Description
Comprehensive Statistical Analysis of Plant Breeding Experiments.
Description
Performs statistical data analysis of various Plant Breeding experiments. Contains functions for Line by Tester analysis as per Arunachalam, V.(1974) <http://repository.ias.ac.in/89299/> and Diallel analysis as per Griffing, B. (1956) <https://www.publish.csiro.au/bi/pdf/BI9560463>.
README.md
gpbStat
The package is used for statistical analysis of Plant Breeding experiments.
Package Website https://nandp1.github.io/gpbStat/
Note: In the latest version 0.3.1 estimation of Kings Variance is not included.
Installation
Install latest package from Github through
install.packages("devtools")
library(devtools)
install_github("nandp1/gpbStat")
Install gpbStat from CRAN with:
install.packages("gpbStat")
Example
Line by Tester analysis (only crosses).
# Loading the gpbStat package
library(gpbStat)
# Loading dataset
data(rcbdltc)
## Now by using function ltc we analyze the data.
## The first parameter of `ltc` function is "data" followed by replication, line, tester and dependent variable(yield)
results1 = ltc(rcbdltc, replication, line, tester, yield)
#>
#> Analysis of Line x Tester: yield
## Viewing the results
results1
#> $Means
#> Testers
#> Lines 6 7 8
#> 1 68.550 107.640 52.640
#> 2 73.265 97.640 85.650
#> 3 100.885 111.540 117.735
#> 4 105.795 64.450 46.855
#> 5 84.150 81.935 94.820
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 148.436 49.47866 0.509612 6.778194e-01
#> Crosses 14 26199.654 1871.40388 19.274772 6.737492e-14
#> Lines 4 10318.361 2579.59035 27.466791 1.421271e-11
#> Testers 2 1718.926 859.46289 9.151332 4.626865e-04
#> Lines X Testers 8 14162.367 1770.29589 18.849639 4.973396e-12
#> Error 42 4077.815 97.09084 NA NA
#> Total 59 30425.906 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 11.42608
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 455.48131 552.57215 97.09084
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 27.2585365 24.7481829
#> Environmental coefficient of Variation <NA>
#> 11.4260778 0.8242929
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 10318.361 2579.59035 27.466791 1.421271e-11
#> Testers 2 1718.926 859.46289 9.151332 4.626865e-04
#> Lines X Testers 8 14162.367 1770.29589 18.849639 4.973396e-12
#> Error 42 4077.815 97.09084 NA NA
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> -9.960 -0.718 23.817 -13.870 0.732
#>
#> $`GCA testers`
#> 6 7 8
#> 0.292 6.404 -6.697
#>
#> $`SCA crosses`
#> Testers
#> Lines 6 7 8
#> 1 -8.019 24.959 -16.940
#> 2 -12.546 5.717 6.828
#> 3 -9.461 -4.918 14.378
#> 4 33.136 -14.321 -18.815
#> 5 -3.111 -11.438 14.548
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 39.383578 6.560872 54.055550
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> 67.441205 -45.541650
#> Cov H.S. (average) Cov F.S. (average)
#> 2.680894 408.052454
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> 10.723574 5.361787
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> 836.602526 418.301263
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 2.844451 2.203303 4.926734
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 4.022662 3.115940 6.967454
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 5.740335 4.446445 9.942552
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 8.118060 6.288222 14.060892
# Similarly we analyze the line tester data containing only crosses laid out in Alpha lattice design.
# Load the package
library(gpbStat)
# Loading dataset
data("alphaltc")
# Viewing the Structure of dataset
str(alphaltc)
#> 'data.frame': 60 obs. of 5 variables:
#> $ replication: chr "r1" "r1" "r1" "r1" ...
#> $ block : chr "b1" "b1" "b1" "b2" ...
#> $ line : int 5 1 4 4 1 2 2 5 3 1 ...
#> $ tester : int 7 8 8 6 7 7 6 6 8 6 ...
#> $ yield : num 47.3 109.4 36.3 36.2 70.7 ...
# There are five columns replication, block, line, tester and yield.
## Now by using function ltc we analyze the data.
## The first parameter of `ltc` function is "data" followed by replication, line, tester, dependent variable(yield) and block.
## Note: The "block" parameter comes at the end.
results2 = ltc(alphaltc, replication, line, tester, yield, block)
#>
#> Analysis of Line x Tester: yield
## Viewing the results
results2
#> $Means
#> Testers
#> Lines 6 7 8
#> 1 86.47500 88.95833 89.55000
#> 2 88.64667 55.48000 50.12667
#> 3 51.19917 53.28417 36.91583
#> 4 33.47500 34.29833 50.78417
#> 5 45.30417 42.14500 49.98000
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 1586.4934 528.8311 3.1440495 4.213104e-02
#> Crosses 14 23862.0199 1704.4300 10.1333150 3.161969e-07
#> Blocks within Replication 16 2555.9198 159.7450 0.9497288 5.307851e-01
#> Lines 4 18835.3119 4708.8280 24.8833344 6.536498e-11
#> Testers 2 463.1458 231.5729 1.2237239 3.037332e-01
#> Lines X Testers 8 4563.5622 570.4453 3.0144615 8.508293e-03
#> Error 26 4373.2165 168.2006 NA NA
#> Total 59 2561.2067 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 22.70992
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 293.8997 462.1004 168.2006
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 37.6417608 30.0193557
#> Environmental coefficient of Variation <NA>
#> 22.7099195 0.6360084
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 18835.3119 4708.8280 24.883334 6.536498e-11
#> Testers 2 463.1458 231.5729 1.223724 3.037332e-01
#> Lines X Testers 8 4563.5622 570.4453 3.014461 8.508293e-03
#> Error 26 4373.2165 168.2006 NA NA
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> 31.220 7.643 -9.975 -17.589 -11.298
#>
#> $`GCA testers`
#> 6 7 8
#> 3.912 -2.275 -1.637
#>
#> $`SCA crosses`
#> Testers
#> Lines 6 7 8
#> 1 -5.765 2.906 2.859
#> 2 19.984 -6.996 -12.988
#> 3 0.154 8.426 -8.580
#> 4 -9.956 -2.946 12.902
#> 5 -4.417 -1.390 5.807
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 78.934273 1.940933 19.124794
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> 344.86523 -16.94362
#> Cov H.S. (average) Cov F.S. (average)
#> 30.06778 262.35565
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> 120.27111 60.13555
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> 201.12232 15.84306
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 3.743891 2.900005 6.484609
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 5.294661 4.101227 9.170622
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 7.695678 5.961047 13.329305
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 10.883332 8.430193 18.850484
# Line x Tester analysis for multiple traits laid in Alpha lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data("alphaltcmt")
# View the structure of dataframe.
str(alphaltcmt)
#> spc_tbl_ [60 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
#> $ replication: chr [1:60] "r1" "r3" "r2" "r4" ...
#> $ block : chr [1:60] "b2" "b2" "b4" "b5" ...
#> $ line : chr [1:60] "DIL 2" "DIL 2" "DIL 2" "DIL 2" ...
#> $ tester : chr [1:60] "DIL-101" "DIL-101" "DIL-101" "DIL-101" ...
#> $ hsw : num [1:60] 25.7 24.5 23.7 25.1 23 ...
#> $ sh : num [1:60] 81.7 83.3 86 84.6 85.5 ...
#> $ gy : num [1:60] 25.9 41 65.7 47.3 30.8 ...
#> - attr(*, "spec")=List of 3
#> ..$ cols :List of 7
#> .. ..$ replication: list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ block : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ line : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ tester : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ hsw : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_double" "collector"
#> .. ..$ sh : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_double" "collector"
#> .. ..$ gy : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_double" "collector"
#> ..$ default: list()
#> .. ..- attr(*, "class")= chr [1:2] "collector_guess" "collector"
#> ..$ delim : chr ","
#> ..- attr(*, "class")= chr "col_spec"
#> - attr(*, "problems")=<externalptr>
# Conduct Line x Tester analysis
result3 = ltcmt(alphaltcmt, replication, line, tester, alphaltcmt[,5:7], block)
#>
#> Analysis of Line x Tester for Multiple traits
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
# View the output
result3
#> $Mean
#> $Mean$hsw
#> Tester
#> Line DIL-101 DIL-103 DIL 102
#> DIL-1 24.2800 26.4325 24.3900
#> DIL-4 25.3625 26.3225 26.5250
#> DIL 2 24.7525 23.8525 23.1800
#> DIL 3 22.1300 25.4675 25.0975
#> DIL 5 24.4075 22.9050 23.8625
#>
#> $Mean$sh
#> Tester
#> Line DIL-101 DIL-103 DIL 102
#> DIL-1 82.9375 84.2025 83.8700
#> DIL-4 84.2775 81.8175 84.3250
#> DIL 2 83.8950 83.7725 84.6225
#> DIL 3 83.6100 83.0450 84.4600
#> DIL 5 83.0425 84.8300 82.5875
#>
#> $Mean$gy
#> Tester
#> Line DIL-101 DIL-103 DIL 102
#> DIL-1 54.2675 44.7525 48.8625
#> DIL-4 60.5650 53.7975 52.1400
#> DIL 2 44.9575 47.3975 45.3125
#> DIL 3 46.0625 55.0550 54.7700
#> DIL 5 58.2675 53.5525 53.5300
#>
#>
#> $ANOVA
#> $ANOVA$hsw
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 123.534952 41.178317 5.2008236 0.006007676
#> Blocks within Replication 16 159.578141 9.973634 1.2596705 0.292005429
#> Crosses 14 95.647543 6.831967 0.8628778 0.602918614
#> Lines 4 44.421693 11.105423 1.0220298 0.406231362
#> Testers 2 6.558103 3.279052 0.3017705 0.740992561
#> Lines X Testers 8 44.667747 5.583468 0.5138454 0.839635289
#> Error 26 205.858982 7.917653 NA NA
#> Total 59 584.619618 NA NA NA
#>
#> $ANOVA$sh
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 47.847660 15.9492200 5.5792805 0.004311049
#> Blocks within Replication 16 61.895494 3.8684684 1.3532492 0.239549969
#> Crosses 14 39.935293 2.8525210 0.9978553 0.482967180
#> Lines 4 3.050693 0.7626733 0.1864544 0.944255260
#> Testers 2 2.468943 1.2344717 0.3017971 0.740973054
#> Lines X Testers 8 34.415657 4.3019571 1.0517198 0.413116072
#> Error 26 74.324946 2.8586518 NA NA
#> Total 59 224.003393 NA NA NA
#>
#> $ANOVA$gy
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 3171.01367 1057.00456 7.6631523 0.0007893935
#> Blocks within Replication 16 2338.12660 146.13291 1.0594455 0.4352040161
#> Crosses 14 1411.65982 100.83284 0.7310257 0.7261397075
#> Lines 4 787.60961 196.90240 0.9741847 0.4310920496
#> Testers 2 48.49009 24.24505 0.1199536 0.8872442280
#> Lines X Testers 8 575.56012 71.94502 0.3559517 0.9380005166
#> Error 26 3586.26808 137.93339 NA NA
#> Total 59 10507.06817 NA NA NA
#>
#>
#> $GCA.Line
#> hsw sh gy
#> DIL-1 0.4363333 -0.01633333 -2.2585000
#> DIL-4 1.4721667 -0.21300000 3.9481667
#> DIL 2 -0.6695000 0.41033333 -5.6635000
#> DIL 3 -0.3661667 0.01866667 0.4098333
#> DIL 5 -0.8728333 -0.19966667 3.5640000
#>
#> $GCA.Tester
#> hsw sh gy
#> DIL-101 -0.41133333 -0.1338333 1.2713333
#> DIL-103 0.39816667 -0.1528333 -0.6416667
#> DIL 102 0.01316667 0.2866667 -0.6296667
#>
#> $SCA
#> $SCA$hsw
#> Tester
#> Line DIL-101 DIL-103 DIL 102
#> DIL-1 -0.3428333 1.0001667 -0.6573333
#> DIL-4 -0.2961667 -0.1456667 0.4418333
#> DIL 2 1.2355000 -0.4740000 -0.7615000
#> DIL 3 -1.6903333 0.8376667 0.8526667
#> DIL 5 1.0938333 -1.2181667 0.1243333
#>
#> $SCA$sh
#> Tester
#> Line DIL-101 DIL-103 DIL 102
#> DIL-1 -0.59866667 0.6853333 -0.08666667
#> DIL-4 0.93800000 -1.5030000 0.56500000
#> DIL 2 -0.06783333 -0.1713333 0.23916667
#> DIL 3 0.03883333 -0.5071667 0.46833333
#> DIL 5 -0.31033333 1.4961667 -1.18583333
#>
#> $SCA$gy
#> Tester
#> Line DIL-101 DIL-103 DIL 102
#> DIL-1 3.702000 -3.900000 0.198000
#> DIL-4 3.792833 -1.061667 -2.731167
#> DIL 2 -2.203000 2.150000 0.053000
#> DIL 3 -7.171333 3.734167 3.437167
#> DIL 5 1.879500 -0.922500 -0.957000
#>
#>
#> $CV
#> hsw sh gy
#> 11.439351 2.020348 22.781566
#>
#> $Genetic.Variance.Covariance.
#> Phenotypic Variance Genotypic Variance Environmental Variance
#> hsw -0.6689343 -8.586587 7.917653
#> sh -0.4155230 -3.274175 2.858652
#> gy -101.1095400 -239.042928 137.933388
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> hsw NaN NaN
#> sh NaN NaN
#> gy NaN NaN
#> Environmental coefficient of Variation Broad sense heritability
#> hsw 11.439351 12.836220
#> sh 2.020348 7.879648
#> gy 22.781566 2.364198
#>
#> $Std.Error
#> S.E. gca for line S.E. gca for tester S.E. sca effect S.E. (gi - gj)line
#> hsw 0.8122835 0.6291921 1.4069162 1.1487423
#> sh 0.4880789 0.3780643 0.8453774 0.6902478
#> gy 3.3903464 2.6261511 5.8722523 4.7946739
#> S.E. (gi - gj)tester S.E. (sij - skl)tester
#> hsw 0.8898120 1.989680
#> sh 0.5346636 1.195544
#> gy 3.7139384 8.304619
#>
#> $C.D.
#> C.D. gca for line C.D. gca for tester C.D. sca effect C.D. (gi - gj)line
#> hsw 1.669673 1.2933228 2.891958 2.361274
#> sh 1.003260 0.7771222 1.737698 1.418825
#> gy 6.968957 5.3981308 12.070587 9.855593
#> C.D. (gi - gj)tester C.D. (sij - skl)tester
#> hsw 1.829035 4.089846
#> sh 1.099017 2.457476
#> gy 7.634110 17.070388
#>
#> $Add.Dom.Var
#> Cov H.S. (line) Cov H.S. (tester) Cov H.S. (average) Cov F.S. (average)
#> hsw 0.4601629 -0.1152208 0.03310414 -0.3374874
#> sh -0.2949403 -0.1533743 -0.03843202 -0.1641164
#> gy 10.4131155 -2.3849984 0.76596517 -10.5696184
#> Addittive Variance(F=0) Addittive Variance(F=1) Dominance Variance(F=0)
#> hsw 0.1324166 0.06620828 -1.1670924
#> sh -0.1537281 -0.07686404 0.7216527
#> gy 3.0638607 1.53193033 -32.9941861
#> Dominance Variance(F=1)
#> hsw -0.5835462
#> sh 0.3608263
#> gy -16.4970931
#>
#> $Contribution.of.Line.Tester
#> Lines Tester Line x Tester
#> hsw 46.443110 6.856531 46.70036
#> sh 7.639091 6.182359 86.17855
#> gy 55.793159 3.434970 40.77187