#Procedures for genotype selection
The EstimateBreed package provides several useful functions for selecting superior genotypes.
##Heterosis and heterobeltiosis of hybrids
The calculation of heterosis and heterobeltiosis is crucial for hybrid selection, as it measures the hybrid’s performance relative to its parents. Heterosis reflects the overall vigor, while heterobeltiosis compares the hybrid to the best parent. These metrics help identify superior hybrids with desirable traits like higher productivity and better disease resistance.
These parameters can be easily calculated with the het()
function.
library(EstimateBreed)
data("maize")
#Extract heterosis and heterobeltiosis
with(maize,het(GEN,GM,GP,PR,REP,param="all"))
#> GEN Heterosis Heterobeltiosis
#> 1 HIB1 71.70025 51.199637
#> 2 HIB1 51.97650 37.288820
#> 3 HIB1 88.45976 87.525920
#> 4 HIB2 124.81676 100.825736
#> 5 HIB2 117.88532 87.407158
#> 6 HIB2 151.90865 95.751797
#> 7 HIB3 86.77350 50.399284
#> 8 HIB3 90.83780 53.375374
#> 9 HIB3 98.53781 57.174523
#> 10 HIB4 70.53690 1.978555
#> 11 HIB4 69.12610 2.696836
#> 12 HIB4 69.48340 2.121636
#Only extract heterosis
with(maize,het(GEN,GM,GP,PR,REP,param = "het"))
#> GEN Heterosis
#> 1 HIB1 71.70025
#> 2 HIB1 51.97650
#> 3 HIB1 88.45976
#> 4 HIB2 124.81676
#> 5 HIB2 117.88532
#> 6 HIB2 151.90865
#> 7 HIB3 86.77350
#> 8 HIB3 90.83780
#> 9 HIB3 98.53781
#> 10 HIB4 70.53690
#> 11 HIB4 69.12610
#> 12 HIB4 69.48340
#Extract only heterobeltiosis
with(maize,het(GEN,GM,GP,PR,REP,param = "hetb"))
#> GEN Heterobeltiosis
#> 1 HIB1 51.199637
#> 2 HIB1 37.288820
#> 3 HIB1 87.525920
#> 4 HIB2 100.825736
#> 5 HIB2 87.407158
#> 6 HIB2 95.751797
#> 7 HIB3 50.399284
#> 8 HIB3 53.375374
#> 9 HIB3 57.174523
#> 10 HIB4 1.978555
#> 11 HIB4 2.696836
#> 12 HIB4 2.121636##Industrial quality indicators
Industrial quality indicators are very important for the selection of genotypes with industrial aptitude. They are widely applied to cereals (oats, wheat, barley, rye and corn).
Some interesting functions offered by the package are:
rend_ind(), to calculate the hulling index and
industrial yield of white oats.
library(EstimateBreed)
data("aveia")
# Calculate the industrial yield without extracting the average
with(aveia, rend_ind(GEN,NG2M,MG,MC,RG))
#> GEN ID RI
#> 1 G1 0.6421053 248.0992
#> 2 G1 0.7058824 259.2127
#> 3 G1 0.7263158 401.2875
#> 4 G1 0.6626506 142.5706
#> 5 G2 0.7636364 513.0272
#> 6 G2 0.7589286 473.7050
#> 7 G2 0.7882353 421.0346
#> 8 G2 0.7943925 735.9787
#> 9 G3 0.7659574 517.4221
#> 10 G3 0.7333333 198.2880
#> 11 G3 0.6808511 189.6073
#> 12 G3 0.7362637 257.6884
#> 13 G4 0.7844828 1309.5622
#> 14 G4 0.7551020 557.8128
#> 15 G4 0.7608696 608.3568
#> 16 G4 0.7530864 299.6963
#> 17 G5 0.7346939 698.7208
#> 18 G5 0.7583333 687.4180
#> 19 G5 0.6547619 144.2462
#> 20 G6 0.7083333 421.3280
#> 21 G6 0.7547170 376.3683
#> 22 G6 0.6822430 201.4227
#> 23 G6 0.6179775 241.5106
#> 24 G7 0.6893939 418.2682
#> 25 G7 0.7475728 409.8992
#> 26 G7 0.6818182 258.0423
#> 27 G8 0.6694915 779.4310
#> 28 G8 0.7117117 319.0226
#> 29 G8 0.6400000 436.5363
#> 30 G8 0.6666667 326.3160
#> 31 G9 0.7019231 679.3385
#> 32 G9 0.8080808 482.9684
#> 33 G9 0.7809524 685.0514
#> 34 G9 0.5595238 159.5463
#> 35 G10 0.7570093 920.7979
#> 36 G10 0.7578947 388.1068
#> 37 G10 0.7767857 617.4250
#> 38 G10 0.7578947 579.7885
#> 39 G11 0.7589286 536.0166
#> 40 G11 0.7943925 600.1238
#> 41 G11 0.7282609 281.4175
#> 42 G11 0.5384615 271.5605
#> 43 G12 0.7678571 694.0707
#> 44 G12 0.7631579 900.9143
#> 45 G12 0.7572816 665.8663
#> 46 G12 0.7478992 957.2217
#> 47 G13 0.6976744 503.7428
#> 48 G13 0.5543478 265.6668
#> 49 G13 0.7565217 575.4152
#> 50 G13 0.7636364 585.0671
#> 51 G14 0.6547619 374.1069
#> 52 G14 0.7325581 662.9329
#> 53 G14 0.5609756 330.6989
#> 54 G14 0.7222222 575.8133
# Calculate the industrial yield by extracting the average per genotype
with(aveia, rend_ind(GEN,NG2M,MG,MC,RG,stat="mean"))
#> GEN ID RI
#> 1 G1 0.6842385 262.7925
#> 2 G10 0.7623961 626.5295
#> 3 G11 0.7050109 422.2796
#> 4 G12 0.7590489 804.5182
#> 5 G13 0.6930451 482.4730
#> 6 G14 0.6676295 485.8880
#> 7 G2 0.7762982 535.9364
#> 8 G3 0.7291014 290.7514
#> 9 G4 0.7633852 693.8570
#> 10 G5 0.7159297 510.1284
#> 11 G6 0.6908177 310.1574
#> 12 G7 0.7062616 362.0699
#> 13 G8 0.6719675 465.3265
#> 14 G9 0.7126200 501.7261indviab(), to estimate viability parameters with traits
measured in wheat crops.
library(EstimateBreed)
data("trigo")
#Ear viability index
with(trigo,indviab(TEST,NGE,NEE))
#> Genotype Index
#> 1 T1 0.7270983
#> 2 T2 0.7927928
#> 3 T3 0.7572954
#> 4 T4 0.7951413
#> 5 T5 0.7578163
#> 6 T6 0.7882816
#> 7 T7 0.7781609
#> 8 T8 0.7793054
#> 9 T9 0.8141160
#> 10 T10 0.8498195
#> 11 T11 0.8438819
#> 12 T12 0.8014337
#> 13 T13 0.7719665
#> 14 T14 0.8245132
#> 15 T15 0.8051075
#> 16 T16 0.7022956
#> 17 T17 0.7624164
#> 18 T18 0.7773723
#> 19 T19 0.7438854
#Ear harvest index
with(trigo,indviab(TEST,MGE,ME))
#> Genotype Index
#> 1 T1 0.7530794
#> 2 T2 0.7211403
#> 3 T3 0.7250430
#> 4 T4 0.7276371
#> 5 T5 0.7527310
#> 6 T6 0.7404977
#> 7 T7 0.7513300
#> 8 T8 0.7555921
#> 9 T9 0.7464156
#> 10 T10 0.7605856
#> 11 T11 0.7486986
#> 12 T12 0.7393468
#> 13 T13 0.7484841
#> 14 T14 0.7646920
#> 15 T15 0.7515557
#> 16 T16 0.6933280
#> 17 T17 0.7543860
#> 18 T18 0.7340161
#> 19 T19 0.7276199
#Spikelet deposition index in the ear
with(trigo,indviab(TEST,NEE,CE))
#> Genotype Index
#> 1 T1 6.682692
#> 2 T2 6.148688
#> 3 T3 6.207658
#> 4 T4 6.286344
#> 5 T5 6.517241
#> 6 T6 6.135952
#> 7 T7 6.561086
#> 8 T8 6.169643
#> 9 T9 6.276316
#> 10 T10 6.276435
#> 11 T11 6.301329
#> 12 T12 6.065217
#> 13 T13 6.298682
#> 14 T14 6.298701
#> 15 T15 6.514886
#> 16 T16 5.824513
#> 17 T17 6.493023
#> 18 T18 6.061947
#> 19 T19 6.470234hw(), which applies a linear model to obtain the
hectoliter weight of wheat, oat, barley and rye crops.
library(EstimateBreed)
GEN <- rep(paste("G", 1:5, sep=""), each = 3)
REP <- rep(1:3, times = 5)
MG <- c(78.5, 80.2, 79.1, 81.3, 82.0, 80.8, 76.9, 78.1, 77.5, 83.2,
84.1, 82.9, 77.4, 78.9, 79.3)
data <- data.frame(GEN, REP, MG)
with(data,hw(GEN,MG,crop="trit"))
#> GEN HL HW
#> 1 G1 78.5 25.53219
#> 2 G1 80.2 26.30029
#> 3 G1 79.1 25.80328
#> 4 G2 81.3 26.79729
#> 5 G2 82.0 27.11356
#> 6 G2 80.8 26.57138
#> 7 G3 76.9 24.80928
#> 8 G3 78.1 25.35146
#> 9 G3 77.5 25.08037
#> 10 G4 83.2 27.65575
#> 11 G4 84.1 28.06239
#> 12 G4 82.9 27.52020
#> 13 G5 77.4 25.03519
#> 14 G5 78.9 25.71292
#> 15 G5 79.3 25.89365
#Extract the average PH per genotype
with(data,hw(GEN,MG,crop="trit",stat="mean"))
#> GEN HW
#> 1 G1 25.87859
#> 2 G2 26.82741
#> 3 G3 25.08037
#> 4 G4 27.74611
#> 5 G5 25.54725##ISGR
Obtain the genetic selection index for resilience
(isgr()) for selecting genotypes for environmental
stressors, as described by Bandeira et
al. (2024).
library(EstimateBreed)
#Obtain environmental deviations
data("desvamb")
head(desvamb)
#> # A tibble: 6 × 3
#> ENV TMED PREC
#> <chr> <dbl> <dbl>
#> 1 E1 22.1 0
#> 2 E1 22.7 0
#> 3 E1 24.5 0.03
#> 4 E1 22.3 4.49
#> 5 E1 21.7 3.91
#> 6 E1 19.6 0.04
#Use DPclim for the ISGR function to identify deviations correctly
DPclim <- with(desvamb,desv_clim(ENV,TMED,PREC))
#Calculate the ISGR
data("genot")
head(genot)
#> # A tibble: 6 × 5
#> GEN ENV NG MG CICLO
#> <chr> <chr> <dbl> <dbl> <dbl>
#> 1 L445 E1 1017. 142. 146
#> 2 L162 E2 847. 140. 150
#> 3 L277 E2 789. 131. 150
#> 4 L155 E2 735. 122. 150
#> 5 L166 E2 695. 117. 150
#> 6 L26 E2 664. 113. 150
isgr_index <- with(genot, isgr(GEN,ENV,NG,MG,CICLO))
#Define the water requirement per stage
isgr_index <- with(genot, isgr(GEN,ENV,NG,MG,CICLO,req=5,stage="rep"))##Restriction of controls variability
It restricts the variability of witnesses for less biased genetic
parameter estimates, as described by Carvalho et al. (2023). This can be
accomplished with the restr() function.
library(EstimateBreed)
TEST <- rep(paste("T", 1:5, sep=""), each=3)
REP <- rep(1:3, times=5)
Xi <- rnorm(15, mean=10, sd=2)
data <- data.frame(TEST,REP,Xi)
#Apply the witness variability constraint
Control <- with(data, restr(TEST,REP,Xi,scenario = "restr",zstat = FALSE))
#Apply witness variability restriction with normalization (Z statistic)
Control <- with(data, restr(TEST,REP,Xi,scenario = "restr",zstat = TRUE))The inbreeding coefficient and genetic parameters are key for evaluating genetic diversity and optimizing breeding strategies. The inbreeding coefficient indicates genetic relatedness, while genetic parameters guide the selection of superior genotypes, improving traits and maintaining long-term sustainability.
The inbreeding coefficient can be obtained with the
COI() function.
library(EstimateBreed)
var <- c("A","B","C","D","E")
VF <- c(2.5, 3.0, 2.8, 3.2, 2.7)
VG <- c(1.2, 1.5, 1.3, 1.6, 1.4)
data <- data.frame(var,VG,VF)
#Calculating for just one generation
with(data,COI(var,VG,VF,generation = "F3"))
#> $Variances
#> Generation var VA_Total VD_Total VA_Between VD_Between VA_Within
#> F3.1 F3 A 0.8000000 1.600000 1.2 4.8 2.4
#> F3.2 F3 B 1.0000000 2.000000 1.5 6.0 3.0
#> F3.3 F3 C 0.8666667 1.733333 1.3 5.2 2.6
#> F3.4 F3 D 1.0666667 2.133333 1.6 6.4 3.2
#> F3.5 F3 E 0.9333333 1.866667 1.4 5.6 2.8
#> VD_Within
#> F3.1 2.4
#> F3.2 3.0
#> F3.3 2.6
#> F3.4 3.2
#> F3.5 2.8
#>
#> $Heritabilities
#> Generation var hVaT hVdT hVaE hVdE hVaD hVdD
#> F3.1 F3 A 0.3200000 0.6400000 0.4800000 1.920000 0.9600000 0.9600000
#> F3.2 F3 B 0.3333333 0.6666667 0.5000000 2.000000 1.0000000 1.0000000
#> F3.3 F3 C 0.3095238 0.6190476 0.4642857 1.857143 0.9285714 0.9285714
#> F3.4 F3 D 0.3333333 0.6666667 0.5000000 2.000000 1.0000000 1.0000000
#> F3.5 F3 E 0.3456790 0.6913580 0.5185185 2.074074 1.0370370 1.0370370Genetic parameters for balanced experiments can be estimated from the
genpar() function. The methodology was described by Yadav
et al. (2024).
library(EstimateBreed)
data("genot2")
#Geting parameters without cheking model assumptions
parameters <- genpar(genot2,Gen,Rep,var =c("VAR1", "VAR2"))
#>
#> ==================================================
#> Analyzing Variable: VAR1
#> ==================================================
#>
#> Genotypic effect was significant for variable: VAR1
#>
#> ==================================================
#> Analyzing Variable: VAR2
#> ==================================================
#>
#> Genotypic effect was NOT significant for variable: VAR2
parameters$anova
#> $VAR1
#> Df Sum Sq Mean Sq F value Pr(>F)
#> GEN 19 8972.7 472.25 120.9202 <2e-16 ***
#> REP 2 1.4 0.71 0.1828 0.8337
#> Residuals 38 148.4 3.91
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $VAR2
#> Df Sum Sq Mean Sq F value Pr(>F)
#> GEN 19 40.282 2.1201 1.5122 0.1365
#> REP 2 0.931 0.4655 0.3320 0.7195
#> Residuals 38 53.276 1.4020
parameters$gp
#> $VAR1
#> Parameter VAR1
#> 1 sigmaE 3.9054433
#> 2 sigmaG 156.1138901
#> 3 sigmaP 160.0193334
#> 4 ECV 6.5587072
#> 5 GCV 41.4671174
#> 6 PCV 41.9825972
#> 7 H2 0.9755939
#> 8 GA 0.6247277
#> 9 GAM 2.0733559
#Checking model assumptions
parameters <- genpar(genot2,Gen,Rep,var =c("VAR1", "VAR2"),check=TRUE)
#>
#> ==================================================
#> Analyzing Variable: VAR1
#> ==================================================
#>
#> Performing assumption tests...
#> Shapiro-Wilk Normality Test: p-value = 0.22358
#> Bartlett Homogeneity Test: p-value = 0.12747
#> Levene Homogeneity Test: p-value = 0.72326
#> Breusch-Pagan Heteroscedasticity Test: p-value = 0.05089
#>
#> --------------------------------------------------
#>
#> Genotypic effect was significant for variable: VAR1
#>
#> ==================================================
#> Analyzing Variable: VAR2
#> ==================================================
#>
#> Performing assumption tests...
#> Shapiro-Wilk Normality Test: p-value = 0.48831
#> Bartlett Homogeneity Test: p-value = 0.60586
#> Levene Homogeneity Test: p-value = 0.99062
#> Breusch-Pagan Heteroscedasticity Test: p-value = 0.06705
#>
#> --------------------------------------------------
#>
#> Genotypic effect was NOT significant for variable: VAR2
parameters$anova
#> $VAR1
#> Df Sum Sq Mean Sq F value Pr(>F)
#> GEN 19 8972.7 472.25 120.9202 <2e-16 ***
#> REP 2 1.4 0.71 0.1828 0.8337
#> Residuals 38 148.4 3.91
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $VAR2
#> Df Sum Sq Mean Sq F value Pr(>F)
#> GEN 19 40.282 2.1201 1.5122 0.1365
#> REP 2 0.931 0.4655 0.3320 0.7195
#> Residuals 38 53.276 1.4020
parameters$gp
#> $VAR1
#> Parameter VAR1
#> 1 sigmaE 3.9054433
#> 2 sigmaG 156.1138901
#> 3 sigmaP 160.0193334
#> 4 ECV 6.5587072
#> 5 GCV 41.4671174
#> 6 PCV 41.9825972
#> 7 H2 0.9755939
#> 8 GA 0.6247277
#> 9 GAM 2.0733559