ANOVA
This report presents the results of a linear model analysis for multiple response variables (traits) measured on different genotypes (gen) and blocks (bloc). For each trait, we fit a linear model:
\(Y_{ijk}=\mu+g_i+b_j+e_{ijk}\)
and perform:
Analysis of variance (ANOVA) to test the significance of genotype and block effects.
Shapiro–Wilk test on the residuals to check normality.
Bartlett’s test for homogeneity of variances across genotypes.
Finally, we compute genotype means, overall trait means, and the range (min/max) for each trait.
rm(list=ls())
library(readxl)
dados <- read_xlsx(path="C:\\Users\\os\\Downloads\\dados p Noé.xlsx",sheet="data")
dados$bloc=as.factor(dados$bloc)
dados$gen=as.factor(dados$gen)
str(dados)## tibble [88 × 9] (S3: tbl_df/tbl/data.frame)
## $ gen : Factor w/ 22 levels "BR 17 Gurguéia",..: 8 8 8 8 10 10 10 10 16 16 ...
## $ bloc: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
## $ ph : num [1:88] 62 63.4 67.5 58.1 73.9 76.6 67.6 69.8 62.7 60.1 ...
## $ hf : num [1:88] 54.3 56.7 64.5 50.2 61.5 57.9 64.4 60.1 54.2 50.6 ...
## $ pp : num [1:88] 7.44 6.78 7.56 7.22 7 ...
## $ pl : num [1:88] 22.3 22.4 23.2 19.3 19.3 ...
## $ ng : num [1:88] 106.7 94.9 105.8 104.3 69.7 ...
## $ we : num [1:88] 199 201 206 192 161 ...
## $ gy : num [1:88] 1832 1907 1968 1787 1376 ...head(dados)## # A tibble: 6 × 9
## gen bloc ph hf pp pl ng we gy
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 FCB 208 1 62 54.3 7.44 22.3 107. 199. 1832.
## 2 FCB 208 2 63.4 56.7 6.78 22.4 94.9 201. 1907.
## 3 FCB 208 3 67.5 64.5 7.56 23.2 106. 206. 1968.
## 4 FCB 208 4 58.1 50.2 7.22 19.3 104. 192. 1787.
## 5 FCB 406 1 73.9 61.5 7 19.3 69.7 161. 1376.
## 6 FCB 406 2 76.6 57.9 5 17.5 56.7 159. 1433.for (i in 3:9) {
print(names(dados)[i])
m=lm(dados[[i]]~gen+bloc,data=dados)
print(anova(m))
print(shapiro.test(residuals(m)))
print(bartlett.test(residuals(m)~dados$gen))
anova(m)$`Mean Sq`[3]/mean(dados[[i]]) #CV
}## [1] "ph"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 3186.7 151.75 4.0105 9.802e-06 ***
## bloc 3 1516.2 505.39 13.3565 7.540e-07 ***
## Residuals 63 2383.8 37.84
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.98351, p-value = 0.328
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 19.827, df = 21, p-value = 0.5322
##
## [1] "hf"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 2334.95 111.188 3.8996 1.455e-05 ***
## bloc 3 570.77 190.255 6.6726 0.0005532 ***
## Residuals 63 1796.32 28.513
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.97774, p-value = 0.1343
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 16.928, df = 21, p-value = 0.7155
##
## [1] "pp"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 143.381 6.8277 20.932 < 2.2e-16 ***
## bloc 3 4.656 1.5520 4.758 0.004711 **
## Residuals 63 20.550 0.3262
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.98174, p-value = 0.2512
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 26.643, df = 21, p-value = 0.183
##
## [1] "pl"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 315.025 15.0012 16.9626 < 2.2e-16 ***
## bloc 3 18.421 6.1403 6.9431 0.0004127 ***
## Residuals 63 55.715 0.8844
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.98877, p-value = 0.6555
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 31.268, df = 21, p-value = 0.06931
##
## [1] "ng"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 17692.5 842.50 14.2662 < 2.2e-16 ***
## bloc 3 1594.9 531.64 9.0024 4.783e-05 ***
## Residuals 63 3720.5 59.06
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.98996, p-value = 0.7416
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 32.14, df = 21, p-value = 0.05666
##
## [1] "we"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 42154 2007.32 64.2737 <2e-16 ***
## bloc 3 152 50.66 1.6223 0.1931
## Residuals 63 1968 31.23
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.98569, p-value = 0.4466
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 12.861, df = 21, p-value = 0.9134
##
## [1] "gy"
## Analysis of Variance Table
##
## Response: dados[[i]]
## Df Sum Sq Mean Sq F value Pr(>F)
## gen 21 9145266 435489 48.209 <2e-16 ***
## bloc 3 28510 9503 1.052 0.3759
## Residuals 63 569102 9033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Shapiro-Wilk normality test
##
## data: residuals(m)
## W = 0.98965, p-value = 0.7191
##
##
## Bartlett test of homogeneity of variances
##
## data: residuals(m) by dados$gen
## Bartlett's K-squared = 26.783, df = 21, p-value = 0.1782library(matrixStats)
medias=aggregate(cbind(ph,hf,pp,pl,ng,we,gy)~gen,data=dados,FUN=mean)
colMaxs(as.matrix(medias[,-1]))## ph hf pp pl ng we gy
## 73.57500 65.75000 10.86000 21.81944 110.84062 241.29446 2269.11796colMeans(medias[,-1])## ph hf pp pl ng we
## 63.354545 55.740909 6.437386 18.808439 79.109248 191.984060
## gy
## 1467.947469colMins(as.matrix(medias[,-1]))## ph hf pp pl ng we gy
## 52.950000 46.550000 5.111111 15.166667 61.715123 143.429718 944.007184Scott-Knott test
This script performs the Scott-Knott (SK) clustering test for multiple traits simultaneously using a loop. The SK test is a post-hoc procedure used after ANOVA to compare treatment means and group them into homogeneous clusters.
library(ScottKnott)
for (i in 3:9) {
print(names(dados)[i])
frm <- as.formula(paste(names(dados)[i], "~ gen + bloc"))
print(SK(frm, which="gen", data=dados))
}## [1] "ph"
## Results
## Means G1 G2
## P.-de-ouro 73.58 a
## Novaera 72.53 a
## FCB 406 71.98 a
## BRS Guariba 71.75 a
## FCB 1402 70.40 a
## FCM 608 66.23 a
## FCB 2309 66.18 a
## FCB 1103 66.15 a
## BR 17 Gurguéia 65.85 a
## FCB 2007 65.60 a
## FCB 208 62.75 b
## FCB 508 61.53 b
## FCB 2006 61.33 b
## FCB 2009 60.58 b
## FCM 505 60.50 b
## FCB 601 59.70 b
## FCB 603 59.43 b
## FCM 604 59.00 b
## FCB 509 56.60 b
## FCB 602 54.95 b
## FCM 906 54.28 b
## FCM 609 52.95 b
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 49 30 19.3 0.00018 9.5 63
## Clus 2 13 17 8.8 0.13941 9.5 63
## Clus 3 14 19 10.5 0.22452 9.5 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: P.-de-ouro Novaera FCB 406 BRS Guariba FCB 1402 FCM 608 FCB 2309 FCB 1103 BR 17 Gurguéia FCB 2007
## {G2}: FCB 208 FCB 508 FCB 2006 FCB 2009 FCM 505 FCB 601 FCB 603 FCM 604 FCB 509 FCB 602 FCM 906 FCM 609
## ################# Cluster 2 ################
## {G1}: P.-de-ouro Novaera FCB 406 BRS Guariba FCB 1402
## {G2}: FCM 608 FCB 2309 FCB 1103 BR 17 Gurguéia FCB 2007
## ################# Cluster 3 ################
## {G1}: FCB 208 FCB 508 FCB 2006 FCB 2009 FCM 505 FCB 601 FCB 603 FCM 604
## {G2}: FCB 509 FCB 602 FCM 906 FCM 609
## [1] "hf"
## Results
## Means G1 G2
## P.-de-ouro 65.75 a
## FCB 1402 62.95 a
## Novaera 62.20 a
## FCB 406 60.97 a
## FCB 1103 59.45 a
## FCM 608 59.42 a
## FCB 2007 59.35 a
## BR 17 Gurguéia 58.87 a
## FCB 2309 57.97 a
## FCB 208 56.42 a
## BRS Guariba 56.05 a
## FCB 2006 55.73 a
## FCB 508 55.25 a
## FCB 601 55.25 a
## FCB 2009 53.82 b
## FCB 603 53.55 b
## FCM 604 51.45 b
## FCM 505 50.25 b
## FCB 509 48.72 b
## FCM 609 48.52 b
## FCB 602 47.77 b
## FCM 906 46.55 b
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 45.6 30 19 0.00064 7.1 63
## Clus 2 16.3 21 12 0.19119 7.1 63
## Clus 3 7.7 14 7 0.36173 7.1 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: P.-de-ouro FCB 1402 Novaera FCB 406 FCB 1103 FCM 608 FCB 2007 BR 17 Gurguéia FCB 2309 FCB 208 BRS Guariba FCB 2006 FCB 508 FCB 601
## {G2}: FCB 2009 FCB 603 FCM 604 FCM 505 FCB 509 FCM 609 FCB 602 FCM 906
## ################# Cluster 2 ################
## {G1}: P.-de-ouro FCB 1402 Novaera FCB 406
## {G2}: FCB 1103 FCM 608 FCB 2007 BR 17 Gurguéia FCB 2309 FCB 208 BRS Guariba FCB 2006 FCB 508 FCB 601
## ################# Cluster 3 ################
## {G1}: FCB 2009 FCB 603 FCM 604
## {G2}: FCM 505 FCB 509 FCM 609 FCB 602 FCM 906
## [1] "pp"
## Results
## Means G1 G2 G3 G4
## FCB 601 10.86 a
## FCM 608 8.43 b
## FCB 508 8.22 b
## FCB 208 7.25 c
## FCM 505 6.83 c
## FCM 609 6.61 c
## P.-de-ouro 6.56 c
## FCB 2309 6.33 c
## FCB 602 6.28 c
## FCB 509 6.19 c
## FCB 2006 6.06 d
## FCB 1103 6.01 d
## FCM 906 6.00 d
## FCB 2009 5.95 d
## FCB 406 5.86 d
## FCM 604 5.81 d
## Novaera 5.61 d
## FCB 2007 5.58 d
## FCB 603 5.50 d
## BR 17 Gurguéia 5.39 d
## FCB 1402 5.19 d
## BRS Guariba 5.11 d
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 73.97 30.5 19.3 2.4e-08 0.082 63
## Clus 2 41.23 7.2 2.6 3.3e-09 0.082 63
## Clus 3 0.36 5.5 1.8 7.9e-01 0.082 63
## Clus 4 38.15 27.1 16.6 2.0e-03 0.082 63
## Clus 5 9.70 12.8 6.1 1.5e-01 0.082 63
## Clus 6 14.79 19.0 10.5 1.7e-01 0.082 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: FCB 601 FCM 608 FCB 508
## {G2}: FCB 208 FCM 505 FCM 609 P.-de-ouro FCB 2309 FCB 602 FCB 509 FCB 2006 FCB 1103 FCM 906 FCB 2009 FCB 406 FCM 604 Novaera FCB 2007 FCB 603 BR 17 Gurguéia FCB 1402 BRS Guariba
## ################# Cluster 2 ################
## {G1}: FCB 601
## {G2}: FCM 608 FCB 508
## ################# Cluster 3 ################
## {G1}: FCM 608
## {G2}: FCB 508
## ################# Cluster 4 ################
## {G1}: FCB 208 FCM 505 FCM 609 P.-de-ouro FCB 2309 FCB 602 FCB 509
## {G2}: FCB 2006 FCB 1103 FCM 906 FCB 2009 FCB 406 FCM 604 Novaera FCB 2007 FCB 603 BR 17 Gurguéia FCB 1402 BRS Guariba
## ################# Cluster 5 ################
## {G1}: FCB 208 FCM 505
## {G2}: FCM 609 P.-de-ouro FCB 2309 FCB 602 FCB 509
## ################# Cluster 6 ################
## {G1}: FCB 2006 FCB 1103 FCM 906 FCB 2009 FCB 406 FCM 604
## {G2}: Novaera FCB 2007 FCB 603 BR 17 Gurguéia FCB 1402 BRS Guariba
## [1] "pl"
## Results
## Means G1 G2 G3 G4
## FCB 208 21.82 a
## FCB 508 21.51 a
## BR 17 Gurguéia 21.16 a
## FCM 608 21.16 a
## FCM 604 21.04 a
## FCB 2009 20.91 a
## FCB 2309 20.60 a
## FCM 505 19.72 b
## P.-de-ouro 19.27 b
## FCB 2007 19.06 b
## FCB 2006 18.95 b
## Novaera 18.47 c
## FCB 1402 17.64 c
## FCB 509 17.63 c
## FCB 406 17.61 c
## FCB 603 17.61 c
## BRS Guariba 17.20 c
## FCM 906 16.93 c
## FCB 1103 16.93 c
## FCB 602 16.86 c
## FCM 609 16.54 c
## FCB 601 15.17 d
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 76.9 30.5 19.3 7.7e-09 0.22 63
## Clus 2 38.9 17.8 9.6 2.0e-05 0.22 63
## Clus 3 4.4 12.8 6.1 6.4e-01 0.22 63
## Clus 4 1.9 8.7 3.5 6.7e-01 0.22 63
## Clus 5 20.8 17.8 9.6 1.9e-02 0.22 63
## Clus 6 12.1 16.6 8.8 1.9e-01 0.22 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: FCB 208 FCB 508 BR 17 Gurguéia FCM 608 FCM 604 FCB 2009 FCB 2309 FCM 505 P.-de-ouro FCB 2007 FCB 2006
## {G2}: Novaera FCB 1402 FCB 509 FCB 406 FCB 603 BRS Guariba FCM 906 FCB 1103 FCB 602 FCM 609 FCB 601
## ################# Cluster 2 ################
## {G1}: FCB 208 FCB 508 BR 17 Gurguéia FCM 608 FCM 604 FCB 2009 FCB 2309
## {G2}: FCM 505 P.-de-ouro FCB 2007 FCB 2006
## ################# Cluster 3 ################
## {G1}: FCB 208 FCB 508
## {G2}: BR 17 Gurguéia FCM 608 FCM 604 FCB 2009 FCB 2309
## ################# Cluster 4 ################
## {G1}: FCM 505
## {G2}: P.-de-ouro FCB 2007 FCB 2006
## ################# Cluster 5 ################
## {G1}: Novaera FCB 1402 FCB 509 FCB 406 FCB 603 BRS Guariba FCM 906 FCB 1103 FCB 602 FCM 609
## {G2}: FCB 601
## ################# Cluster 6 ################
## {G1}: Novaera FCB 1402 FCB 509 FCB 406 FCB 603
## {G2}: BRS Guariba FCM 906 FCB 1103 FCB 602 FCM 609
## [1] "ng"
## Results
## Means G1 G2 G3 G4
## FCB 508 110.84 a
## FCM 608 110.56 a
## FCB 208 102.92 a
## FCM 609 92.49 b
## FCM 505 92.11 b
## FCB 2309 87.05 b
## FCB 601 82.58 c
## P.-de-ouro 79.61 c
## FCM 604 78.11 c
## FCB 2009 77.75 c
## FCB 602 75.14 c
## FCB 509 75.06 c
## BR 17 Gurguéia 71.12 d
## FCB 2006 70.86 d
## FCB 406 69.74 d
## FCM 906 69.08 d
## FCB 1103 69.02 d
## Novaera 67.23 d
## FCB 1402 67.04 d
## FCB 603 66.35 d
## BRS Guariba 64.03 d
## FCB 2007 61.72 d
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 73.7 30.5 19.3 2.7e-08 15 63
## Clus 2 30.2 11.5 5.3 1.7e-05 15 63
## Clus 3 3.8 7.2 2.6 2.3e-01 15 63
## Clus 4 1.8 7.2 2.6 5.5e-01 15 63
## Clus 5 30.3 23.7 14.0 6.9e-03 15 63
## Clus 6 2.7 11.5 5.3 7.7e-01 15 63
## Clus 7 5.6 16.6 8.8 7.6e-01 15 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: FCB 508 FCM 608 FCB 208 FCM 609 FCM 505 FCB 2309
## {G2}: FCB 601 P.-de-ouro FCM 604 FCB 2009 FCB 602 FCB 509 BR 17 Gurguéia FCB 2006 FCB 406 FCM 906 FCB 1103 Novaera FCB 1402 FCB 603 BRS Guariba FCB 2007
## ################# Cluster 2 ################
## {G1}: FCB 508 FCM 608 FCB 208
## {G2}: FCM 609 FCM 505 FCB 2309
## ################# Cluster 3 ################
## {G1}: FCB 508 FCM 608
## {G2}: FCB 208
## ################# Cluster 4 ################
## {G1}: FCM 609 FCM 505
## {G2}: FCB 2309
## ################# Cluster 5 ################
## {G1}: FCB 601 P.-de-ouro FCM 604 FCB 2009 FCB 602 FCB 509
## {G2}: BR 17 Gurguéia FCB 2006 FCB 406 FCM 906 FCB 1103 Novaera FCB 1402 FCB 603 BRS Guariba FCB 2007
## ################# Cluster 6 ################
## {G1}: FCB 601 P.-de-ouro
## {G2}: FCM 604 FCB 2009 FCB 602 FCB 509
## ################# Cluster 7 ################
## {G1}: BR 17 Gurguéia FCB 2006 FCB 406 FCM 906 FCB 1103 Novaera FCB 1402 FCB 603
## {G2}: BRS Guariba FCB 2007
## [1] "we"
## Results
## Means G1 G2 G3 G4 G5 G6 G7
## FCB 508 241.29 a
## BRS Guariba 214.56 b
## FCB 601 214.11 b
## Novaera 213.86 b
## FCB 603 210.03 b
## FCM 505 209.45 b
## FCB 208 199.52 c
## FCM 608 198.02 c
## FCM 604 196.84 c
## P.-de-ouro 196.68 c
## FCB 509 196.42 c
## FCB 1103 194.04 c
## BR 17 Gurguéia 193.09 c
## FCM 609 192.44 c
## FCB 1402 185.07 d
## FCB 2309 183.72 d
## FCB 2006 182.25 d
## FCB 2009 175.28 e
## FCB 602 170.35 e
## FCB 406 159.37 f
## FCB 2007 153.84 f
## FCM 906 143.43 g
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 69.42 30.5 19.3 1.4e-07 7.8 63
## Clus 2 58.75 21.4 12.3 4.8e-08 7.8 63
## Clus 3 54.51 11.5 5.3 2.3e-10 7.8 63
## Clus 4 4.28 10.1 4.4 4.2e-01 7.8 63
## Clus 5 6.35 14.1 7.0 5.0e-01 7.8 63
## Clus 6 62.37 14.1 7.0 5.1e-11 7.8 63
## Clus 7 20.41 10.1 4.4 6.0e-04 7.8 63
## Clus 8 0.56 7.2 2.6 8.6e-01 7.8 63
## Clus 9 2.16 5.5 1.8 2.9e-01 7.8 63
## Clus 10 16.87 7.2 2.6 4.9e-04 7.8 63
## Clus 11 2.70 5.5 1.8 2.2e-01 7.8 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: FCB 508 BRS Guariba FCB 601 Novaera FCB 603 FCM 505 FCB 208 FCM 608 FCM 604 P.-de-ouro FCB 509 FCB 1103 BR 17 Gurguéia FCM 609
## {G2}: FCB 1402 FCB 2309 FCB 2006 FCB 2009 FCB 602 FCB 406 FCB 2007 FCM 906
## ################# Cluster 2 ################
## {G1}: FCB 508 BRS Guariba FCB 601 Novaera FCB 603 FCM 505
## {G2}: FCB 208 FCM 608 FCM 604 P.-de-ouro FCB 509 FCB 1103 BR 17 Gurguéia FCM 609
## ################# Cluster 3 ################
## {G1}: FCB 508
## {G2}: BRS Guariba FCB 601 Novaera FCB 603 FCM 505
## ################# Cluster 4 ################
## {G1}: BRS Guariba FCB 601 Novaera
## {G2}: FCB 603 FCM 505
## ################# Cluster 5 ################
## {G1}: FCB 208 FCM 608 FCM 604 P.-de-ouro FCB 509
## {G2}: FCB 1103 BR 17 Gurguéia FCM 609
## ################# Cluster 6 ################
## {G1}: FCB 1402 FCB 2309 FCB 2006 FCB 2009 FCB 602
## {G2}: FCB 406 FCB 2007 FCM 906
## ################# Cluster 7 ################
## {G1}: FCB 1402 FCB 2309 FCB 2006
## {G2}: FCB 2009 FCB 602
## ################# Cluster 8 ################
## {G1}: FCB 1402 FCB 2309
## {G2}: FCB 2006
## ################# Cluster 9 ################
## {G1}: FCB 2009
## {G2}: FCB 602
## ################# Cluster 10 ################
## {G1}: FCB 406 FCB 2007
## {G2}: FCM 906
## ################# Cluster 11 ################
## {G1}: FCB 406
## {G2}: FCB 2007
## [1] "gy"
## Results
## Means G1 G2 G3 G4 G5 G6 G7
## FCB 601 2269.12 a
## FCB 508 1925.30 b
## FCB 208 1873.65 b
## FCM 505 1802.30 b
## FCM 608 1666.55 c
## FCM 609 1659.11 c
## P.-de-ouro 1605.12 c
## FCB 2309 1568.07 c
## FCB 602 1540.25 c
## FCB 603 1540.08 c
## FCB 2007 1513.42 c
## FCB 406 1454.41 d
## FCB 2009 1376.64 d
## Novaera 1375.00 d
## BR 17 Gurguéia 1341.29 d
## FCM 604 1300.69 e
## FCB 1402 1224.42 e
## BRS Guariba 1209.53 e
## FCB 1103 1145.35 f
## FCM 906 984.62 g
## FCB 509 975.91 g
## FCB 2006 944.01 g
##
## Sig.level
## 0.05
##
## Statistics
## lambda chisq dfchisq pvalue evmean dferror
## Clus 1 69.41 30.5 19.3 1.4e-07 2258 63
## Clus 2 57.03 17.8 9.6 9.3e-09 2258 63
## Clus 3 41.22 8.7 3.5 1.2e-08 2258 63
## Clus 4 3.81 7.2 2.6 2.3e-01 2258 63
## Clus 5 10.69 12.8 6.1 1.0e-01 2258 63
## Clus 6 55.01 17.8 9.6 2.2e-08 2258 63
## Clus 7 17.65 12.8 6.1 7.8e-03 2258 63
## Clus 8 3.76 8.7 3.5 3.6e-01 2258 63
## Clus 9 2.89 7.2 2.6 3.4e-01 2258 63
## Clus 10 13.02 8.7 3.5 7.4e-03 2258 63
## Clus 11 0.56 7.2 2.6 8.6e-01 2258 63
##
##
## Clusters
## ################# Cluster 1 ################
## {G1}: FCB 601 FCB 508 FCB 208 FCM 505 FCM 608 FCM 609 P.-de-ouro FCB 2309 FCB 602 FCB 603 FCB 2007
## {G2}: FCB 406 FCB 2009 Novaera BR 17 Gurguéia FCM 604 FCB 1402 BRS Guariba FCB 1103 FCM 906 FCB 509 FCB 2006
## ################# Cluster 2 ################
## {G1}: FCB 601 FCB 508 FCB 208 FCM 505
## {G2}: FCM 608 FCM 609 P.-de-ouro FCB 2309 FCB 602 FCB 603 FCB 2007
## ################# Cluster 3 ################
## {G1}: FCB 601
## {G2}: FCB 508 FCB 208 FCM 505
## ################# Cluster 4 ################
## {G1}: FCB 508 FCB 208
## {G2}: FCM 505
## ################# Cluster 5 ################
## {G1}: FCM 608 FCM 609 P.-de-ouro
## {G2}: FCB 2309 FCB 602 FCB 603 FCB 2007
## ################# Cluster 6 ################
## {G1}: FCB 406 FCB 2009 Novaera BR 17 Gurguéia FCM 604 FCB 1402 BRS Guariba
## {G2}: FCB 1103 FCM 906 FCB 509 FCB 2006
## ################# Cluster 7 ################
## {G1}: FCB 406 FCB 2009 Novaera BR 17 Gurguéia
## {G2}: FCM 604 FCB 1402 BRS Guariba
## ################# Cluster 8 ################
## {G1}: FCB 406
## {G2}: FCB 2009 Novaera BR 17 Gurguéia
## ################# Cluster 9 ################
## {G1}: FCM 604
## {G2}: FCB 1402 BRS Guariba
## ################# Cluster 10 ################
## {G1}: FCB 1103
## {G2}: FCM 906 FCB 509 FCB 2006
## ################# Cluster 11 ################
## {G1}: FCM 906 FCB 509
## {G2}: FCB 2006MGIDI and Smith-Hazel indices
This script computes the MGIDI (multi-trait genotype-ideotype distance index) to rank genotypes based on predefined economic weights. The KMO (Kaiser-Meyer-Olkin) test is applied to the MGIDI correlation matrix to verify the adequacy of the factor analysis structure. The classical Smith-Hazel linear selection index is also calculated using the phenotypic and genotypic covariance matrices. Both indices use identical weights and a fixed selection intensity of 20 % (SI = 20) to ensure a fair comparison. Finally, the coincidence index measures the agreement between the genotypes selected by MGIDI and Smith-Hazel.
library(metan)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## |=========================================================|## | Multi-Environment Trial Analysis (metan) v1.18.0 |## | Author: Tiago Olivoto |## | Type 'citation('metan')' to know how to cite metan |## | Type 'vignette('metan_start')' for a short tutorial |## | Visit 'https://bit.ly/pkgmetan' for a complete tutorial |## |=========================================================|library(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:metan':
##
## skewmod=gafem(.data=dados,gen=gen,rep=bloc,resp=c(ph,hf,pp,pl,ng,we,gy))## Evaluating trait ph |====== | 14% 00:00:00 Evaluating trait hf |============= | 29% 00:00:00 Evaluating trait pp |=================== | 43% 00:00:00 Evaluating trait pl |========================= | 57% 00:00:01 Evaluating trait ng |=============================== | 71% 00:00:01 Evaluating trait we |====================================== | 86% 00:00:01 Evaluating trait gy |============================================| 100% 00:00:01
## ---------------------------------------------------------------------------
## One-way ANOVA table (Randomized complete block design)
## ---------------------------------------------------------------------------
## model ph hf pp pl ng we gy
## REP 7.54e-07 5.53e-04 4.71e-03 4.13e-04 4.78e-05 1.93e-01 3.76e-01
## GEN 9.80e-06 1.45e-05 7.27e-21 1.69e-18 1.26e-16 1.19e-34 5.60e-31
## Residuals NA NA NA NA NA NA NA
## ---------------------------------------------------------------------------
## Variables with nonsignificant genotype effect
##
## ---------------------------------------------------------------------------mg=mgidi(mod,weights=c(0.2,1,1,1,1,1,1),SI=20)##
## -------------------------------------------------------------------------------
## Principal Component Analysis
## -------------------------------------------------------------------------------
## # A tibble: 7 × 4
## PC Eigenvalues `Variance (%)` `Cum. variance (%)`
## <chr> <dbl> <dbl> <dbl>
## 1 PC1 2.79 39.8 39.8
## 2 PC2 2.05 29.3 69.2
## 3 PC3 1.07 15.2 84.4
## 4 PC4 0.65 9.26 93.7
## 5 PC5 0.25 3.55 97.2
## 6 PC6 0.14 1.95 99.2
## 7 PC7 0.06 0.83 100
## -------------------------------------------------------------------------------
## Factor Analysis - factorial loadings after rotation-
## -------------------------------------------------------------------------------
## # A tibble: 7 × 6
## VAR FA1 FA2 FA3 Communality Uniquenesses
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 ph 0.07 -0.98 -0.04 0.96 0.04
## 2 hf -0.05 -0.97 -0.07 0.94 0.06
## 3 pp -0.91 0.17 0.08 0.86 0.14
## 4 pl -0.05 -0.14 -0.97 0.96 0.04
## 5 ng -0.72 0.22 -0.58 0.89 0.11
## 6 we -0.65 -0.19 -0.17 0.48 0.52
## 7 gy -0.9 -0.02 -0.05 0.81 0.19
## -------------------------------------------------------------------------------
## Comunalit Mean: 0.8441209
## -------------------------------------------------------------------------------
## Selection differential
## -------------------------------------------------------------------------------
## # A tibble: 7 × 11
## VAR Factor Xo Xs SD SDperc h2 SG SGperc sense goal
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
## 1 pp FA1 6.44 7.68 1.25 19.3 0.952 1.19 18.4 increa… 100
## 2 ng FA1 79.1 104. 25.0 31.6 0.930 23.2 29.4 increa… 100
## 3 we FA1 192. 212. 20.1 10.5 0.984 19.8 10.3 increa… 100
## 4 gy FA1 1468. 1817. 349. 23.8 0.979 342. 23.3 increa… 100
## 5 ph FA2 63.4 62.8 -0.605 -0.954 0.751 -0.454 -0.716 increa… 0
## 6 hf FA2 55.7 55.3 -0.403 -0.724 0.744 -0.300 -0.538 increa… 0
## 7 pl FA3 18.8 21.1 2.24 11.9 0.941 2.11 11.2 increa… 100
## ------------------------------------------------------------------------------
## Selected genotypes
## -------------------------------------------------------------------------------
## FCB 508 FCM 608 FCB 208 FCM 505
## -------------------------------------------------------------------------------print(mg)## -------------------------------------------------------------------------------
## Correlation matrix used used in factor analysis
## -------------------------------------------------------------------------------
## ph hf pp pl ng we gy
## ph 1.000 0.919 -0.230 0.16 -0.22 0.12 -0.042
## hf 0.919 1.000 -0.074 0.21 -0.12 0.11 0.079
## pp -0.230 -0.074 1.000 -0.03 0.65 0.39 0.753
## pl 0.161 0.211 -0.030 1.00 0.52 0.18 0.135
## ng -0.216 -0.116 0.655 0.52 1.00 0.44 0.624
## we 0.125 0.114 0.387 0.18 0.44 1.00 0.443
## gy -0.042 0.079 0.753 0.13 0.62 0.44 1.000
## -------------------------------------------------------------------------------
## Principal component analysis
## -------------------------------------------------------------------------------
## # A tibble: 7 × 4
## PC Eigenvalues `Variance (%)` `Cum. variance (%)`
## <chr> <dbl> <dbl> <dbl>
## 1 PC1 2.788 39.82 39.82
## 2 PC2 2.054 29.34 69.17
## 3 PC3 1.067 15.25 84.41
## 4 PC4 0.6479 9.256 93.67
## 5 PC5 0.2485 3.550 97.22
## 6 PC6 0.1364 1.948 99.17
## 7 PC7 0.05838 0.8340 100
## -------------------------------------------------------------------------------
## Initial loadings
## -------------------------------------------------------------------------------
## # A tibble: 7 × 4
## VAR PC1 PC2 PC3
## <chr> <dbl> <dbl> <dbl>
## 1 ph 0.2011 -0.9481 0.1531
## 2 hf 0.07740 -0.9514 0.1686
## 3 pp -0.8437 0.1266 0.3586
## 4 pl -0.3434 -0.3892 -0.8331
## 5 ng -0.8903 0.01616 -0.3186
## 6 we -0.6299 -0.2694 0.1190
## 7 gy -0.8498 -0.09670 0.2777
## -------------------------------------------------------------------------------
## Loadings after varimax rotation
## -------------------------------------------------------------------------------
## # A tibble: 7 × 4
## VAR FA1 FA2 FA3
## <chr> <dbl> <dbl> <dbl>
## 1 ph 0.06967 -0.9779 -0.03987
## 2 hf -0.05137 -0.9657 -0.06727
## 3 pp -0.9057 0.1723 0.08166
## 4 pl -0.04973 -0.1403 -0.9702
## 5 ng -0.7155 0.2212 -0.5774
## 6 we -0.6475 -0.1896 -0.1682
## 7 gy -0.8974 -0.02431 -0.05159
## -------------------------------------------------------------------------------
## Scores for genotypes-ideotype
## -------------------------------------------------------------------------------
## # A tibble: 23 × 4
## GEN FA1 FA2 FA3
## <chr> <dbl> <dbl> <dbl>
## 1 BR 17 Gurguéia -0.9483 -2.373 -2.384
## 2 BRS Guariba -1.156 -2.749 -0.6532
## 3 FCB 1103 -1.230 -2.439 -0.5479
## 4 FCB 1402 -0.9393 -3.098 -0.8501
## 5 FCB 2006 -0.6903 -1.595 -1.541
## 6 FCB 2007 -0.7968 -2.304 -1.161
## 7 FCB 2009 -0.9886 -1.336 -2.397
## 8 FCB 208 -2.534 -1.711 -2.992
## 9 FCB 2309 -1.632 -2.150 -2.316
## 10 FCB 406 -1.129 -2.907 -0.7026
## # ℹ 13 more rows
## -------------------------------------------------------------------------------
## Multi-trait genotype-ideotype distance index
## -------------------------------------------------------------------------------
## # A tibble: 22 × 2
## Genotype MGIDI
## <chr> <dbl>
## 1 FCB 508 1.503
## 2 FCM 608 1.972
## 3 FCB 208 2.370
## 4 FCM 505 2.677
## 5 FCB 2309 3.141
## 6 P.-de-ouro 3.224
## 7 FCB 601 3.500
## 8 FCM 609 3.639
## 9 FCB 603 3.689
## 10 Novaera 3.701
## # ℹ 12 more rows
## -------------------------------------------------------------------------------
## Selection differential
## -------------------------------------------------------------------------------
## # A tibble: 7 × 11
## VAR Factor Xo Xs SD SDperc h2 SG SGperc sense
## <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 pp FA1 6.437 7.683 1.245 19.34 0.9522 1.186 18.42 incre…
## 2 ng FA1 79.11 104.1 25.00 31.60 0.9299 23.25 29.39 incre…
## 3 we FA1 192.0 212.1 20.09 10.46 0.9844 19.77 10.30 incre…
## 4 gy FA1 1468. 1817. 349.0 23.77 0.9793 341.8 23.28 incre…
## 5 ph FA2 63.35 62.75 -0.6045 -0.9542 0.7507 -0.4538 -0.7163 incre…
## 6 hf FA2 55.74 55.34 -0.4034 -0.7237 0.7436 -0.3000 -0.5381 incre…
## 7 pl FA3 18.81 21.05 2.244 11.93 0.9410 2.112 11.23 incre…
## # ℹ 1 more variable: goal <dbl>
## -------------------------------------------------------------------------------
## Selected genotypes
## -------------------------------------------------------------------------------
## FCB 508 FCM 608 FCB 208 FCM 505print(KMO(mg$cormat))## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = mg$cormat)
## Overall MSA = 0.55
## MSA for each item =
## ph hf pp pl ng we gy
## 0.49 0.46 0.55 0.31 0.60 0.78 0.81vcov <- covcor_design(.data = dados,gen = gen,rep = bloc,
resp = c(ph, hf, pp, pl, ng, we, gy))
means <- as.matrix(vcov$means)
pcov <- vcov$phen_cov
gcov <- vcov$geno_cov
sh=Smith_Hazel(means,use_data = "pheno",pcov = pcov,
gcov = gcov,SI=20, weights = c(0.2,1,1,1,1,1,1))
print(sh)##
## -----------------------------------------------------------------------------------
## Index coefficients
## -----------------------------------------------------------------------------------
## # A tibble: 7 × 3
## VAR b gen_weights
## <chr> <dbl> <dbl>
## 1 ph 0.2589 0.2
## 2 hf 0.6203 1
## 3 pp 6.502 1
## 4 pl 1.545 1
## 5 ng 1.137 1
## 6 we 0.9914 1
## 7 gy 0.9643 1
##
## -----------------------------------------------------------------------------------
## Genetic worth
## -----------------------------------------------------------------------------------
## GEN V1
## 1 FCB 601 2638.112
## 2 FCB 508 2358.756
## 3 FCB 208 2253.734
## 4 FCM 505 2172.130
## 5 FCM 608 2070.611
## 6 FCM 609 2008.206
## 7 P.-de-ouro 1965.605
## 8 FCB 2309 1919.342
## 9 FCB 603 1880.382
## 10 FCB 602 1850.344
## 11 FCB 2007 1801.665
## 12 FCB 406 1761.602
## 13 Novaera 1736.793
## 14 FCB 2009 1709.729
## 15 BR 17 Gurguéia 1687.042
## 16 FCM 604 1655.692
## 17 BRS Guariba 1565.049
## 18 FCB 1402 1558.737
## 19 FCB 1103 1494.570
## 20 FCB 509 1333.561
## 21 FCB 2006 1290.686
## 22 FCM 906 1278.339
##
## -----------------------------------------------------------------------------------
## Selection gain
## -----------------------------------------------------------------------------------
## # A tibble: 7 × 7
## VAR Xo Xs SD SDperc sense goal
## <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
## 1 ph 63.35 61.12 -2.236 -3.529 increase 0
## 2 hf 55.74 54.29 -1.447 -2.596 increase 0
## 3 pp 6.437 8.291 1.854 28.80 increase 100
## 4 pl 18.81 19.55 0.7457 3.965 increase 100
## 5 ng 79.11 97.12 18.01 22.76 increase 100
## 6 we 192.0 216.1 24.11 12.56 increase 100
## 7 gy 1468. 1968. 499.6 34.04 increase 100
##
## -----------------------------------------------------------------------------------
## Phenotypic variance-covariance matrix
## -----------------------------------------------------------------------------------
## ph hf pp pl ng we gy
## ph 50.6 29.84 -1.852 1.919 -19.3 17.2 -86
## hf 29.8 37.06 -0.507 2.149 -8.8 13.4 138
## pp -1.9 -0.51 2.276 -0.076 12.4 11.3 325
## pl 1.9 2.15 -0.076 5.000 14.5 7.9 86
## ng -19.3 -8.84 12.417 14.498 280.8 144.1 2989
## we 17.2 13.44 11.322 7.861 144.1 669.1 3278
## gy -85.8 138.00 324.727 86.158 2988.5 3277.6 145163
##
## -----------------------------------------------------------------------------------
## Genotypic variance-covariance matrix
## -----------------------------------------------------------------------------------
## ph hf pp pl ng we gy
## ph 38.0 23.48 -1.659 2.073 -17.6 17.4 -96
## hf 23.5 27.56 -0.440 2.054 -7.9 14.3 127
## pp -1.7 -0.44 2.167 -0.069 11.8 11.2 328
## pl 2.1 2.05 -0.069 4.706 14.7 8.3 86
## ng -17.6 -7.90 11.850 14.725 261.1 142.3 3018
## we 17.4 14.31 11.160 8.274 142.3 658.7 3248
## gy -96.4 126.82 328.036 86.315 3018.1 3248.2 142152coincidence_index(sel1 = sh$sel_gen, sel2 = mg$sel_gen, total = 22)## [1] 69.5122