Datos de Diseño Experimental Genotipo x Ambiente

Los siguientes datos corresponden a un diseño de experimentos de evaluación de rendimiento de diversos genotipos de papa en varios ambientes (zonas con climas diversos).

require(ggplot2)
require(plotly)
require(agricolae)

data("genxenv")
head(genxenv,3)
##   ENV GEN      YLD
## 1   1   1 17.62333
## 2   1   2 26.98333
## 3   1   3 23.55000
#y=YLD (yield=rendimiento -toneladas por hectarea)
#x1=GEN (Genotype - variedad)
#x2=ENV (Enviroment - Ambiente)
genxenv$ENV=as.factor(genxenv$ENV)
genxenv$GEN=as.factor(genxenv$GEN)

ggplot(genxenv,aes(x=YLD))+geom_histogram()+theme_bw()

ggplot(genxenv,aes(x=YLD,fill=ENV))+geom_histogram()+theme_bw()

ggplot(genxenv,aes(y=YLD,x=ENV,fill=ENV))+geom_boxplot()+theme_bw()

Se observa que la variable rendimiento presenta gran variabilidad de acuerdo al histograma y muestra un comportamiento de subgrupos. Cuando realizamos la comparación por ambientes se logra observar que parte de esas diferencias de los grupos se debe a los ambientes. Por ejemplo el 1 y 2 presentan bajos rendimientos y el 3 y 4 son mas altos.

Modelo para Comparar Solo Ambientes

mod1=lm(YLD~ENV,data=genxenv)
anova(mod1)
## Analysis of Variance Table
## 
## Response: YLD
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## ENV         4 242922   60731  695.09 < 2.2e-16 ***
## Residuals 245  21406      87                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(mod1)
## 
## Call:
## lm(formula = YLD ~ ENV, data = genxenv)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.359  -4.555   0.040   4.232  32.125 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   24.047      1.322  18.191  < 2e-16 ***
## ENV2          -7.505      1.869  -4.015 7.91e-05 ***
## ENV3          54.383      1.869  29.090  < 2e-16 ***
## ENV4          70.295      1.869  37.602  < 2e-16 ***
## ENV5           8.813      1.869   4.714 4.07e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.347 on 245 degrees of freedom
## Multiple R-squared:  0.919,  Adjusted R-squared:  0.9177 
## F-statistic: 695.1 on 4 and 245 DF,  p-value: < 2.2e-16

La tabla anova nos muestra que existen diferencias significativas entre los ambientes, con resumen podemos observar que algunos se destacan mas que otros como el 3 y 4. Sin embargo para contrastar todas combinaciones y obtener los mejores ambientes debemos usar una prueba postanova.

post1=LSD.test(mod1,"ENV")
post1
## $statistics
##    MSerror  Df     Mean       CV  t.value      LSD
##   87.37046 245 49.24373 18.98153 1.969694 3.682231
## 
## $parameters
##         test p.ajusted name.t ntr alpha
##   Fisher-LSD      none    ENV   5  0.05
## 
## $means
##        YLD       std  r      LCL      UCL      Min       Max      Q25      Q50
## 1 24.04653  7.340494 50 21.44280 26.65026 12.65667  42.47000 18.55583 22.80167
## 2 16.54113  3.192049 50 13.93740 19.14486  9.90000  26.13000 14.19250 17.13833
## 3 78.42927  9.398327 50 75.82554 81.03300 58.09000 100.79667 72.75083 78.33500
## 4 94.34200 16.242465 50 91.73827 96.94573 56.98333 126.46667 84.28500 97.17167
## 5 32.85973  4.542469 50 30.25600 35.46346 23.39667  48.00667 29.26250 32.81000
##         Q75
## 1  27.44333
## 2  18.63750
## 3  84.74917
## 4 101.56500
## 5  35.84833
## 
## $comparison
## NULL
## 
## $groups
##        YLD groups
## 4 94.34200      a
## 3 78.42927      b
## 5 32.85973      c
## 1 24.04653      d
## 2 16.54113      e
## 
## attr(,"class")
## [1] "group"
bar.group(post1$groups,ylim=c(0,120))

Se observa en el postanova que los ambientes 4 y 3 son los de mayor rendimiento mientras que el 2 es el menos favorable para la productividad de la papa.

Modelo para Comparar Genotipos pero teniendo en cuenta el Ambiente

mod2=lm(YLD~ENV+GEN,data=genxenv)
anova(mod2)
## Analysis of Variance Table
## 
## Response: YLD
##            Df Sum Sq Mean Sq  F value    Pr(>F)    
## ENV         4 242922   60731 876.7745 < 2.2e-16 ***
## GEN        49   7830     160   2.3069 2.833e-05 ***
## Residuals 196  13576      69                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
post2=LSD.test(mod2,"GEN")
post2
## $statistics
##    MSerror  Df     Mean       CV  t.value      LSD
##   69.26587 196 49.24373 16.90085 1.972141 10.38072
## 
## $parameters
##         test p.ajusted name.t ntr alpha
##   Fisher-LSD      none    GEN  50  0.05
## 
## $means
##         YLD      std r      LCL      UCL       Min       Max      Q25      Q50
## 1  44.73733 32.55482 5 37.39705 52.07761 17.216667  82.85333 17.62333 28.94000
## 10 49.12000 40.48756 5 41.77972 56.46028 13.493333  99.30333 20.24333 26.00667
## 11 51.56800 30.84790 5 44.22772 58.90828 19.290000  93.99667 35.60667 35.86333
## 12 52.51733 35.94814 5 45.17705 59.85761 15.406667 105.09667 34.25667 35.34000
## 13 57.65067 43.27937 5 50.31039 64.99095 17.623333 115.90333 26.97333 36.69000
## 14 64.09733 45.74939 5 56.75705 71.43761 21.623333 125.92333 31.50667 42.47000
## 15 52.62067 38.08023 5 45.28039 59.96095 18.986667 103.66333 27.31333 30.18667
## 16 48.59400 37.48420 5 41.25372 55.93428 12.826667 100.56667 17.38333 39.46667
## 17 43.45400 30.58004 5 36.11372 50.79428 15.513333  83.68333 20.12000 29.79333
## 18 49.40933 29.50659 5 42.06905 56.74961 17.916667  83.28000 23.02667 48.00667
## 19 52.11800 38.79318 5 44.77772 59.45828 18.546667  98.24000 19.70000 34.51000
## 2  41.30933 26.25397 5 33.96905 48.64961 13.530000  73.83667 26.98333 27.71000
## 20 36.84867 25.66660 5 29.50839 44.18895  9.933333  67.17333 12.65667 37.49667
## 21 53.49600 41.25961 5 46.15572 60.83628 17.206667 108.85333 22.73333 32.76000
## 22 46.17067 34.89814 5 38.83039 53.51095 15.666667  98.92667 21.58333 30.74667
## 23 47.99933 30.50167 5 40.65905 55.33961 15.970000  81.68000 29.39333 33.33333
## 24 51.72800 35.76393 5 44.38772 59.06828 18.560000  93.37667 27.44333 31.64000
## 25 44.28533 31.68427 5 36.94505 51.62561 12.070000  81.48667 18.89000 35.24667
## 26 44.66800 36.89362 5 37.32772 52.00828 10.216667  86.38000 17.13000 26.93333
## 27 55.91267 38.47252 5 48.57239 63.25295 18.783333 108.54667 31.05000 37.03667
## 28 55.01400 45.72438 5 47.67372 62.35428 14.310000 119.46667 17.81000 38.53333
## 29 51.27000 43.61796 5 43.92972 58.61028 14.200000 108.40667 17.81667 28.27667
## 3  39.73800 23.44033 5 32.39772 47.07828 17.733333  71.78000 23.55000 28.56667
## 30 53.61667 48.21166 5 46.27639 60.95695 13.886667 126.46667 19.86667 28.70667
## 31 44.21600 33.28330 5 36.87572 51.55628  9.900000  87.70000 22.46333 30.38000
## 32 50.18867 30.00424 5 42.84839 57.52895 17.096667  93.79333 35.67333 38.30000
## 33 50.08400 35.97018 5 42.74372 57.42428 18.366667  97.54333 25.59667 29.16667
## 34 53.06600 44.81368 5 45.72572 60.40628 14.190000 117.64000 22.22333 29.30000
## 35 47.95667 31.64728 5 40.61639 55.29695 15.706667  84.62000 27.44333 32.86000
## 36 44.87800 35.30855 5 37.53772 52.21828 13.946667  90.73333 13.98667 32.30000
## 37 56.21200 32.37567 5 48.87172 63.55228 22.750000  98.92333 36.38000 41.51000
## 38 53.11600 38.60790 5 45.77572 60.45628 19.313333 101.00000 22.87000 33.98333
## 39 49.98400 36.97341 5 42.64372 57.32428 13.893333 100.31667 23.20333 35.80333
## 4  49.17867 32.27384 5 41.83839 56.51895 20.080000  88.26667 24.50333 33.33667
## 40 51.01133 35.81602 5 43.67105 58.35161 18.786667 100.99667 27.10000 31.68667
## 41 43.11400 30.96953 5 35.77372 50.45428 14.600000  84.17333 14.78333 36.68333
## 42 50.19867 36.14306 5 42.85839 57.53895 18.583333  98.85667 20.02000 36.01667
## 43 52.61333 40.78926 5 45.27305 59.95361 15.990000 101.75333 17.40000 37.49000
## 44 46.83600 34.78686 5 39.49572 54.17628 13.086667  86.79667 15.41667 39.44333
## 45 50.23933 35.09432 5 42.89905 57.57961 17.180000  99.40000 22.03333 39.74000
## 46 38.99600 27.77105 5 31.65572 46.33628 14.446667  77.47667 15.71667 29.25000
## 47 49.96933 36.64249 5 42.62905 57.30961 17.483333 104.58333 28.35667 28.91000
## 48 50.18533 32.24445 5 42.84505 57.52561 22.240000  94.51667 26.13000 33.96333
## 49 43.69333 26.76515 5 36.35305 51.03361 18.663333  80.75333 21.84333 35.56667
## 5  35.21400 25.26154 5 27.87372 42.55428 13.690000  65.74000 14.10667 23.39667
## 50 46.10933 32.40048 5 38.76905 53.44961 17.013333  85.18000 24.25667 26.77000
## 6  54.46800 38.67896 5 47.12772 61.80828 16.620000 100.51333 31.12333 32.27667
## 7  51.20667 32.50882 5 43.86639 58.54695 17.986667  96.80000 34.08333 34.34000
## 8  50.75667 33.79318 5 43.41639 58.09695 18.923333  91.75000 29.48667 30.84667
## 9  60.75200 49.47199 5 53.41172 68.09228 14.436667 126.08000 27.37667 35.07000
##          Q75
## 1   77.05333
## 10  86.55333
## 11  73.08333
## 12  72.48667
## 13  91.06333
## 14  98.96333
## 15  82.95333
## 16  72.72667
## 17  68.16000
## 18  74.81667
## 19  89.59333
## 2   64.48667
## 20  56.98333
## 21  85.92667
## 22  63.93000
## 23  79.62000
## 24  87.62000
## 25  73.73333
## 26  82.68000
## 27  84.14667
## 28  84.95000
## 29  87.65000
## 3   57.06000
## 30  79.15667
## 31  70.63667
## 32  66.08000
## 33  79.74667
## 34  81.97667
## 35  79.15333
## 36  73.42333
## 37  81.49667
## 38  88.41333
## 39  76.70333
## 4   79.70667
## 40  76.48667
## 41  65.33000
## 42  77.51667
## 43  90.43333
## 44  79.43667
## 45  72.84333
## 46  58.09000
## 47  70.51333
## 48  74.07667
## 49  61.64000
## 5   59.13667
## 50  77.32667
## 6   91.80667
## 7   72.82333
## 8   82.77667
## 9  100.79667
## 
## $comparison
## NULL
## 
## $groups
##         YLD    groups
## 14 64.09733         a
## 9  60.75200        ab
## 13 57.65067       abc
## 37 56.21200      abcd
## 27 55.91267      abcd
## 28 55.01400     abcde
## 6  54.46800    abcdef
## 30 53.61667    bcdefg
## 21 53.49600    bcdefg
## 38 53.11600   bcdefgh
## 34 53.06600   bcdefgh
## 15 52.62067   bcdefgh
## 43 52.61333   bcdefgh
## 12 52.51733   bcdefgh
## 19 52.11800   bcdefgh
## 24 51.72800   bcdefgh
## 11 51.56800  bcdefghi
## 29 51.27000  bcdefghi
## 7  51.20667  bcdefghi
## 40 51.01133  bcdefghi
## 8  50.75667  bcdefghi
## 45 50.23933   cdefghi
## 42 50.19867   cdefghi
## 32 50.18867   cdefghi
## 48 50.18533   cdefghi
## 33 50.08400  cdefghij
## 39 49.98400  cdefghij
## 47 49.96933  cdefghij
## 18 49.40933  cdefghij
## 4  49.17867 cdefghijk
## 10 49.12000 cdefghijk
## 16 48.59400 cdefghijk
## 23 47.99933 cdefghijk
## 35 47.95667 cdefghijk
## 44 46.83600 defghijkl
## 22 46.17067 defghijkl
## 50 46.10933 defghijkl
## 36 44.87800 efghijklm
## 1  44.73733 efghijklm
## 26 44.66800 efghijklm
## 25 44.28533  fghijklm
## 31 44.21600  fghijklm
## 49 43.69333   ghijklm
## 17 43.45400   ghijklm
## 41 43.11400    hijklm
## 2  41.30933     ijklm
## 3  39.73800      jklm
## 46 38.99600       klm
## 20 36.84867        lm
## 5  35.21400         m
## 
## attr(,"class")
## [1] "group"
bar.group(post2$groups,xlim=c(0,90),horiz = T,las=2)

Se observa diferencias significativas entre los genotipos, destacando el 14 como el de mejor desempeño y el 5 el de menor desempeño. Sin embargo algunos adicionnales como el 13 y 9 presentaron desempeños similares al 14.