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augmentedRCBD (version 0.1.7)

gva.augmentedRCBD: Perform Genetic Variability Analysis on augmentedRCBD Output

Description

gva.augmentedRCBD performs genetic variability analysis on an object of class augmentedRCBD.

Usage

gva.augmentedRCBD(aug, k = 2.063)

Value

A list with the following descriptive statistics:

Mean

The mean value.

PV

Phenotyic variance.

GV

Genotyipc variance.

EV

Environmental variance.

GCV

Genotypic coefficient of variation

GCV category

The GCV category according to sivasubramaniam_genotypic_1973;textualaugmentedRCBD.

PCV

Phenotypic coefficient of variation

PCV category

The PCV category according to sivasubramaniam_genotypic_1973;textualaugmentedRCBD.

ECV

Environmental coefficient of variation

hBS

The broad-sense heritability (H^2) lush_intra-sire_1940augmentedRCBD.

hBS category

The H^2 category according to robinson_quantitative_1966;textualaugmentedRCBD.

GA

Genetic advance johnson_estimates_1955augmentedRCBD.

GAM

Genetic advance as per cent of mean johnson_estimates_1955augmentedRCBD.

GAM category

The GAM category according to johnson_estimates_1955;textualaugmentedRCBD.

Arguments

aug

An object of class augmentedRCBD.

k

The standardized selection differential or selection intensity. Default is 2.063 for 5% selection proportion (see Details).

Details

gva.augmentedRCBD performs genetic variability analysis from the ANOVA results in an object of class augmentedRCBD and computes several variability estimates.

The phenotypic, genotypic and environmental variance (^2_p, ^2_g and ^2_e ) are obtained from the ANOVA tables according to the expected value of mean square described by Federer and Searle (1976) as follows:

^2_g = ^2_p - ^2_e

Phenotypic and genotypic coefficients of variation (PCV and GCV) are estimated according to Burton (1951, 1952) as follows:

GCV = ^2_gx 100

Where x is the mean.

The estimates of PCV and GCV are categorised according to Sivasubramanian and Madhavamenon (1978) as follows:

CV (%)Category
x < 10Low
10 x < 20Medium
20High

The broad-sense heritability (H^2) is calculated according to method of Lush (1940) as follows:

H^2 = ^2_g^2_p

The estimates of broad-sense heritability (H^2) are categorised according to Robinson (1966) as follows:

H^2Category
x < 30Low
30 x < 60Medium
60High

Genetic advance (GA) is estimated and categorised according to Johnson et al., (1955) as follows:

GA = k _g H^2100

Where the constant k is the standardized selection differential or selection intensity. The value of k at 5% proportion selected is 2.063. Values of k at other selected proportions are available in Appendix Table A of Falconer and Mackay (1996).

Selection intensity (k) can also be computed in R as below:

If p is the proportion of selected individuals, then deviation of truncation point from mean (x) and selection intensity (k) are as follows:

x = qnorm(1-p)

k = dnorm(qnorm(1 - p))/p

Using the same the Appendix Table A of Falconer and Mackay (1996) can be recreated as follows.


TableA <- data.frame(p = c(seq(0.01, 0.10, 0.01), NA,
                           seq(0.10, 0.50, 0.02), NA,
                           seq(1, 5, 0.2), NA,
                           seq(5, 10, 0.5), NA,
                           seq(10, 50, 1)))
TableA$x <- qnorm(1-(TableA$p/100))
TableA$i <- dnorm(qnorm(1 - (TableA$p/100)))/(TableA$p/100)

Appendix Table A (Falconer and Mackay, 1996)

p%xi
0.013.719016493.9584797
0.023.540083803.7892117
0.033.431614403.6869547
0.043.352794783.6128288
0.053.290526733.5543807
0.063.238880123.5059803
0.073.194651053.4645890
0.083.155906763.4283756
0.093.121389153.3961490
0.103.090232313.3670901
<><><>
0.103.090232313.3670901
0.123.035672373.3162739
0.142.988882273.2727673
0.162.947842553.2346647
0.182.911237733.2007256
0.202.878161743.1700966
0.222.847963293.1421647
0.242.820158063.1164741
0.262.794375873.0926770
0.282.770327233.0705013
0.302.747781393.0497304
0.322.726551323.0301887
0.342.706483313.0117321
0.362.687449452.9942406
0.382.669342092.9776133
0.402.652069812.9617646
0.422.635554242.9466212
0.442.619727712.9321196
0.462.604531362.9182048
0.482.589913682.9048286
0.502.575829302.8919486
<><><>
1.002.326347872.6652142
1.202.257129242.6028159
1.402.197286382.5490627
1.602.144410622.5017227
1.802.096927432.4593391
2.002.053748912.4209068
2.202.014090812.3857019
2.401.977368432.3531856
2.601.943133752.3229451
2.801.911035652.2946575
3.001.880793612.2680650
3.201.852179862.2429584
3.401.825006822.2191656
3.601.799118112.1965431
3.801.774381912.1749703
4.001.750686072.1543444
4.201.727934322.1345772
4.401.706043402.1155928
4.601.684940772.0973249
4.801.664562862.0797152
5.001.644853632.0627128
<><><>
5.001.644853632.0627128
5.501.598193142.0225779
6.001.554773591.9853828
6.501.514101891.9506784
7.001.475791031.9181131
7.501.439531471.8874056
8.001.405071561.8583278
8.501.372203811.8306916
9.001.340755031.8043403
9.501.310579111.7791417
10.001.281551571.7549833
<><><>
10.001.281551571.7549833
11.001.226528121.7094142
12.001.174986791.6670040
13.001.126391131.6272701
14.001.080319341.5898336
15.001.036433391.5543918
16.000.994457881.5206984
17.000.954165251.4885502
18.000.915365091.4577779
19.000.877896301.4282383
20.000.841621231.3998096
21.000.806421251.3723871
22.000.772193211.3458799
23.000.738846851.3202091
24.000.706302561.2953050
25.000.674489751.2711063
26.000.643345411.2475585
27.000.612812991.2246130
28.000.582841511.2022262
29.000.553384721.1803588
30.000.524400511.1589754
31.000.495850351.1380436
32.000.467698801.1175342
33.000.439913171.0974204
34.000.412463131.0776774
35.000.385320471.0582829
36.000.358458791.0392158
37.000.331853351.0204568
38.000.305480791.0019882
39.000.279319030.9837932
40.000.253347100.9658563
41.000.227544980.9481631
42.000.201893480.9306998
43.000.176374160.9134539
44.000.150969220.8964132
45.000.125661350.8795664
46.000.100433720.8629028
47.000.075269860.8464123
48.000.050153580.8300851
49.000.025068910.8139121
50.000.000000000.7978846

Where p% is the selected percentage of individuals from a population, x is the deviation of the point of truncation of selected individuals from population mean and i is the selection intensity.

Genetic advance as per cent of mean (GAM) are estimated and categorised according to Johnson et al., (1955) as follows:

GAM = GAx 100

GAMCategory
x < 10Low
10 x < 20Medium
20High

References

lush_intra-sire_1940augmentedRCBD

burton_quantitative_1951augmentedRCBD

burton_qualitative_1952augmentedRCBD

johnson_estimates_1955augmentedRCBD

robinson_genetic_1955augmentedRCBD

robinson_quantitative_1966augmentedRCBD

dudley_interpretation_1969augmentedRCBD

sivasubramaniam_genotypic_1973augmentedRCBD

federerModelConsiderationsVariance1976augmentedRCBD

falconer_introduction_1996augmentedRCBD

See Also

augmentedRCBD

Examples

Run this code
# Example data
blk <- c(rep(1,7),rep(2,6),rep(3,7))
trt <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77, 78, 78,
        70, 75, 74)
y2 <- c(258, 224, 238, 278, 347, 300, 289, 260, 220, 237, 227, 281, 311, 250,
        240, 268, 287, 226, 395, 450)
data <- data.frame(blk, trt, y1, y2)
# Convert block and treatment to factors
data$blk <- as.factor(data$blk)
data$trt <- as.factor(data$trt)
# Results for variable y1
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
                      alpha = 0.05, group = TRUE, console = TRUE)
# Results for variable y2
out2 <- augmentedRCBD(data$blk, data$trt, data$y2, method.comp = "lsd",
                     alpha = 0.05, group = TRUE, console = TRUE)

# Genetic variability analysis
gva.augmentedRCBD(out1)
gva.augmentedRCBD(out2)

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