augmentedRCBD Outputgva.augmentedRCBD performs genetic variability analysis on an object of
class augmentedRCBD.
gva.augmentedRCBD(aug, k = 2.063)An object of class augmentedRCBD.
The standardized selection differential or selection intensity. Default is 2.063 for 5% selection proportion (see Details).
A list with the following descriptive statistics:
The mean value.
Phenotyic variance.
Genotyipc variance.
Environmental variance.
Genotypic coefficient of variation
The GCV category according to sivasubramaniam_genotypic_1973;textualaugmentedRCBD.
Phenotypic coefficient of variation
The PCV category according to sivasubramaniam_genotypic_1973;textualaugmentedRCBD.
Environmental coefficient of variation
The broad-sense heritability () lush_intra-sire_1940augmentedRCBD.
The category according to robinson_quantitative_1966;textualaugmentedRCBD.
Genetic advance johnson_estimates_1955augmentedRCBD.
Genetic advance as per cent of mean johnson_estimates_1955augmentedRCBD.
The GAM category according to johnson_estimates_1955;textualaugmentedRCBD.
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 (,
and
) are obtained from the ANOVA tables according to the expected value of mean square described by Federer and Searle (1976) as follows:
Phenotypic and genotypic coefficients of variation ( and ) are estimated according to Burton (1951, 1952) as follows:
Where is the mean.
The estimates of and are categorised according to Sivasubramanian and Madhavamenon (1978) as follows:
| CV (%) | Category |
| x 10 | Low |
| 10 x 20 | Medium |
The broad-sense heritability () is calculated according to method of Lush (1940) as follows:
The estimates of broad-sense heritability () are categorised according to Robinson (1966) as follows:
| Category | |
| x 30 | Low |
| 30 x 60 | Medium |
Genetic advance () is estimated and categorised according to Johnson et al., (1955) as follows:
Where the constant is the standardized selection differential or selection intensity. The value of at 5% proportion selected is 2.063. Values of at other selected proportions are available in Appendix Table A of Falconer and Mackay (1996).
Selection intensity () 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% | x | i |
| 0.01 | 3.71901649 | 3.9584797 |
| 0.02 | 3.54008380 | 3.7892117 |
| 0.03 | 3.43161440 | 3.6869547 |
| 0.04 | 3.35279478 | 3.6128288 |
| 0.05 | 3.29052673 | 3.5543807 |
| 0.06 | 3.23888012 | 3.5059803 |
| 0.07 | 3.19465105 | 3.4645890 |
| 0.08 | 3.15590676 | 3.4283756 |
| 0.09 | 3.12138915 | 3.3961490 |
| 0.10 | 3.09023231 | 3.3670901 |
| <> | <> | <> |
| 0.10 | 3.09023231 | 3.3670901 |
| 0.12 | 3.03567237 | 3.3162739 |
| 0.14 | 2.98888227 | 3.2727673 |
| 0.16 | 2.94784255 | 3.2346647 |
| 0.18 | 2.91123773 | 3.2007256 |
| 0.20 | 2.87816174 | 3.1700966 |
| 0.22 | 2.84796329 | 3.1421647 |
| 0.24 | 2.82015806 | 3.1164741 |
| 0.26 | 2.79437587 | 3.0926770 |
| 0.28 | 2.77032723 | 3.0705013 |
| 0.30 | 2.74778139 | 3.0497304 |
| 0.32 | 2.72655132 | 3.0301887 |
| 0.34 | 2.70648331 | 3.0117321 |
| 0.36 | 2.68744945 | 2.9942406 |
| 0.38 | 2.66934209 | 2.9776133 |
| 0.40 | 2.65206981 | 2.9617646 |
| 0.42 | 2.63555424 | 2.9466212 |
| 0.44 | 2.61972771 | 2.9321196 |
| 0.46 | 2.60453136 | 2.9182048 |
| 0.48 | 2.58991368 | 2.9048286 |
| 0.50 | 2.57582930 | 2.8919486 |
| <> | <> | <> |
| 1.00 | 2.32634787 | 2.6652142 |
| 1.20 | 2.25712924 | 2.6028159 |
| 1.40 | 2.19728638 | 2.5490627 |
| 1.60 | 2.14441062 | 2.5017227 |
| 1.80 | 2.09692743 | 2.4593391 |
| 2.00 | 2.05374891 | 2.4209068 |
| 2.20 | 2.01409081 | 2.3857019 |
| 2.40 | 1.97736843 | 2.3531856 |
| 2.60 | 1.94313375 | 2.3229451 |
| 2.80 | 1.91103565 | 2.2946575 |
| 3.00 | 1.88079361 | 2.2680650 |
| 3.20 | 1.85217986 | 2.2429584 |
| 3.40 | 1.82500682 | 2.2191656 |
| 3.60 | 1.79911811 | 2.1965431 |
| 3.80 | 1.77438191 | 2.1749703 |
| 4.00 | 1.75068607 | 2.1543444 |
| 4.20 | 1.72793432 | 2.1345772 |
| 4.40 | 1.70604340 | 2.1155928 |
| 4.60 | 1.68494077 | 2.0973249 |
| 4.80 | 1.66456286 | 2.0797152 |
| 5.00 | 1.64485363 | 2.0627128 |
| <> | <> | <> |
| 5.00 | 1.64485363 | 2.0627128 |
| 5.50 | 1.59819314 | 2.0225779 |
| 6.00 | 1.55477359 | 1.9853828 |
| 6.50 | 1.51410189 | 1.9506784 |
| 7.00 | 1.47579103 | 1.9181131 |
| 7.50 | 1.43953147 | 1.8874056 |
| 8.00 | 1.40507156 | 1.8583278 |
| 8.50 | 1.37220381 | 1.8306916 |
| 9.00 | 1.34075503 | 1.8043403 |
| 9.50 | 1.31057911 | 1.7791417 |
| 10.00 | 1.28155157 | 1.7549833 |
| <> | <> | <> |
| 10.00 | 1.28155157 | 1.7549833 |
| 11.00 | 1.22652812 | 1.7094142 |
| 12.00 | 1.17498679 | 1.6670040 |
| 13.00 | 1.12639113 | 1.6272701 |
| 14.00 | 1.08031934 | 1.5898336 |
| 15.00 | 1.03643339 | 1.5543918 |
| 16.00 | 0.99445788 | 1.5206984 |
| 17.00 | 0.95416525 | 1.4885502 |
| 18.00 | 0.91536509 | 1.4577779 |
| 19.00 | 0.87789630 | 1.4282383 |
| 20.00 | 0.84162123 | 1.3998096 |
| 21.00 | 0.80642125 | 1.3723871 |
| 22.00 | 0.77219321 | 1.3458799 |
| 23.00 | 0.73884685 | 1.3202091 |
| 24.00 | 0.70630256 | 1.2953050 |
| 25.00 | 0.67448975 | 1.2711063 |
| 26.00 | 0.64334541 | 1.2475585 |
| 27.00 | 0.61281299 | 1.2246130 |
| 28.00 | 0.58284151 | 1.2022262 |
| 29.00 | 0.55338472 | 1.1803588 |
| 30.00 | 0.52440051 | 1.1589754 |
| 31.00 | 0.49585035 | 1.1380436 |
| 32.00 | 0.46769880 | 1.1175342 |
| 33.00 | 0.43991317 | 1.0974204 |
| 34.00 | 0.41246313 | 1.0776774 |
| 35.00 | 0.38532047 | 1.0582829 |
| 36.00 | 0.35845879 | 1.0392158 |
| 37.00 | 0.33185335 | 1.0204568 |
| 38.00 | 0.30548079 | 1.0019882 |
| 39.00 | 0.27931903 | 0.9837932 |
| 40.00 | 0.25334710 | 0.9658563 |
| 41.00 | 0.22754498 | 0.9481631 |
| 42.00 | 0.20189348 | 0.9306998 |
| 43.00 | 0.17637416 | 0.9134539 |
| 44.00 | 0.15096922 | 0.8964132 |
| 45.00 | 0.12566135 | 0.8795664 |
| 46.00 | 0.10043372 | 0.8629028 |
| 47.00 | 0.07526986 | 0.8464123 |
| 48.00 | 0.05015358 | 0.8300851 |
| 49.00 | 0.02506891 | 0.8139121 |
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 () are estimated and categorised according to Johnson et al., (1955) as follows:
| GAM | Category |
| x 10 | Low |
| 10 x 20 | Medium |
lush_intra-sire_1940augmentedRCBD
burton_quantitative_1951augmentedRCBD
burton_qualitative_1952augmentedRCBD
johnson_estimates_1955augmentedRCBD
robinson_quantitative_1966augmentedRCBD
dudley_interpretation_1969augmentedRCBD
sivasubramaniam_genotypic_1973augmentedRCBD
federerModelConsiderationsVariance1976augmentedRCBD
falconer_introduction_1996augmentedRCBD
# NOT RUN {
# 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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