents used for crosses includes Europe, the USA, ICARDA, and Ethiopia. The European sources are known for their malt quality and high yield under favorable farming conditions but also for late heading date, short plant height, and susceptibility against leaf diseases. USA sources excel for their resistance to insects such as aphids, ICARDA lines are good sources for stem stiffness and drought tolerance and are well adapted to the Ethiopian environment whereas the Ethiopian sources are generally innate with, e.g., good adaptation to low soil pH and resistance to other biotic and abiotic stress.Table 1
List of the 17 parental lines, origin, and their agronomic profile.
SNParentsOriginDescription1BurtonUSA, UMResistant to pests (such as aphids and others)2M135USA, UM3MN BriteUSA, UM4G 13–64EuropeMalt quality and high Yield, Late heading, short height, but susceptible to leaf disease5PlanetEurope6IBON 14/15–144ICARDAStem stiffness, drought tolerance, and well adapted to the Ethiopian environment7IBON 13/2ICARDA8IBON 13/33ICARDA9ICARDA GP-67ICARDA10ICARDA GP-75ICARDA11IBON 13/14–129ICARDA12MBHIBYT-23ICARDA13MBHIBYT-22ICARDA14IBON 13/14–128ICARDA15IBON 13/14–41ICARDA16HB1963EthiopiaResistance to biotic and a biotic stress and well adapted17Bekoji-1 x GraceEthiopiaSource: HARC, 2020, UM = University of Minnesota.


### 2.2. Experimental Design and Field Management

The experiment was conducted in 2020 at two Agricultural Research Stations Holeta (altitude 2390 m.a.s.l with an average annual rainfall of 1100 mm and Max and Min temperature of 22.2 and 6.13°C) and Bekoji (substation of Kulumsa Agricultural Research Center) (altitude of 2780 m.a.s.l. with an annual mean rainfall of 1049.6 mm and Max and Min temperature is 19.6 and 8.3°C), respectively. A modified split-plotp-rep design was used in which crosses were allocated to main plots and RILs of a given cross were randomized as subplots within the main plots. The main plots were nested within blocks. The total entry number was 900 (30 crosses by 30 RIL each), from which 450 entries were replicated at Holeta and the remaining were replicated at Bekoji. In addition, the parents of the crosses and check varieties were tested in 5 replicates per site. Thus, the main plot comprised 50 subplots with 15 RIL replicated twice, 15 unreplicated RIL, and 5 parents/checks). Entries were grown in two-rowed observation plots with plot lengths of 1 m, 0.2 m spacing between rows, and 1 m path which made a net plot area of 0.4 m2.


### 2.3. Agronomic Data

Data were recorded on 8 quantitative characters of each at both locations using tablets equipped with field scorer 4 android Katmandoo applications, developed and supported by the Department of Agriculture and Fisheries in Queensland. The following data were recorded as indicated in Table2.


### 2.4. Data Analysis

Data were subjected to statistical analysis to test for outliers, homogeneity of variance, and normality of residuals using R software, version 3.4.2 (R core Team, 2017). Estimation of variance components among parents (checks), crosses, and RIL within crosses was computed based on mixed model procedures using asreml-r (Commercial Package based on R software). The basic model assumption was checked with a graphical overview and outliers were replaced by NA (NA stands for not available in R syntax). The group which contains checks were considered fixed whereas the genotype which contains parents, crosses, and RILs with crosses was considered a random factor.


#### 2.4.1. Estimation of Variance Components

A spatial model was fitted to produce adjusted genotype means for each environment [20, 21]. After spatial adjustment, a combined analysis was conducted across the environment [22, 23]. The linear mixed model for the combined analysis contains different dummy groups to predict the adjusted mean precisely [24]. The model was defined as(4)Y=μ+group+pg+loc+cross+cross:loc+Entry+Entry:loc+row:loc+col:mainp:loc+e.Attaching the dummies to (group {groupRILs, groupCHK}), parental group (pg) (pgParent, pgechk) where pgParent is parents that are used in the cross, and pgechk is nonparents that are included as additional checks. In addition, for each treatment factor (cross and entry), dummies have been attached as shown in the following model, and the respective design factors for rows, columns, and main plots were considered per location.(5)Y=μ+group+pg+loc+cross:pgParent+cross:pgParent:loc+Entry:pgechk+Entry:pgechk:loc+Entry:groupCHK:pgParent+Entry:groupRIL+Entry:groupCHK:pgParent:loc+Entry:groupRIL:loc+row:loc+col:mainp:loc+e,where Y is the total observation for the trait of interest, μ is the overall mean of RIL, group is to identify checks, and RIL is the only fixed factor, and crosses, checks, and RILs within crosses are assigned as genotypes in the model. Dummies were included to estimate the effect of one factor by switching off other effects. Accordingly, for pgParent, pgechk, groupCHK, and groupRIL dummies were attached to estimate the effect of parents, echek, checks, and RIL by switching off one factor over the other. echk identifies extra checks besides the 17 parents actually used in crossing, CHK represents the total checks used in the experiment (i.e., including both parents and nonparents), RIL is recombinant inbred lines derived from the crosses, and loc assigns locations. An example of other interactions with environments (Entry.loc) is defined as the interaction between location and set of genotype groups, i.e., crosses, checks, RILs within crosses. row.loc and (mp.col.loc) are rows, columns, and main plots effects, respectively, nested within locations, and e is the random error for the model.


#### 2.4.2. Estimate of Heritability (Broad Sense)

Heritability was estimated based on Cullis et al. [25]. Specific allocation for checks crosses and RIL was taken into account when estimating their respective heritability.(6)H2Cullis=1−average standard error from BLUP2∗σg2,where σg2 is genotype variance from a model construct.


#### 2.4.3. Theory Assumptions

We assume that RIL represents a line population developed under a single seed descent (SSD) procedure:(i)
Forces driving changes of allele frequencies such as selection, migration, drift, and mutation [15] are assumed to be negligible(ii)
Linkage equilibrium [15] between QTL controlling a trait is given(iii)
Epistasis is absent or of minor importanceWith these assumptions given a simple additive genetic model can be used as suggested by [6, 25].


#### 2.4.4. Parameters Estimation for Phenotypic Data

Best Linear Unbiased Predictions (BLUPs) were computed for means of parents, crosses, and RILs within crosses and estimated as random effects with distributionµ∼MVN (0, ∑σμ2) being ∑σμ2 a relationship matrix among the level of the random effect. The genetic variance of mid-parents was estimated from the genetic variance of the female (σf2) and male (σm2) parental lines (σp2) σp2 = (σm2 + σf2)/2. The genetic variance among crosses σc2 is the variance component accounting for variation between the 30 crosses and is estimated as the variance component assuming crosses as random [6]. The average segregation variance σg2 is the variation of RILs within crosses. Under the assumptions specified above, a quantitative genetic interpretation of the breeding parameters is given in Table 3.Table 2
List of agronomic and quality parameters collected.
SNVariablesCodeNature of VariablesCollection method1Heading dateDHQuantitativeNumber of days from date of sowing till about 75% of plants in the plot was flowering2Maturity dateDMQuantitativeNumber of days from sowing to the date when 75% of the peduncle turned to yellow straw color and when no green color remained on glumes and peduncles of the tagged plant3Plant heightPHQuantitativeThe actual measurement of plant height from ground level to the tip of the spike excluding the awns and recorded as the average of five randomly selected plants in each plot4Thousand kernel weightTKWQuantitativeWeights were measured by taking the mass of carefully counted a thousand kernels on sensitive electronic balance (±0.1 g) after kernels were adjusted to 12.5% moisture content5Grain protein concentrationGPCQuantitativeTotal protein content in the grain, expressed as a percentage. estimated using the NIRS machine6Malt extractMEQuantitativeSolid material extracted from finely ground malt, expressed as a percentage. estimated using the NIRS machine7FriabilityFRQuantitativeIndicator of endosperm modification after malting by a simple milling test in a friabilimeter, expressed as a percentage. estimated using the NIRS machine8Beta-glucanBGQuantitativea principal constituent of the barley endosperm cell wall, expressed as mg/estimated using the NIRS machine


## 2.1. Germplasm

Thirty (30) crosses derived from 17 parents were conducted at Holeta Agricultural Research Center in the year 2018 (Table1), and 30 RIL per cross had been developed in an SSD procedure in the following growing seasons. RILs used for testing descend from F4 single plants and were tested in F5-generation (F4:5-L). Thus, RIL populations comprising 900 entries were used in this study. The 17 parental lines and 13 well-known malt barley varieties were included as checks. The parental lines used in the crossing program were organized from released malt barley varieties and elite germplasm selected from national variety trials based on their good line per se performance. The parental selection and combination were based on criteria such as high yield, adaptiveness to the Ethiopian environment, and good malt quality. The origin of the parents used for crosses includes Europe, the USA, ICARDA, and Ethiopia. The European sources are known for their malt quality and high yield under favorable farming conditions but also for late heading date, short plant height, and susceptibility against leaf diseases. USA sources excel for their resistance to insects such as aphids, ICARDA lines are good sources for stem stiffness and drought tolerance and are well adapted to the Ethiopian environment whereas the Ethiopian sources are generally innate with, e.g., good adaptation to low soil pH and resistance to other biotic and abiotic stress.Table 1
List of the 17 parental lines, origin, and their agronomic profile.
SNParentsOriginDescription1BurtonUSA, UMResistant to pests (such as aphids and others)2M135USA, UM3MN BriteUSA, UM4G 13–64EuropeMalt quality and high Yield, Late heading, short height, but susceptible to leaf disease5PlanetEurope6IBON 14/15–144ICARDAStem stiffness, drought tolerance, and well adapted to the Ethiopian environment7IBON 13/2ICARDA8IBON 13/33ICARDA9ICARDA GP-67ICARDA10ICARDA GP-75ICARDA11IBON 13/14–129ICARDA12MBHIBYT-23ICARDA13MBHIBYT-22ICARDA14IBON 13/14–128ICARDA15IBON 13/14–41ICARDA16HB1963EthiopiaResistance to biotic and a biotic stress and well adapted17Bekoji-1 x GraceEthiopiaSource: HARC, 2020, UM = University of Minnesota.


## 2.2. Experimental Design and Field Management

The experiment was conducted in 2020 at two Agricultural Research Stations Holeta (altitude 2390 m.a.s.l with an average annual rainfall of 1100 mm and Max and Min temperature of 22.2 and 6.13°C) and Bekoji (substation of Kulumsa Agricultural Research Center) (altitude of 2780 m.a.s.l. with an annual mean rainfall of 1049.6 mm and Max and Min temperature is 19.6 and 8.3°C), respectively. A modified split-plotp-rep design was used in which crosses were allocated to main plots and RILs of a given cross were randomized as subplots within the main plots. The main plots were nested within blocks. The total entry number was 900 (30 crosses by 30 RIL each), from which 450 entries were replicated at Holeta and the remaining were replicated at Bekoji. In addition, the parents of the crosses and check varieties were tested in 5 replicates per site. Thus, the main plot comprised 50 subplots with 15 RIL replicated twice, 15 unreplicated RIL, and 5 parents/checks). Entries were grown in two-rowed observation plots with plot lengths of 1 m, 0.2 m spacing between rows, and 1 m path which made a net plot area of 0.4 m2.


## 2.3. Agronomic Data

Data were recorded on 8 quantitative characters of each at both locations using tablets equipped with field scorer 4 android Katmandoo applications, developed and supported by the Department of Agriculture and Fisheries in Queensland. The following data were recorded as indicated in Table2.


## 2.4. Data Analysis

Data were subjected to statistical analysis to test for outliers, homogeneity of variance, and normality of residuals using R software, version 3.4.2 (R core Team, 2017). Estimation of variance components among parents (checks), crosses, and RIL within crosses was computed based on mixed model procedures using asreml-r (Commercial Package based on R software). The basic model assumption was checked with a graphical overview and outliers were replaced by NA (NA stands for not available in R syntax). The group which contains checks were considered fixed whereas the genotype which contains parents, crosses, and RILs with crosses was considered a random factor.


### 2.4.1. Estimation of Variance Components

A spatial model was fitted to produce adjusted genotype means for each environment [20, 21]. After spatial adjustment, a combined analysis was conducted across the environment [22, 23]. The linear mixed model for the combined analysis contains different dummy groups to predict the adjusted mean precisely [24]. The model was defined as(4)Y=μ+group+pg+loc+cross+cross:loc+Entry+Entry:loc+row:loc+col:mainp:loc+e.Attaching the dummies to (group {groupRILs, groupCHK}), parental group (pg) (pgParent, pgechk) where pgParent is parents that are used in the cross, and pgechk is nonparents that are included as additional checks. In addition, for each treatment factor (cross and entry), dummies have been attached as shown in the following model, and the respective design factors for rows, columns, and main plots were considered per location.(5)Y=μ+group+pg+loc+cross:pgParent+cross:pgParent:loc+Entry:pgechk+Entry:pgechk:loc+Entry:groupCHK:pgParent+Entry:groupRIL+Entry:groupCHK:pgParent:loc+Entry:groupRIL:loc+row:loc+col:mainp:loc+e,where Y is the total observation for the trait of interest, μ is the overall mean of RIL, group is to identify checks, and RIL is the only fixed factor, and crosses, checks, and RILs within crosses are assigned as genotypes in the model. Dummies were included to estimate the effect of one factor by switching off other effects. Accordingly, for pgParent, pgechk, groupCHK, and groupRIL dummies were attached to estimate the effect of parents, echek, checks, and RIL by switching off one factor over the other. echk identifies extra checks besides the 17 parents actually used in crossing, CHK represents the total checks used in the experiment (i.e., including both parents and nonparents), RIL is recombinant inbred lines derived from the crosses, and loc assigns locations. An example of other interactions with environments (Entry.loc) is defined as the interaction between location and set of genotype groups, i.e., crosses, checks, RILs within crosses. row.loc and (mp.col.loc) are rows, columns, and main plots effects, respectively, nested within locations, and e is the random error for the model.


### 2.4.2. Estimate of Heritability (Broad Sense)

Heritability was estimated based on Cullis et al. [25]. Specific allocation for checks crosses and RIL was taken into account when estimating their respective heritability.(6)H2Cullis=1−average standard error from BLUP2∗σg2,where σg2 is genotype variance from a model construct.


### 2.4.3. Theory Assumptions

We assume that RIL represents a line population developed under a single seed descent (SSD) procedure:(i)
Forces driving changes of allele frequencies such as selection, migration, drift, and mutation [15] are assumed to be negligible(ii)
Linkage equilibrium [15] between QTL controlling a trait is given(iii)
Epistasis is absent or of minor importanceWith these assumptions given a simple additive genetic model can be used as suggested by [6, 25].


### 2.4.4. Parameters Estimation for Phenotypic Data

Best Linear Unbiased Predictions (BLUPs) were computed for means of parents, crosses, and RILs within crosses and estimated as random effects with distributionµ∼MVN (0, ∑σμ2) being ∑σμ2 a relationship matrix among the level of the random effect. The genetic variance of mid-parents was estimated from the genetic variance of the female (σf2) and male (σm2) parental lines (σp2) σp2 = (σm2 + σf2)/2. The genetic variance among crosses σc2 is the variance component accounting for variation between the 30 crosses and is estimated as the variance component assuming crosses as random [6]. The average segregation variance σg2 is the variation of RILs within crosses. Under the assumptions specified above, a quantitative genetic interpretation of the breeding parameters is given in Table 3.Table 2
List of agronomic and quality parameters collected.
SNVariablesCodeNature of VariablesCollection method1Heading dateDHQuantitativeNumber of days from date of sowing till about 75% of plants in the plot was flowering2Maturity dateDMQuantitativeNumber of days from sowing to the date when 75% of the peduncle turned to yellow straw color and when no green color remained on glumes and peduncles of the tagged plant3Plant heightPHQuantitativeThe actual measurement of plant height from ground level to the tip of the spike excluding the awns and recorded as the average of five randomly selected plants in each plot4Thousand kernel weightTKWQuantitativeWeights were measured by taking the mass of carefully counted a thousand kernels on sensitive electronic balance (±0.1 g) after kernels were adjusted to 12.5% moisture content5Grain protein concentrationGPCQuantitativeTotal protein content in the grain, expressed as a percentage. estimated using the NIRS machine6Malt extractMEQuantitativeSolid material extracted from finely ground malt, expressed as a percentage. estimated using the NIRS machine7FriabilityFRQuantitativeIndicator of endosperm modification after malting by a simple milling test in a friabilimeter, expressed as a percentage. estimated using the NIRS machine8Beta-glucanBGQuantitativea principal constituent of the barley endosperm cell wall, expressed as mg/estimated using the NIRS machine


## 2.4.1. Estimation of Variance Components

A spatial model was fitted to produce adjusted genotype means for each environment [20, 21]. After spatial adjustment, a combined analysis was conducted across the environment [22, 23]. The linear mixed model for the combined analysis contains different dummy groups to predict the adjusted mean precisely [24]. The model was defined as(4)Y=μ+group+pg+loc+cross+cross:loc+Entry+Entry:loc+row:loc+col:mainp:loc+e.Attaching the dummies to (group {groupRILs, groupCHK}), parental group (pg) (pgParent, pgechk) where pgParent is parents that are used in the cross, and pgechk is nonparents that are included as additional checks. In addition, for each treatment factor (cross and entry), dummies have been attached as shown in the following model, and the respective design factors for rows, columns, and main plots were considered per location.(5)Y=μ+group+pg+loc+cross:pgParent+cross:pgParent:loc+Entry:pgechk+Entry:pgechk:loc+Entry:groupCHK:pgParent+Entry:groupRIL+Entry:groupCHK:pgParent:loc+Entry:groupRIL:loc+row:loc+col:mainp:loc+e,where Y is the total observation for the trait of interest, μ is the overall mean of RIL, group is to identify checks, and RIL is the only fixed factor, and crosses, checks, and RILs within crosses are assigned as genotypes in the model. Dummies were included to estimate the effect of one factor by switching off other effects. Accordingly, for pgParent, pgechk, groupCHK, and groupRIL dummies were attached to estimate the effect of parents, echek, checks, and RIL by switching off one factor over the other. echk identifies extra checks besides the 17 parents actually used in crossing, CHK represents the total checks used in the experiment (i.e., including both parents and nonparents), RIL is recombinant inbred lines derived from the crosses, and loc assigns locations. An example of other interactions with environments (Entry.loc) is defined as the interaction between location and set of genotype groups, i.e., crosses, checks, RILs within crosses. row.loc and (mp.col.loc) are rows, columns, and main plots effects, respectively, nested within locations, and e is the random error for the model.


## 2.4.2. Estimate of Heritability (Broad Sense)

Heritability was estimated based on Cullis et al. [25]. Specific allocation for checks crosses and RIL was taken into account when estimating their respective heritability.(6)H2Cullis=1−average standard error from BLUP2∗σg2,where σg2 is genotype variance from a model construct.


## 2.4.3. Theory Assumptions

We assume that RIL represents a line population developed under a single seed descent (SSD) procedure:(i)
Forces driving changes of allele frequencies such as selection, migration, drift, and mutation [15] are assumed to be negligible(ii)
Linkage equilibrium [15] between QTL controlling a trait is given(iii)
Epistasis is absent or of minor importanceWith these assumptions given a simple additive genetic model can be used as suggested by [6, 25].


## 2.4.4. Parameters Estimation for Phenotypic Data

Best Linear Unbiased Predictions (BLUPs) were computed for means of parents, crosses, and RILs within crosses and estimated as random effects with distributionµ∼MVN (0, ∑σμ2) being ∑σμ2 a relationship matrix among the level of the random effect. The genetic variance of mid-parents was estimated from the genetic variance of the female (σf2) and male (σm2) parental lines (σp2) σp2 = (σm2 + σf2)/2. The genetic variance among crosses σc2 is the variance component accounting for variation between the 30 crosses and is estimated as the variance component assuming crosses as random [6]. The average segregation variance σg2 is the variation of RILs within crosses. Under the assumptions specified above, a quantitative genetic interpretation of the breeding parameters is given in Table 3.Table 2
List of agronomic and quality parameters collected.
SNVariablesCodeNature of VariablesCollection method1Heading dateDHQuantitativeNumber of days from date of sowing till about 75% of plants in the plot was flowering2Maturity dateDMQuantitativeNumber of days from sowing to the date when 75% of the peduncle turned to yellow straw color and when no green color remained on glumes and peduncles of the tagged plant3Plant heightPHQuantitativeThe actual measurement of plant height from ground level to the tip of the spike excluding the awns and recorded as the average of five randomly selected plants in each plot4Thousand kernel weightTKWQuantitativeWeights were measured by taking the mass of carefully counted a thousand kernels on sensitive electronic balance (±0.1 g) after kernels were adjusted to 12.5% moisture content5Grain protein concentrationGPCQuantitativeTotal protein content in the grain, expressed as a percentage. estimated using the NIRS machine6Malt extractMEQuantitativeSolid material extracted from finely ground malt, expressed as a percentage. estimated using the NIRS machine7FriabilityFRQuantitativeIndicator of endosperm modification after malting by a simple milling test in a friabilimeter, expressed as a percentage. estimated using the NIRS machine8Beta-glucanBGQuantitativea principal constituent of the barley endosperm cell wall, expressed as mg/estimated using the NIRS machine


## 3. Results

### 3.1. Mean of Parents

The MPV (Table4) of all 30 crosses represents the parental per se performance. Accordingly, Burton with the planet was found to be good in their mean performance in terms of DH (76.6 days), TKW (46.2 g), ME (80.7%), GPC (11.1%), and FR (70%), respectively. Similarly, the planet with MBHIBYT-22 also indicated good performance in terms of DH (80.8 days), PH (89.5 cm), ME (81.4%), GPC (11.1%), and FR (70%), respectively (Table 4). These indicate that the parents involved in the crossing program were relatively early maturing, with good malt quality traits with optimum grain weight. Further, some potential parental lines (e.g., planet or HB1963) have been used by Ethiopian farmers for malt barley production. These lines were taken as reference lines and supposed to be surpassed by the RIL derived from their crosses. We used the variety planet (European origin) in 13 of the crosses to transfer the malting quality and high yield potential under favorable agronomic conditions. Thus, the mid-parents were split into a group with and without a planet as a crossing partner. Hence, considering the difference between the two groups, we had observed −0.8. −0.7, 0.7, and 0.7 for DH, DM, PH, and TKW, respectively. This implied that the variety planet contributed to earliness, tallness, and better TKW. Similarly, the desired difference was observed for FR (1.1) and BG (−15) which revealed that the planet has positive effects on malt quality in terms of ME, FR, and BG. The presence of planet variety resulted in the difference observed between the two groups.Table 3
Parameter estimation and their quantitative genetic expectation assuming an additive model.
ParametersGenetic expectationsReferencesGeneration meansMid-parent valueMPVij = (mi + mj)/2[6]Cross-meanCij = (mi + mj)/2Genetic varianceAmong parentsσp2 = (σm2 + σf2)/2 = σA2Between means of crossesσc2 = σA2Among lines within crossesσg2 = σA2HeritabilityH2Cullis = 1 − average standard error from BLUP/σg2Cullis et al. 2006CorrelationPhenotypicσp2/2=σc2=σg2=σA2.[15]Genotypicrg=COVg1,g2/Varg1Varg2Regression of cross mean on MPVcij = m + bij(MPij) + eij[6]Usefulness of crossesUij = Cij + ΔGij = Cij + ihσgijSchnell & Utz, 1975m, mi, and mj = mean of the RIL population, parent i and j, resp.; MPVij = mid-parent value of parent i and j; Cij = predicted cross-mean; σA2 = variance of additive effects; σc2, σg2 = genotype variance among crosses and among lines within crosses, resp.; rp = phenotypic correlation, COV (trait 1, trait 2) = the covariance between the trait values, the denominator is the product of the square root of the phenotypic variance of trait 1 and trait 2; rg = genetic correlation, COV (g1, g2) = covariance of the genetic effects g1 and g2 for trait 1 and trait 2, the denominator is the product of the square root of genetic variance of trait 1 and trait 2; bij = the slope of regression; εij = error term; Uij is the usefulness of the cross Cij,, Rij = genetic gain, which is a result of segregation variance, heritability (h2) within the cross, and the selection intensity (i).


### 3.2. Mean and Ranges of RIL

The mean of the RIL population (Table5) estimated overall RIL within and across crosses reflects the general performance of the progeny produced from the parental lines. RIL performance ranged from 74.64 to 88.76 days for DH (mean 81.20 days), 126.50 to 139.60 days for DM (mean 133.10 days), 75.09 to 102.50 cm for PH (mean 91.51 cm), 79.4 to 81.39% for ME (mean of 80.68%), and 10.52 to 12.13% for GPC (mean11.21%). Minimum and maximum values and the respective standard deviation (SD) reveal a considerable variation that can be exploited by selection. For all traits, SD is higher than SE of means indicating that phenotypic variation is influenced by genetic variation.Table 4
BLUP predicted mid-parent values across two environments.
P1P2CrossDHDMPHTKWMEGPCFRBGPlanetMBHIBYT-23Cr182.0133.790.948.380.611.168.0338.9IBON 13/2G13–64Cr1080.7131.492.948.280.411.266.7376.7BurtonICARDA GP-67Cr1180.4131.792.046.080.611.168.2373.3G13-64MBHIBYT-22Cr1281.6134.087.645.681.111.169.9352.1PlanetIBON 14/15–144Cr1381.1132.991.147.881.111.168.7342.0PlanetIBON 13/14–128Cr1481.0133.389.846.780.911.267.5352.5PlanetIBON 14/15–129Cr1580.9134.591.247.381.411.168.4337.9PlanetIBON 13/14–41Cr1682.7136.293.349.380.711.266.5338.6PlanetMBHIBYT-22Cr1780.8133.089.546.781.411.170.0348.2M 135G13–64Cr1881.2134.191.547.180.611.267.0360.3PlanetICARDA GP–75Cr1980.4132.890.847.680.911.267.1341.1MN BriteIBON 13/14–128Cr279.6131.588.745.280.711.267.5398.3BurtonG13–64Cr2079.7130.290.746.580.611.267.4373.5G13-64ICARDA GP-75Cr2181.1133.889.046.480.611.267.0345.0IBON 13/2ICARDA GP-67Cr2281.3132.994.247.780.411.167.6376.6BurtonPlanetCr2379.6130.590.346.280.711.169.5369.8BurtonIBON 13/14–128Cr2480.1131.389.446.080.611.267.3382.3IBON 13/33G13–64Cr2581.1130.286.543.280.811.267.8314.0M 135PlanetCr2681.1134.491.146.880.811.169.1356.6IBON 13/2PlanetCr2780.6131.792.547.980.611.168.8373.1M 135IBON 13/14–128Cr2881.6135.290.246.680.611.266.9369.1(Bekoji-1 xGrace)PlanetCr2981.3132.492.547.281.011.169.7359.0HB 1963IBON 14/15–144Cr381.8134.089.246.680.811.168.7345.9PlanetICARDA GP–67Cr3081.3133.792.446.781.011.168.4343.5G13-64IBON 13/14–128Cr481.7134.387.945.680.611.267.5356.4IBON 14/15-144IBON 13/14–128Cr581.2131.589.443.680.611.267.4388.9IBON 14/15-144ICARDA GP-67Cr681.5132.092.043.680.611.168.3379.9MN BritePlanetCr779.2130.889.645.480.911.169.7385.8HB 1963IBON 13/14–128Cr882.0133.188.946.180.411.266.9387.1ICARDA GP-67HB 1963Cr985.8138.093.348.981.311.268.6348.4Mean81.1133.090.646.680.811.168.1360.5LSD0.450.670.690.530.100.020.397.31Mean planet crosses (N = 9)∗)80.5132.690.846.980.911.168.7357.0Mean Nonplanet crosses (N = 13)∗)81.3133.390.146.280.711.267.6372.0Δ(Nonplanet vs. planet crosses∗))−0.8−0.70.70.70.20.01.1−15.0∗crosses had been selected to balance the gametic contributions of parental lines in the two groups. P1, P2 = Parent 1 and Parent 2, DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, FR = friability, GPC = gain protein concentration, BG = beta-glucan.


### 3.3. Variance among Parents, Crosses, and Lines within Crosses

Analysis of variance (Table6) revealed significant (P<0.05) genetic variation among parents for DH, PH, and GPC, while other traits showed nonsignificant differences among parents. Significant genetic variances among crosses were observed for DH, DM, TKW, ME, FR, and GPC but not for PH, and BG. Genetic variance among RIL within crosses was highly significant (P<0.001) almost for all traits except for ME and GPC. For two traits (DM, ME), the ratio of genetic variancesσc2: σp2/2 was estimated to be larger than one. In contrast, the ratio for PH was found to be significantly smaller than one. Significant (P<0.05) genotype × location interaction variances were consistently observed for parents, crosses, and RIL for DM, PH, TKW, FR, and BG which indicates that genotypes differ in response to the two environments.Table 5
Mean, minimum and maximum values estimated from 30 F4:5 RIL per cross based on 30 crosses tested across two environments.
DHDMPHTKWMEFRGPCBGMin74.64126.5075.0935.1679.7652.4010.52317.40Max88.76139.60102.5058.1681.3976.1712.13430.00Mean81.20133.1091.5146.8880.6866.6511.21363.40SD2.471.993.492.740.240.232.9615.55SE0.080.070.120.090.010.010.100.52LSD0.1630.1430.250.1840.020.020.2041.06DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, FR = friability, GPC = gain protein concentration, BG = beta-glucan, SD = standard deviation, SE = standard error of RIL means.


### 3.4. Genetic Variance within Crosses (σg2)

The average genetic variance of RIL within crosses was estimated in a combined analysis as shown in Table6. Besides, for each of the 30 crosses, the variance of RIL was estimated separately (Table 7) hypothesizing that the genetic variance (σg2) and/or their genotype × location interaction variance are different from cross to cross. Except for ME, FR, and BG relevant differences between the crosses with regard to σg2 were observed. The range of σg2 was very high for DH (2.56–10.48), DM (1.25–7.7), PH (3.0–29.7), TKW (1.92–36.28), FR (3.12–23.6), and BG (114.2–455.7), and for these traits, the respective SD exceeds SE (Table 7). It is noteworthy that there is a difference between the estimates shown in Table 6 to the genetic variance of RIL explained in Table 7. The genetic variance of RILs shown in Table 6 is generated from BLUE, whereas the genetic variance shown in Table 7 is generated from BLUP predicted mean values. These BLUP predicted mean values are actually penalized by the shrinkage effect, which leads to much smaller estimates in Table 6 compared to Table 7.Table 6
Variance components for the genetic and genotype × location effects of parents, crosses, and RIL within crosses estimated from the combined analysis over locations.
Source of variationDFDHDMPHTKWMEFRGPCBGParents (σp2)1627.01∗13.64240.65∗15.700.6855.990.67∗7725.53Parent: Loc162.6014.21∗22.92∗4.79∗1.2429.63∗0.154401.44∗Crosses (σc2)297.90∗20.36∗15.1310.87∗0.82∗25.88∗0.07∗3398.14Cross: Loc290.992.66∗55.70∗3.11∗0.30∗14.94∗0.256762.4∗RIL (σg2)87011.14∗∗∗9.15∗∗∗30.66∗∗∗14.13∗∗∗0.34∗27.17∗∗0.1961811.44∗RIL: Loc8703.55∗∗8.29∗∗∗39.28∗∗∗2.82∗∗0.27∗42.69∗∗∗0.11∗13984.4∗∗∗Ratioσc2: σp2/20.602.99∗∗0.13∗∗1.392.41∗∗0.920.220.89Ratioσc2: σg20.712.23∗∗0.50∗∗0.772.41∗∗0.950.371.88∗∗∗, ∗∗, ∗∗∗significance at α = 0.05, 0.01, 0.001, respectively, DF = degree of freedom, DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, FR = friability, GPC = gain protein concentration, BG = beta-glucan.


### 3.5. Broad Sense Heritability (H2) of Traits among Parents, Crosses, and RIL

Heritability across both environments (Figure1) showed moderate to high estimates with a range of 27.4 to 87.4% depending on the source of genetic variation (parents, crosses, and RIL) and trait (Figure 1). For the parents, H2 ranges from 49.5% for ME to 93.6% for PH, for the crosses H2 ranges from 29.5% for GPC to 87.0% for DM, whereas for the RIL H2 extends from 27.4% for BG to 73.6 for TKW, respectively. Compared to parents and crosses, H2 for RIL are smaller for most traits. This is in line with the genetic and the interaction location variance components shown in Table 5. Concerning the average standard error going into the H2 formula, it has to be taken into account that testing intensity for parents is higher compared to RIL.Figure 1
Heritability of traits for parents, crosses, and RILs across. DH=days to heading, DM=days to maturity, PH=plant height, TKW=thousand kernel weight, ME=malt extract, GPC=gain protein concentration, FR=friability, BG=beta-glucan, Hol=Holeta, Bek=Bekoji.


### 3.6. Phenotypic and Genotypic Correlation between Traits

The phenotypic and genotypic trait correlation values obtained were low to moderate with absolute values ranging between 0.00 and 0.78 (Table8). Accordingly, positive and significant (P<0.01) phenotypic and genotypic correlations were found between ME and FR (r = 0.58 and 0.60) and DH and DM (r = 0.65 and 0.78) whereas the negative and significant phenotypic and genotypic correlation was between FR and GPC (r = −0.60 and−0.73), respectively (Table 8). The positive significant correlation observed between ME versus FR and DH versus DM reveals that selection for one trait will lead to automatic selection for the other, leading to more rapid progress in selection for both traits, whereas in the case of negative correlation, simultaneous improvement of the traits is difficult. Overall, correlations among malting quality traits were higher than the correlations among agronomic traits.Table 7
Mean minimum and maximum genetic variances (σg2) among RILs within crosses estimated from 900F4:5 based on the 30 malt barley crosses for traits studied.
DH days to heading, DM days to maturity, PH plant height, TKW thousand kernel weight, ME malt extract, FR friability, GPC gain protein concentration, BG beta-glucan, SD standard deviation, SE standard error.


### 3.7. Regression of Cross-Mean (CM) on Mid-Parent Value (MPV)

Regression coefficients of the cross-mean on mid-parent values studied were highly significantly different from zero for all traits (Table9). The portion of the cross-mean variance attributed to the regression coefficient is quantified by the coefficient of determination (R2). R2 ranges from 0.27 to 0.70 and is higher than 0.5 for most of the traits. This indicates that the MPV was an accurate predictor of the CM performance. Regression and determination coefficients increase if the phenotypic covariance between MPV and CMs in the nominator is large and vice versa they decrease if phenotypic variances in the denominator are large. H2 for MPV and CM indicates how much phenotypic variance is inflated compared to their genotypic variances.Table 8
Correlation of traits studied (genotypic correlation above diagonal).
Deep green desired direction and strong relation, light green desired direction and moderate correlation, very light green desired direction and weak correlation, deep red undesired direction and moderate correlation, light red undesired direction and weak correlation, correlations values above 0.2 and below ‐0.2 are significant (P < 0.01).


### 3.8. Usefulness of Crosses

Since the interest of the breeding program is typically both increasing the mean value of the breeding population and identifying superior RIL, crosses can be ranked based on the usefulness criterion (Schnell and Utz, 1975). To illustrate a practical application of the usefulness parameter (Table10), the 30 crosses of the experiment were evaluated for their potential to deliver a RIL that can outperform the well-known malting variety planet for five important field and malt quality traits (PH, TKW, ME, FR, and BG). U has been calculated as Uij = Cij + ihσ, and as selection intensity U(i = 1) was chosen. This selection intensity corresponds to a selection rate of α∼0.3. The best 8 crosses surpass the planet with their selected fraction U(i = 1) for all 5 traits. Thus, assuming sufficient RILs/crosses are available, there is a good chance to select one “all-rounder” RIL out of these crosses, which has a good performance for all 5 traits green color in Table 10. The second-best group of 8 crosses fits the U criterion for 4 traits (blue color). The third and fourth groups (9 and 5 crosses, respectively) are considered inferior because for more traits compromises have to be accepted. If the breeder could predict the most attractive crosses at the beginning of the breeding cycle, he would invest in higher numbers of RIL of these crosses and discard the low-performing crosses to save breeding capacity.Table 9
Association of Mid-Parent Values (MPV) to Cross Means (CM).
ParameterTraitDHDMPHTKWMEFRGPCBGRegression coefficient1.51∗∗∗1.60∗∗∗0.84∗∗∗1.61∗∗∗2.07∗∗∗2.17∗∗2.64∗∗1.35∗∗∗SE0.270.300.150.200.320.620.760.26R20.520.500.520.700.580.280.270.47H2 crosses0.810.870.370.730.690.680.420.49H2 parents0.870.720.930.730.490.740.810.83∗, ∗∗, ∗∗∗indicates significance at P=0.05, 0.01, and 0.001, resp. DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, GPC = gain protein concentration, FR = friability, BG = beta-glucan.Table 10
Usefulness of crosses (Ui = 1).


## 3.1. Mean of Parents

The MPV (Table4) of all 30 crosses represents the parental per se performance. Accordingly, Burton with the planet was found to be good in their mean performance in terms of DH (76.6 days), TKW (46.2 g), ME (80.7%), GPC (11.1%), and FR (70%), respectively. Similarly, the planet with MBHIBYT-22 also indicated good performance in terms of DH (80.8 days), PH (89.5 cm), ME (81.4%), GPC (11.1%), and FR (70%), respectively (Table 4). These indicate that the parents involved in the crossing program were relatively early maturing, with good malt quality traits with optimum grain weight. Further, some potential parental lines (e.g., planet or HB1963) have been used by Ethiopian farmers for malt barley production. These lines were taken as reference lines and supposed to be surpassed by the RIL derived from their crosses. We used the variety planet (European origin) in 13 of the crosses to transfer the malting quality and high yield potential under favorable agronomic conditions. Thus, the mid-parents were split into a group with and without a planet as a crossing partner. Hence, considering the difference between the two groups, we had observed −0.8. −0.7, 0.7, and 0.7 for DH, DM, PH, and TKW, respectively. This implied that the variety planet contributed to earliness, tallness, and better TKW. Similarly, the desired difference was observed for FR (1.1) and BG (−15) which revealed that the planet has positive effects on malt quality in terms of ME, FR, and BG. The presence of planet variety resulted in the difference observed between the two groups.Table 3
Parameter estimation and their quantitative genetic expectation assuming an additive model.
ParametersGenetic expectationsReferencesGeneration meansMid-parent valueMPVij = (mi + mj)/2[6]Cross-meanCij = (mi + mj)/2Genetic varianceAmong parentsσp2 = (σm2 + σf2)/2 = σA2Between means of crossesσc2 = σA2Among lines within crossesσg2 = σA2HeritabilityH2Cullis = 1 − average standard error from BLUP/σg2Cullis et al. 2006CorrelationPhenotypicσp2/2=σc2=σg2=σA2.[15]Genotypicrg=COVg1,g2/Varg1Varg2Regression of cross mean on MPVcij = m + bij(MPij) + eij[6]Usefulness of crossesUij = Cij + ΔGij = Cij + ihσgijSchnell & Utz, 1975m, mi, and mj = mean of the RIL population, parent i and j, resp.; MPVij = mid-parent value of parent i and j; Cij = predicted cross-mean; σA2 = variance of additive effects; σc2, σg2 = genotype variance among crosses and among lines within crosses, resp.; rp = phenotypic correlation, COV (trait 1, trait 2) = the covariance between the trait values, the denominator is the product of the square root of the phenotypic variance of trait 1 and trait 2; rg = genetic correlation, COV (g1, g2) = covariance of the genetic effects g1 and g2 for trait 1 and trait 2, the denominator is the product of the square root of genetic variance of trait 1 and trait 2; bij = the slope of regression; εij = error term; Uij is the usefulness of the cross Cij,, Rij = genetic gain, which is a result of segregation variance, heritability (h2) within the cross, and the selection intensity (i).


## 3.2. Mean and Ranges of RIL

The mean of the RIL population (Table5) estimated overall RIL within and across crosses reflects the general performance of the progeny produced from the parental lines. RIL performance ranged from 74.64 to 88.76 days for DH (mean 81.20 days), 126.50 to 139.60 days for DM (mean 133.10 days), 75.09 to 102.50 cm for PH (mean 91.51 cm), 79.4 to 81.39% for ME (mean of 80.68%), and 10.52 to 12.13% for GPC (mean11.21%). Minimum and maximum values and the respective standard deviation (SD) reveal a considerable variation that can be exploited by selection. For all traits, SD is higher than SE of means indicating that phenotypic variation is influenced by genetic variation.Table 4
BLUP predicted mid-parent values across two environments.
P1P2CrossDHDMPHTKWMEGPCFRBGPlanetMBHIBYT-23Cr182.0133.790.948.380.611.168.0338.9IBON 13/2G13–64Cr1080.7131.492.948.280.411.266.7376.7BurtonICARDA GP-67Cr1180.4131.792.046.080.611.168.2373.3G13-64MBHIBYT-22Cr1281.6134.087.645.681.111.169.9352.1PlanetIBON 14/15–144Cr1381.1132.991.147.881.111.168.7342.0PlanetIBON 13/14–128Cr1481.0133.389.846.780.911.267.5352.5PlanetIBON 14/15–129Cr1580.9134.591.247.381.411.168.4337.9PlanetIBON 13/14–41Cr1682.7136.293.349.380.711.266.5338.6PlanetMBHIBYT-22Cr1780.8133.089.546.781.411.170.0348.2M 135G13–64Cr1881.2134.191.547.180.611.267.0360.3PlanetICARDA GP–75Cr1980.4132.890.847.680.911.267.1341.1MN BriteIBON 13/14–128Cr279.6131.588.745.280.711.267.5398.3BurtonG13–64Cr2079.7130.290.746.580.611.267.4373.5G13-64ICARDA GP-75Cr2181.1133.889.046.480.611.267.0345.0IBON 13/2ICARDA GP-67Cr2281.3132.994.247.780.411.167.6376.6BurtonPlanetCr2379.6130.590.346.280.711.169.5369.8BurtonIBON 13/14–128Cr2480.1131.389.446.080.611.267.3382.3IBON 13/33G13–64Cr2581.1130.286.543.280.811.267.8314.0M 135PlanetCr2681.1134.491.146.880.811.169.1356.6IBON 13/2PlanetCr2780.6131.792.547.980.611.168.8373.1M 135IBON 13/14–128Cr2881.6135.290.246.680.611.266.9369.1(Bekoji-1 xGrace)PlanetCr2981.3132.492.547.281.011.169.7359.0HB 1963IBON 14/15–144Cr381.8134.089.246.680.811.168.7345.9PlanetICARDA GP–67Cr3081.3133.792.446.781.011.168.4343.5G13-64IBON 13/14–128Cr481.7134.387.945.680.611.267.5356.4IBON 14/15-144IBON 13/14–128Cr581.2131.589.443.680.611.267.4388.9IBON 14/15-144ICARDA GP-67Cr681.5132.092.043.680.611.168.3379.9MN BritePlanetCr779.2130.889.645.480.911.169.7385.8HB 1963IBON 13/14–128Cr882.0133.188.946.180.411.266.9387.1ICARDA GP-67HB 1963Cr985.8138.093.348.981.311.268.6348.4Mean81.1133.090.646.680.811.168.1360.5LSD0.450.670.690.530.100.020.397.31Mean planet crosses (N = 9)∗)80.5132.690.846.980.911.168.7357.0Mean Nonplanet crosses (N = 13)∗)81.3133.390.146.280.711.267.6372.0Δ(Nonplanet vs. planet crosses∗))−0.8−0.70.70.70.20.01.1−15.0∗crosses had been selected to balance the gametic contributions of parental lines in the two groups. P1, P2 = Parent 1 and Parent 2, DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, FR = friability, GPC = gain protein concentration, BG = beta-glucan.


## 3.3. Variance among Parents, Crosses, and Lines within Crosses

Analysis of variance (Table6) revealed significant (P<0.05) genetic variation among parents for DH, PH, and GPC, while other traits showed nonsignificant differences among parents. Significant genetic variances among crosses were observed for DH, DM, TKW, ME, FR, and GPC but not for PH, and BG. Genetic variance among RIL within crosses was highly significant (P<0.001) almost for all traits except for ME and GPC. For two traits (DM, ME), the ratio of genetic variancesσc2: σp2/2 was estimated to be larger than one. In contrast, the ratio for PH was found to be significantly smaller than one. Significant (P<0.05) genotype × location interaction variances were consistently observed for parents, crosses, and RIL for DM, PH, TKW, FR, and BG which indicates that genotypes differ in response to the two environments.Table 5
Mean, minimum and maximum values estimated from 30 F4:5 RIL per cross based on 30 crosses tested across two environments.
DHDMPHTKWMEFRGPCBGMin74.64126.5075.0935.1679.7652.4010.52317.40Max88.76139.60102.5058.1681.3976.1712.13430.00Mean81.20133.1091.5146.8880.6866.6511.21363.40SD2.471.993.492.740.240.232.9615.55SE0.080.070.120.090.010.010.100.52LSD0.1630.1430.250.1840.020.020.2041.06DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, FR = friability, GPC = gain protein concentration, BG = beta-glucan, SD = standard deviation, SE = standard error of RIL means.


## 3.4. Genetic Variance within Crosses (σg2)

The average genetic variance of RIL within crosses was estimated in a combined analysis as shown in Table6. Besides, for each of the 30 crosses, the variance of RIL was estimated separately (Table 7) hypothesizing that the genetic variance (σg2) and/or their genotype × location interaction variance are different from cross to cross. Except for ME, FR, and BG relevant differences between the crosses with regard to σg2 were observed. The range of σg2 was very high for DH (2.56–10.48), DM (1.25–7.7), PH (3.0–29.7), TKW (1.92–36.28), FR (3.12–23.6), and BG (114.2–455.7), and for these traits, the respective SD exceeds SE (Table 7). It is noteworthy that there is a difference between the estimates shown in Table 6 to the genetic variance of RIL explained in Table 7. The genetic variance of RILs shown in Table 6 is generated from BLUE, whereas the genetic variance shown in Table 7 is generated from BLUP predicted mean values. These BLUP predicted mean values are actually penalized by the shrinkage effect, which leads to much smaller estimates in Table 6 compared to Table 7.Table 6
Variance components for the genetic and genotype × location effects of parents, crosses, and RIL within crosses estimated from the combined analysis over locations.
Source of variationDFDHDMPHTKWMEFRGPCBGParents (σp2)1627.01∗13.64240.65∗15.700.6855.990.67∗7725.53Parent: Loc162.6014.21∗22.92∗4.79∗1.2429.63∗0.154401.44∗Crosses (σc2)297.90∗20.36∗15.1310.87∗0.82∗25.88∗0.07∗3398.14Cross: Loc290.992.66∗55.70∗3.11∗0.30∗14.94∗0.256762.4∗RIL (σg2)87011.14∗∗∗9.15∗∗∗30.66∗∗∗14.13∗∗∗0.34∗27.17∗∗0.1961811.44∗RIL: Loc8703.55∗∗8.29∗∗∗39.28∗∗∗2.82∗∗0.27∗42.69∗∗∗0.11∗13984.4∗∗∗Ratioσc2: σp2/20.602.99∗∗0.13∗∗1.392.41∗∗0.920.220.89Ratioσc2: σg20.712.23∗∗0.50∗∗0.772.41∗∗0.950.371.88∗∗∗, ∗∗, ∗∗∗significance at α = 0.05, 0.01, 0.001, respectively, DF = degree of freedom, DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, FR = friability, GPC = gain protein concentration, BG = beta-glucan.


## 3.5. Broad Sense Heritability (H2) of Traits among Parents, Crosses, and RIL

Heritability across both environments (Figure1) showed moderate to high estimates with a range of 27.4 to 87.4% depending on the source of genetic variation (parents, crosses, and RIL) and trait (Figure 1). For the parents, H2 ranges from 49.5% for ME to 93.6% for PH, for the crosses H2 ranges from 29.5% for GPC to 87.0% for DM, whereas for the RIL H2 extends from 27.4% for BG to 73.6 for TKW, respectively. Compared to parents and crosses, H2 for RIL are smaller for most traits. This is in line with the genetic and the interaction location variance components shown in Table 5. Concerning the average standard error going into the H2 formula, it has to be taken into account that testing intensity for parents is higher compared to RIL.Figure 1
Heritability of traits for parents, crosses, and RILs across. DH=days to heading, DM=days to maturity, PH=plant height, TKW=thousand kernel weight, ME=malt extract, GPC=gain protein concentration, FR=friability, BG=beta-glucan, Hol=Holeta, Bek=Bekoji.


## 3.6. Phenotypic and Genotypic Correlation between Traits

The phenotypic and genotypic trait correlation values obtained were low to moderate with absolute values ranging between 0.00 and 0.78 (Table8). Accordingly, positive and significant (P<0.01) phenotypic and genotypic correlations were found between ME and FR (r = 0.58 and 0.60) and DH and DM (r = 0.65 and 0.78) whereas the negative and significant phenotypic and genotypic correlation was between FR and GPC (r = −0.60 and−0.73), respectively (Table 8). The positive significant correlation observed between ME versus FR and DH versus DM reveals that selection for one trait will lead to automatic selection for the other, leading to more rapid progress in selection for both traits, whereas in the case of negative correlation, simultaneous improvement of the traits is difficult. Overall, correlations among malting quality traits were higher than the correlations among agronomic traits.Table 7
Mean minimum and maximum genetic variances (σg2) among RILs within crosses estimated from 900F4:5 based on the 30 malt barley crosses for traits studied.
DH days to heading, DM days to maturity, PH plant height, TKW thousand kernel weight, ME malt extract, FR friability, GPC gain protein concentration, BG beta-glucan, SD standard deviation, SE standard error.


## 3.7. Regression of Cross-Mean (CM) on Mid-Parent Value (MPV)

Regression coefficients of the cross-mean on mid-parent values studied were highly significantly different from zero for all traits (Table9). The portion of the cross-mean variance attributed to the regression coefficient is quantified by the coefficient of determination (R2). R2 ranges from 0.27 to 0.70 and is higher than 0.5 for most of the traits. This indicates that the MPV was an accurate predictor of the CM performance. Regression and determination coefficients increase if the phenotypic covariance between MPV and CMs in the nominator is large and vice versa they decrease if phenotypic variances in the denominator are large. H2 for MPV and CM indicates how much phenotypic variance is inflated compared to their genotypic variances.Table 8
Correlation of traits studied (genotypic correlation above diagonal).
Deep green desired direction and strong relation, light green desired direction and moderate correlation, very light green desired direction and weak correlation, deep red undesired direction and moderate correlation, light red undesired direction and weak correlation, correlations values above 0.2 and below ‐0.2 are significant (P < 0.01).


## 3.8. Usefulness of Crosses

Since the interest of the breeding program is typically both increasing the mean value of the breeding population and identifying superior RIL, crosses can be ranked based on the usefulness criterion (Schnell and Utz, 1975). To illustrate a practical application of the usefulness parameter (Table10), the 30 crosses of the experiment were evaluated for their potential to deliver a RIL that can outperform the well-known malting variety planet for five important field and malt quality traits (PH, TKW, ME, FR, and BG). U has been calculated as Uij = Cij + ihσ, and as selection intensity U(i = 1) was chosen. This selection intensity corresponds to a selection rate of α∼0.3. The best 8 crosses surpass the planet with their selected fraction U(i = 1) for all 5 traits. Thus, assuming sufficient RILs/crosses are available, there is a good chance to select one “all-rounder” RIL out of these crosses, which has a good performance for all 5 traits green color in Table 10. The second-best group of 8 crosses fits the U criterion for 4 traits (blue color). The third and fourth groups (9 and 5 crosses, respectively) are considered inferior because for more traits compromises have to be accepted. If the breeder could predict the most attractive crosses at the beginning of the breeding cycle, he would invest in higher numbers of RIL of these crosses and discard the low-performing crosses to save breeding capacity.Table 9
Association of Mid-Parent Values (MPV) to Cross Means (CM).
ParameterTraitDHDMPHTKWMEFRGPCBGRegression coefficient1.51∗∗∗1.60∗∗∗0.84∗∗∗1.61∗∗∗2.07∗∗∗2.17∗∗2.64∗∗1.35∗∗∗SE0.270.300.150.200.320.620.760.26R20.520.500.520.700.580.280.270.47H2 crosses0.810.870.370.730.690.680.420.49H2 parents0.870.720.930.730.490.740.810.83∗, ∗∗, ∗∗∗indicates significance at P=0.05, 0.01, and 0.001, resp. DH = days to heading, DM = days to maturity, PH = plant height, TKW = thousand kernel weight, ME = malt extract, GPC = gain protein concentration, FR = friability, BG = beta-glucan.Table 10
Usefulness of crosses (Ui = 1).


## 4. Discussion

### 4.1. Comparison of Generation Means

Means of 30 mid-parents values (μMPV) and their 900 derived RIL (μRIL) were estimated across Holeta and Bekoji (Table 11). Differences Δ (μMPV–μRIL) across all crosses were small in general and nonsignificant in a t-test. On average, RIL was found to be slightly later and taller and provided with a higher TKW. With regard to malt quality traits, RIL deviated slightly in the undesired direction. Three driving forces for deviations between generation means shall be discussed in the following.(i)
Differences between generation means could be due to shortcomings in the accuracy of our experimental data. Compared to Bekoji, the accuracy of Holeta was lower. Alternative designs to the p-rep design chosen might lead to higher accuracies and are discussed below.(ii)
Selection and also drift effects during line development from F2- to F4- generation are potential reasons for a difference between generation means. In these generations, entries are grown as single plants which could efficiently be selected on traits such as DH, PH, or TKW. Because not more than 30 RIL/cross had been sampled, drift effects cannot be excluded.(iii)
Based on the genetic architecture of the traits, epistasis could be an explanation for the difference between the two generations. The absence of significant differences between the generations’ means would suggest the following: (1) epistatic effects are of minor importance in the germplasm investigated and/or (2) positive and negative epistatic effects have canceled each other. In line with this, [6] reported that epistatic effect was the main reason for the observed difference between generations' mean. The fact that deviations between parents and RIL were larger and differing in sign when considering the planet and nonplanet crosses separately speaks in favor of the second “canceling” hypothesis. In any case, epistasis can be considered a potential source of bias and breeders should try to limit its impact. For example, in the future, when assessing mid-parent values, breeders could estimate the breeding value instead of the genotypic value of the putative parental lines and use them to predict cross-means. In line with this, many studies showed the involvement of epistasis in generation mean on barley [25], durum wheat [28], or bread wheat [29–32].(iv)
Finally, all three driving forces might be confounded in the phenotypic data and might have canceled each other to a certain extent.


### 4.2. Variance among Mid-Parents, Crosses, and Lines within Crosses

In the previous sections of this study, a simple genetical model has been proposed. In short, this model assumes that all parental lines (i) originate from one random mating population in linkage equilibrium and (ii) are mated randomly to form crosses. (iii) Parental lines are assumed to be homozygous. (iv) From these crosses, homozygous RILs are derived by an SSD process in the absence of forces driving changes in allele frequency. (v) As a mode of inheritance, additive gene action and absence of epistasis have been postulated. With this model, we expect the genetical variances of parents, crosses, and RILs:(7)σp22=σc2=σg2=σA2.The following deviations of the breeding population studied in the real experiment from the idealized population described above will be addressed. In particular, the impacts of these deviations on genetic variances are discussed.(i)
17 parental lines have been used to produce crosses. As shown in Table1, lines have different geographical origins such as the USA, Europe, Ethiopia, and ICARDA. Diversity analysis based on KASP markers (Marker data not shown) groups the lines into 3 (sub)populations. Thus, the assumption that parental lines originate from one population is not met in our experiment. If populations differ in their allele frequencies and means, crosses between them will lead to more heterozygous F1 plants. Variance within crosses derived from these F1 genotypes will be increased compared to the variance among crosses [6] and accordingly shrink the ratio σc2: σg2.(iii)
Another model assumption is that parental lines are randomly intercrossed. With 17 parental lines (17 × 16)/2 = 136 crosses are feasible. Out of these potential 136 crosses, only 30 crosses had been investigated for our experiment. This small section led to variation in the gametic contributions of the parental lines. For example, the planet had been involved in 13 crosses, whereas Bekoji × Grace contributed only to one cross. Further, the small sample of crosses could have led to assortative or disassortative mating [15], which means that lines with a similar or dissimilar genotype for a given trait have been crossed more often than those that would occur by chance. Assortative mating increases the variance between crosses and decreases the variance within crosses. The opposite holds true for disassortative mating. Breeders often follow these nonrandom matings by “best × best” and “parents complementary” crossing designs, respectively. Which of these forces leading to deviation from random mating predominated in our case has to be inspected for each trait separately.(iii)
Parents were assumed to be homozygous. Adopting the homogeneity threshold of 95%, we know this assumption does not hold true for 6 out of the 17 parents (marker data not shown). The more heterogeneous lines taken for crosses are, the more the variance within crosses increases, and correspondingly, the variance among crosses decreases.(iv)
RILs used in our experiment are lines derived from individual F4-SP and tested in F5-generation. F4-SP is expected to be homozygous for 87.5% of the loci having been heterozygous in the ancestral F1 genotype. The remaining 12.5% of the loci are still heterozygous and do not contribute to segregation variance between RILs within a given cross. In case fully homozygous RILs were produced, e.g., by double haploid culture, 100% of the loci would have been homozygous and a higher segregation variance is expected. As a consequence, the RIL generation chosen for our experiment will contribute to inflating the ratioσc2: σg2. In the SSD procedure leading to the final RILs, no change of allele frequency due to drift, selection, migration, and mutation has been assumed. In practical breeding, drift could occur due to bottlenecks in the preceding generations. Selection on traits such as earliness, plant height, or TKW is straightforward to have happened. (Im)migration of foreign germplasm into the progeny of a cross can be caused by, e.g., technical mixture or wrong pedigree assignment.(v)
From analyzing the generation means in the previous chapter, we should be careful to regard epistatic effects and their respective variance as nonexistent. This conclusion is in line with findings in the literature [6] for wheat and [11] for barley.Recurring to the balance sheet of the genetical variances estimated in our experiment, the following conclusions can be drawn. The parameterσp2/2 subdivides the variance among individual parental lines by 2 and is meant as an estimator of the variance between mid-parents. Taking the arguments summarized under (ii), this estimator is rather imperfect and should be replaced by the variance among mid-parents used in our experiment. Ratio σc2: σg2 was assumed to be equal to one. Taking the arguments summarized under (i)-(iv), we see severe violations of the assumptions made in the initial model, and therefore, we cannot anymore expect these two variances to be equivalent. For DH, PH, TKW, FR, and GPC, we observed a tendency for σc2 to be smaller than σg2. The opposite tendency was found for DM, ME, and BG. In particular, arguments under (ii) are of importance here. In contrast to the companion study of [6], in our case, mating of parental lines is highly unbalanced and cannot be regarded as random.The breeder might use outstanding RILs from this experiment for intercrossing and for starting a new breeding cycle. The resulting population will be much closer to the assumptions defined above than the actual breeding population and deliver variance estimates which are more representative of a situation close to classical second cycle breeding. Nevertheless, the actual estimates are a highly valuable starting point to improve breeding methodology. Irrespective of their actual ratio, the two variances,σc2 and σg2, proved to be significantly deviating from zero for almost all traits. Accordingly, the breeder can exploit both of them for selection. A similar result has been reported on wheat by [6] with large size of σg2 among RIL within crosses.


### 4.3. Genetic Variance within Crosses (σg2)

Combining parents from different genetic backgrounds, origins, and performances, a high variation of the estimates for the genetic variance of RILs within crosses is expected. The results obtained in this study confirmed this expectation for most traits.σg2 estimated varied from cross to cross for DH, DM, PH, TKW, and GPC. In contrast, this had not been observed for the quality traits ME, FR, and BG. As an indicator for the variation of cross-specific σg2, the standard deviation of the estimates in comparison to their mean standard error was taken. The standard error depends on the number of RILs per cross and the testing intensity in terms of testing sites and replications. With only 30 RILs/cross and only two locations, σg2 can only very roughly be estimated for an individual cross. Therefore, for breeding methodological studies, the mean σg2 found in our experiment should be taken as a starting point and as a rule-of-thumb figure. In line with this, [6] reaches a similar conclusion for most traits studied in their winter wheat experiment.


### 4.4. Broad Sense Heritability of Traits

In line with our result, [33] reported a wide heritability value of the same magnitude in some quantitative traits in barley. Similarly, [34] conducted an extensive review on heritability, and [33] in their study on barley genotype under irrigated conditions concluded that for most agronomic traits, heritability values are generally high (>80%). Heritability of malt quality traits ranged from moderate to high value as reported by [35].In our study,H2 of parental lines was higher compared to the estimates for crosses and RIL. A genetic explanation for this finding comes from the model (Table 11) expecting the variance of homozygous parental lines to be twice as large compared to the variance among crosses. Another reason for a higher parental heritability is attributed to experimental design. For the standard scenario, phenotypic variance as a denominator in the heritability formula has been defined as σp2 = σg2 + σgl2/nl + σgy2/ny + σgly2/(nlny) + σe2/(nlnynr) with σg2 variance of the genetic effects, σgl2 variance of the genotype × location interaction effects, σgy2 variance of the genotype × year interaction effects, σgly2 variance of the genotype × location × year interaction effects, σe2 variance of the error effects on a single plot basis, and nl, ny, and nr as the number of locations, years, and replications, respectively. Parents were five times replicated at each location of this experiment. Therefore, the effect of the experimental error on phenotypic variance could be reduced considerably.Table 11
Comparison of generation means of mid-parent values (μMPV) and derived recombinant inbred lines (μRIL) estimated across two environments.
Generation meansDHDMPHTKWMEGPCFRBGMid-ParentsAll crosses (N = 30)81.1133.090.646.680.811.168.1360.5Planet crosses (N = 9)80.5132.690.846.980.911.168.7357.0Nonplanet crosses (N = 13)81.3133.390.146.280.711.267.6372.0RILAll crosses (N = 30)81.2133.191.546.980.711.266.7363.0Planet crosses (N = 9)79.8132.091.046.481.111.268.2347.2Nonplanet crosses (N = 13)81.9134.291.346.680.511.265.8381.9Δ(mMP-mRIL)All crosses (N = 30)−0.1−0.2−0.9−0.30.1−0.11.4−2.5Planet crosses (N = 9)0.70.6−0.20.5−0.2−0.10.59.7Nonplanet crosses (N = 13)−0.5−0.9−1.2−0.40.2−0.11.8−9.9In our study, RILs were tested across two locations in ap-rep design that practiced replicating half of the RILs at each location. So far, comprehensive studies are lacking on how this design increases as compared to a design with a single replication per location such as augmented RCBD. Heritability could be classified as low H2 ≤ 0.2, moderate 0.2 ≤ H2 ≤ 0.50, and high H2 ≥ 0.5, and most of the heritability obtained in this study falls into the moderate and high classes. Taking into account the fact that genetic gain is proportional to the square root of heritability (h) the h-values are even higher.Further, because overall selection intensity has to be distributed to all traits under selection, for the individual trait, only a negative selection with discarding the low performers can be realized. With the h-values achieved in our experiment, the risk is low to falsely discarding an entry that in reality is high performing. Nevertheless, when asking the question of how heritability can be increased, two driving forces can be mentioned besides increasing genetic variances: (i) testing intensity can be enhanced by involving more years, locations, and replications, and (ii) employing trial analytics reduces masking of the genotypic effects. In our case, testing intensity hardly can be increased, because available seeds will suffice for not more than 3 plots. Generally, enhancing testing intensity is costly and will suffer from diminishing returns. In contrast, employing trial designs and analytics with “phenotypic spatial correction, location data quality evaluations, and the generation of breeding values” [36] is hypothesized to be highly effective in terms of optimized use of limited phenotyping capacity.


### 4.5. Phenotypic and Genotypic Correlation between Traits

The strong negative phenotypic and genotypic correlation between GPC and FR (r = −0.60, −0.73) is in line with [12, 37], who suggested that the breeder should take into account this negative relation while conducting selection. Similarly, [38] reported a strong negative correlation between FR and GPC. From F2- to F4-generation, breeders advance their cross progenies as single plants grown in Belg- (F2- and F4-SP) and Meher- (F3-SP). Single plant performance can be used to select field traits such as DH, PH, and TKW. Single plant selection on these traits is known to be cheap and effective when conducted by skilled breeders. As shown in Table 10, the genetic correlation of these traits to malt traits is generally low except the correlation TKW-GPC (rg = 0.39). Apparently, a stringent selection on these traits will hardly affect malt quality, in particular, if only a negative selection for TKW by discarding entries with a very low TKW is practiced. If successfully preselected in the way described in the F4:5 generation, the breeder can focus on selecting the RIL populations on malt traits and can realize higher selection intensity for these traits.When it comes to the selection of malt traits, the breeder should considerrg = 0.60 for ME-FR which is in the direction desired for malt quality improvement. Other significant correlations for ME-GPC (rg = −0.48) and FR-GPC (rg = −0.73) are also in the desired direction if GPC does not fall below the minimum value required for malting. The best way to exploit these trait correlations is to combine all single traits in an index targeting to improve malt quality as a complex trait.


### 4.6. Regression of Cross-Mean (CM) on Mid-Parent Value (MPV)

MPV could be used as a predictor of CM for the traits of interest. For all traits under study, regression coefficients were found to be highly significant deviating from zero (Table8). The corresponding coefficients of determination (R2) indicate how much of the cross-mean variance is explained by the regression coefficient. They were estimated to be higher than 0.5 for all field traits and ME. Lower R2-values were observed for FR, GPC, and BG. Usually, phenotypic data from parental lines are known from the preceding breeding cycle. In case of the breeding scheme currently applied by the Ethiopian barley team, field and quality data are available for two years (PON and PVT) and for grain yield only for one year (PVT). In an additional year, parental lines are tested in a Parental Performance Test (PPT). Aggregating all data from three years, entries have been tested for field and quality traits in 2 + 2+4 = 8 environments from PON, PVT, and PPT, respectively. Analogously, yield data are available in 0 + 2+4 = 6 environments from PON, PVT, and PPT, respectively. Further, in the future, there will be pedigree and phenomic (from NIRS spectra, see [39]), and estimated breeding values are available. By employing all data, very accurate MPV estimates should be used in the future.In our experiment, 17 parental lines were involved. Derived MPV estimates are a powerful tool for the plant breeder as can be demonstrated by the following consideration. In our case, means of (17 × 16)/2 = 136 crosses or 17 × 16 = 272 backcrosses to both parents can be predicted. To predict cross-means and select among crosses is highly advantageous if the variance between crosses is high as has been found in our experiment (Table4).


### 4.7. Usefulness of Crosses

Applying the usefulness criterion for the current study, out of 30 crosses, 16 crosses were classified as superior (Table10). Their U(i=1) surpassed the performance of the best-registered variety “planet” for 4–5 important traits of malt barley. As discussed before, an accurate estimation of cross-specific σg2 is extremely demanding from an experimental point of view. The prediction of this parameter and its integration into the usefulness criterion had been an unsolved problem until the advent of genomic prediction [40, 41]. As a resource for developing and phenotyping candidate entries often is the main limiting factor in breeding programs, focusing on the most promising cross will be the way to obtain outstanding or transgressive segregants in the subsequent generation [6, 40, 42–44].Crosses can be ranked/selected based on usefulness (U) criteria as the interest in breeding is typically both increasing the mean value of the population and identifying superior RIL. Hence, in this study, the known malting variety planet was used as a threshold to select RILs that can outperform the planet using U(i=1). Accordingly, about 16 crosses (8 crosses outperforming the planet at least by 5 economic traits and 8 crosses at least by 4 traits) were selected for further evaluation. If this could be predicted at an early stage of the breeding cycle, the breeder would have a good chance to discard nonuseful and low-performing crosses and save breeding capacity. Applying the usefulness criterion leads to a reduced number of lines contributing to the next breeding cycle and a higher variance of the gametic contribution of the remaining parental lines. In the long run, this could lead to the loss of genetic diversity and genetic gain. To counterbalance this trend, the breeder should follow the recommendation of [41] and generate more RIL in crosses with a lower mean but regarded as indispensable for maintaining genetic diversity. Thus, segregation variance can be exploited more extensively and the chances for RIL meeting the required performance are enhanced.


## 4.1. Comparison of Generation Means

Means of 30 mid-parents values (μMPV) and their 900 derived RIL (μRIL) were estimated across Holeta and Bekoji (Table 11). Differences Δ (μMPV–μRIL) across all crosses were small in general and nonsignificant in a t-test. On average, RIL was found to be slightly later and taller and provided with a higher TKW. With regard to malt quality traits, RIL deviated slightly in the undesired direction. Three driving forces for deviations between generation means shall be discussed in the following.(i)
Differences between generation means could be due to shortcomings in the accuracy of our experimental data. Compared to Bekoji, the accuracy of Holeta was lower. Alternative designs to the p-rep design chosen might lead to higher accuracies and are discussed below.(ii)
Selection and also drift effects during line development from F2- to F4- generation are potential reasons for a difference between generation means. In these generations, entries are grown as single plants which could efficiently be selected on traits such as DH, PH, or TKW. Because not more than 30 RIL/cross had been sampled, drift effects cannot be excluded.(iii)
Based on the genetic architecture of the traits, epistasis could be an explanation for the difference between the two generations. The absence of significant differences between the generations’ means would suggest the following: (1) epistatic effects are of minor importance in the germplasm investigated and/or (2) positive and negative epistatic effects have canceled each other. In line with this, [6] reported that epistatic effect was the main reason for the observed difference between generations' mean. The fact that deviations between parents and RIL were larger and differing in sign when considering the planet and nonplanet crosses separately speaks in favor of the second “canceling” hypothesis. In any case, epistasis can be considered a potential source of bias and breeders should try to limit its impact. For example, in the future, when assessing mid-parent values, breeders could estimate the breeding value instead of the genotypic value of the putative parental lines and use them to predict cross-means. In line with this, many studies showed the involvement of epistasis in generation mean on barley [25], durum wheat [28], or bread wheat [29–32].(iv)
Finally, all three driving forces might be confounded in the phenotypic data and might have canceled each other to a certain extent.


## 4.2. Variance among Mid-Parents, Crosses, and Lines within Crosses

In the previous sections of this study, a simple genetical model has been proposed. In short, this model assumes that all parental lines (i) originate from one random mating population in linkage equilibrium and (ii) are mated randomly to form crosses. (iii) Parental lines are assumed to be homozygous. (iv) From these crosses, homozygous RILs are derived by an SSD process in the absence of forces driving changes in allele frequency. (v) As a mode of inheritance, additive gene action and absence of epistasis have been postulated. With this model, we expect the genetical variances of parents, crosses, and RILs:(7)σp22=σc2=σg2=σA2.The following deviations of the breeding population studied in the real experiment from the idealized population described above will be addressed. In particular, the impacts of these deviations on genetic variances are discussed.(i)
17 parental lines have been used to produce crosses. As shown in Table1, lines have different geographical origins such as the USA, Europe, Ethiopia, and ICARDA. Diversity analysis based on KASP markers (Marker data not shown) groups the lines into 3 (sub)populations. Thus, the assumption that parental lines originate from one population is not met in our experiment. If populations differ in their allele frequencies and means, crosses between them will lead to more heterozygous F1 plants. Variance within crosses derived from these F1 genotypes will be increased compared to the variance among crosses [6] and accordingly shrink the ratio σc2: σg2.(iii)
Another model assumption is that parental lines are randomly intercrossed. With 17 parental lines (17 × 16)/2 = 136 crosses are feasible. Out of these potential 136 crosses, only 30 crosses had been investigated for our experiment. This small section led to variation in the gametic contributions of the parental lines. For example, the planet had been involved in 13 crosses, whereas Bekoji × Grace contributed only to one cross. Further, the small sample of crosses could have led to assortative or disassortative mating [15], which means that lines with a similar or dissimilar genotype for a given trait have been crossed more often than those that would occur by chance. Assortative mating increases the variance between crosses and decreases the variance within crosses. The opposite holds true for disassortative mating. Breeders often follow these nonrandom matings by “best × best” and “parents complementary” crossing designs, respectively. Which of these forces leading to deviation from random mating predominated in our case has to be inspected for each trait separately.(iii)
Parents were assumed to be homozygous. Adopting the homogeneity threshold of 95%, we know this assumption does not hold true for 6 out of the 17 parents (marker data not shown). The more heterogeneous lines taken for crosses are, the more the variance within crosses increases, and correspondingly, the variance among crosses decreases.(iv)
RILs used in our experiment are lines derived from individual F4-SP and tested in F5-generation. F4-SP is expected to be homozygous for 87.5% of the loci having been heterozygous in the ancestral F1 genotype. The remaining 12.5% of the loci are still heterozygous and do not contribute to segregation variance between RILs within a given cross. In case fully homozygous RILs were produced, e.g., by double haploid culture, 100% of the loci would have been homozygous and a higher segregation variance is expected. As a consequence, the RIL generation chosen for our experiment will contribute to inflating the ratioσc2: σg2. In the SSD procedure leading to the final RILs, no change of allele frequency due to drift, selection, migration, and mutation has been assumed. In practical breeding, drift could occur due to bottlenecks in the preceding generations. Selection on traits such as earliness, plant height, or TKW is straightforward to have happened. (Im)migration of foreign germplasm into the progeny of a cross can be caused by, e.g., technical mixture or wrong pedigree assignment.(v)
From analyzing the generation means in the previous chapter, we should be careful to regard epistatic effects and their respective variance as nonexistent. This conclusion is in line with findings in the literature [6] for wheat and [11] for barley.Recurring to the balance sheet of the genetical variances estimated in our experiment, the following conclusions can be drawn. The parameterσp2/2 subdivides the variance among individual parental lines by 2 and is meant as an estimator of the variance between mid-parents. Taking the arguments summarized under (ii), this estimator is rather imperfect and should be replaced by the variance among mid-parents used in our experiment. Ratio σc2: σg2 was assumed to be equal to one. Taking the arguments summarized under (i)-(iv), we see severe violations of the assumptions made in the initial model, and therefore, we cannot anymore expect these two variances to be equivalent. For DH, PH, TKW, FR, and GPC, we observed a tendency for σc2 to be smaller than σg2. The opposite tendency was found for DM, ME, and BG. In particular, arguments under (ii) are of importance here. In contrast to the companion study of [6], in our case, mating of parental lines is highly unbalanced and cannot be regarded as random.The breeder might use outstanding RILs from this experiment for intercrossing and for starting a new breeding cycle. The resulting population will be much closer to the assumptions defined above than the actual breeding population and deliver variance estimates which are more representative of a situation close to classical second cycle breeding. Nevertheless, the actual estimates are a highly valuable starting point to improve breeding methodology. Irrespective of their actual ratio, the two variances,σc2 and σg2, proved to be significantly deviating from zero for almost all traits. Accordingly, the breeder can exploit both of them for selection. A similar result has been reported on wheat by [6] with large size of σg2 among RIL within crosses.


## 4.3. Genetic Variance within Crosses (σg2)

Combining parents from different genetic backgrounds, origins, and performances, a high variation of the estimates for the genetic variance of RILs within crosses is expected. The results obtained in this study confirmed this expectation for most traits.σg2 estimated varied from cross to cross for DH, DM, PH, TKW, and GPC. In contrast, this had not been observed for the quality traits ME, FR, and BG. As an indicator for the variation of cross-specific σg2, the standard deviation of the estimates in comparison to their mean standard error was taken. The standard error depends on the number of RILs per cross and the testing intensity in terms of testing sites and replications. With only 30 RILs/cross and only two locations, σg2 can only very roughly be estimated for an individual cross. Therefore, for breeding methodological studies, the mean σg2 found in our experiment should be taken as a starting point and as a rule-of-thumb figure. In line with this, [6] reaches a similar conclusion for most traits studied in their winter wheat experiment.


## 4.4. Broad Sense Heritability of Traits

In line with our result, [33] reported a wide heritability value of the same magnitude in some quantitative traits in barley. Similarly, [34] conducted an extensive review on heritability, and [33] in their study on barley genotype under irrigated conditions concluded that for most agronomic traits, heritability values are generally high (>80%). Heritability of malt quality traits ranged from moderate to high value as reported by [35].In our study,H2 of parental lines was higher compared to the estimates for crosses and RIL. A genetic explanation for this finding comes from the model (Table 11) expecting the variance of homozygous parental lines to be twice as large compared to the variance among crosses. Another reason for a higher parental heritability is attributed to experimental design. For the standard scenario, phenotypic variance as a denominator in the heritability formula has been defined as σp2 = σg2 + σgl2/nl + σgy2/ny + σgly2/(nlny) + σe2/(nlnynr) with σg2 variance of the genetic effects, σgl2 variance of the genotype × location interaction effects, σgy2 variance of the genotype × year interaction effects, σgly2 variance of the genotype × location × year interaction effects, σe2 variance of the error effects on a single plot basis, and nl, ny, and nr as the number of locations, years, and replications, respectively. Parents were five times replicated at each location of this experiment. Therefore, the effect of the experimental error on phenotypic variance could be reduced considerably.Table 11
Comparison of generation means of mid-parent values (μMPV) and derived recombinant inbred lines (μRIL) estimated across two environments.
Generation meansDHDMPHTKWMEGPCFRBGMid-ParentsAll crosses (N = 30)81.1133.090.646.680.811.168.1360.5Planet crosses (N = 9)80.5132.690.846.980.911.168.7357.0Nonplanet crosses (N = 13)81.3133.390.146.280.711.267.6372.0RILAll crosses (N = 30)81.2133.191.546.980.711.266.7363.0Planet crosses (N = 9)79.8132.091.046.481.111.268.2347.2Nonplanet crosses (N = 13)81.9134.291.346.680.511.265.8381.9Δ(mMP-mRIL)All crosses (N = 30)−0.1−0.2−0.9−0.30.1−0.11.4−2.5Planet crosses (N = 9)0.70.6−0.20.5−0.2−0.10.59.7Nonplanet crosses (N = 13)−0.5−0.9−1.2−0.40.2−0.11.8−9.9In our study, RILs were tested across two locations in ap-rep design that practiced replicating half of the RILs at each location. So far, comprehensive studies are lacking on how this design increases as compared to a design with a single replication per location such as augmented RCBD. Heritability could be classified as low H2 ≤ 0.2, moderate 0.2 ≤ H2 ≤ 0.50, and high H2 ≥ 0.5, and most of the heritability obtained in this study falls into the moderate and high classes. Taking into account the fact that genetic gain is proportional to the square root of heritability (h) the h-values are even higher.Further, because overall selection intensity has to be distributed to all traits under selection, for the individual trait, only a negative selection with discarding the low performers can be realized. With the h-values achieved in our experiment, the risk is low to falsely discarding an entry that in reality is high performing. Nevertheless, when asking the question of how heritability can be increased, two driving forces can be mentioned besides increasing genetic variances: (i) testing intensity can be enhanced by involving more years, locations, and replications, and (ii) employing trial analytics reduces masking of the genotypic effects. In our case, testing intensity hardly can be increased, because available seeds will suffice for not more than 3 plots. Generally, enhancing testing intensity is costly and will suffer from diminishing returns. In contrast, employing trial designs and analytics with “phenotypic spatial correction, location data quality evaluations, and the generation of breeding values” [36] is hypothesized to be highly effective in terms of optimized use of limited phenotyping capacity.


## 4.5. Phenotypic and Genotypic Correlation between Traits

The strong negative phenotypic and genotypic correlation between GPC and FR (r = −0.60, −0.73) is in line with [12, 37], who suggested that the breeder should take into account this negative relation while conducting selection. Similarly, [38] reported a strong negative correlation between FR and GPC. From F2- to F4-generation, breeders advance their cross progenies as single plants grown in Belg- (F2- and F4-SP) and Meher- (F3-SP). Single plant performance can be used to select field traits such as DH, PH, and TKW. Single plant selection on these traits is known to be cheap and effective when conducted by skilled breeders. As shown in Table 10, the genetic correlation of these traits to malt traits is generally low except the correlation TKW-GPC (rg = 0.39). Apparently, a stringent selection on these traits will hardly affect malt quality, in particular, if only a negative selection for TKW by discarding entries with a very low TKW is practiced. If successfully preselected in the way described in the F4:5 generation, the breeder can focus on selecting the RIL populations on malt traits and can realize higher selection intensity for these traits.When it comes to the selection of malt traits, the breeder should considerrg = 0.60 for ME-FR which is in the direction desired for malt quality improvement. Other significant correlations for ME-GPC (rg = −0.48) and FR-GPC (rg = −0.73) are also in the desired direction if GPC does not fall below the minimum value required for malting. The best way to exploit these trait correlations is to combine all single traits in an index targeting to improve malt quality as a complex trait.


## 4.6. Regression of Cross-Mean (CM) on Mid-Parent Value (MPV)

MPV could be used as a predictor of CM for the traits of interest. For all traits under study, regression coefficients were found to be highly significant deviating from zero (Table8). The corresponding coefficients of determination (R2) indicate how much of the cross-mean variance is explained by the regression coefficient. They were estimated to be higher than 0.5 for all field traits and ME. Lower R2-values were observed for FR, GPC, and BG. Usually, phenotypic data from parental lines are known from the preceding breeding cycle. In case of the breeding scheme currently applied by the Ethiopian barley team, field and quality data are available for two years (PON and PVT) and for grain yield only for one year (PVT). In an additional year, parental lines are tested in a Parental Performance Test (PPT). Aggregating all data from three years, entries have been tested for field and quality traits in 2 + 2+4 = 8 environments from PON, PVT, and PPT, respectively. Analogously, yield data are available in 0 + 2+4 = 6 environments from PON, PVT, and PPT, respectively. Further, in the future, there will be pedigree and phenomic (from NIRS spectra, see [39]), and estimated breeding values are available. By employing all data, very accurate MPV estimates should be used in the future.In our experiment, 17 parental lines were involved. Derived MPV estimates are a powerful tool for the plant breeder as can be demonstrated by the following consideration. In our case, means of (17 × 16)/2 = 136 crosses or 17 × 16 = 272 backcrosses to both parents can be predicted. To predict cross-means and select among crosses is highly advantageous if the variance between crosses is high as has been found in our experiment (Table4).


## 4.7. Usefulness of Crosses

Applying the usefulness criterion for the current study, out of 30 crosses, 16 crosses were classified as superior (Table10). Their U(i=1) surpassed the performance of the best-registered variety “planet” for 4–5 important traits of malt barley. As discussed before, an accurate estimation of cross-specific σg2 is extremely demanding from an experimental point of view. The prediction of this parameter and its integration into the usefulness criterion had been an unsolved problem until the advent of genomic prediction [40, 41]. As a resource for developing and phenotyping candidate entries often is the main limiting factor in breeding programs, focusing on the most promising cross will be the way to obtain outstanding or transgressive segregants in the subsequent generation [6, 40, 42–44].Crosses can be ranked/selected based on usefulness (U) criteria as the interest in breeding is typically both increasing the mean value of the population and identifying superior RIL. Hence, in this study, the known malting variety planet was used as a threshold to select RILs that can outperform the planet using U(i=1). Accordingly, about 16 crosses (8 crosses outperforming the planet at least by 5 economic traits and 8 crosses at least by 4 traits) were selected for further evaluation. If this could be predicted at an early stage of the breeding cycle, the breeder would have a good chance to discard nonuseful and low-performing crosses and save breeding capacity. Applying the usefulness criterion leads to a reduced number of lines contributing to the next breeding cycle and a higher variance of the gametic contribution of the remaining parental lines. In the long run, this could lead to the loss of genetic diversity and genetic gain. To counterbalance this trend, the breeder should follow the recommendation of [41] and generate more RIL in crosses with a lower mean but regarded as indispensable for maintaining genetic diversity. Thus, segregation variance can be exploited more extensively and the chances for RIL meeting the required performance are enhanced.


## 5. Conclusions

Genetic variation in a breeding population is the basis for crop improvement and is required to achieve genetic gains in a breeding program. This variation can be exploited through the use of genetic different sources such as landrace, exotic lines, or elite breeding lines in the actual breeding program. This genetic variation could be structured into between crosses and among lines within crosses. The breeder can use the estimates of these variances to optimize his/her breeding resources. Hence, irrespective of their actual ratio, the two variances,σc2 and σg2, in our study proved to be significantly deviating from zero for almost all traits. Accordingly, the breeder can exploit both of them for selection. Further, cross selection based on mid-parent value and usefulness were found parameters to be exploited in practical breeding.



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*Source: 9953200-2022-10-03.xml*