gva.augmentedRCBD {augmentedRCBD} R Documentation

## 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)


### 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 ($$\sigma^{2}_{p}$$, $$\sigma^{2}_{g}$$ and $$\sigma^{2}_{e}$$ ) are obtained from the ANOVA tables according to the expected value of mean square described by Federer and Searle (1976) as follows:

$\sigma^{2}_{g} = \sigma^{2}_{p} - \sigma^{2}_{e}$

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

$GCV = \frac{\sigma^{2}_{g}}{\sqrt{\overline{x}}} \times 100$

Where $$\overline{x}$$ is the mean.

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

 CV (%) Category x $$<$$ 10 Low 10 $$\le$$ x $$<$$ 20 Medium $$\ge$$ 20 High

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

$H^{2} = \frac{\sigma^{2}_{g}}{\sigma^{2}_{p}}$

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

 $$H^{2}$$ Category x $$<$$ 30 Low 30 $$\le$$ x $$<$$ 60 Medium $$\ge$$ 60 High

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

$GA = k \times \sigma_{g} \times \frac{H^{2}}{100}$

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% 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 50.00 0.00000000 0.7978846 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: $GAM = \frac{GA}{\overline{x}} \times 100$  GAM Category x $$<$$ 10 Low 10 $$\le$$ x $$<$$ 20 Medium $$\ge$$ 20 High ### 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 and Madhavamenon (1973). PCV Phenotypic coefficient of variation PCV category The $$PCV$$ category according to Sivasubramaniam and Madhavamenon (1973). ECV Environmental coefficient of variation hBS The broad-sense heritability ($$H^{2}$$) (Lush 1940). hBS category The $$H^{2}$$ category according to Robinson (1966). GA Genetic advance (Johnson et al. 1955). GAM Genetic advance as per cent of mean (Johnson et al. 1955). GAM category The $$GAM$$ category according to Johnson et al. (1955). ### Note Genetic variability analysis needs to be performed only if the sum of squares of "Treatment: Test" are significant. Negative estimates of variance components if computed are not abnormal. For information on how to deal with these, refer Robinson (1955) and Dudley and Moll (1969). ### References Lush JL (1940). “Intra-sire correlations or regressions of offspring on dam as a method of estimating heritability of characteristics.” Proceedings of the American Society of Animal Nutrition, 1940(1), 293–301. Burton GW (1951). “Quantitative inheritance in pearl millet (Pennisetum glaucum).” Agronomy Journal, 43(9), 409–417. Burton GW (1952). “Qualitative inheritance in grasses. Vol. 1.” In Proceedings of the 6th International Grassland Congress, Pennsylvania State College, 17–23. Johnson HW, Robinson HF, Comstock RE (1955). “Estimates of genetic and environmental variability in soybeans.” Agronomy journal, 47(7), 314–318. Robinson HF, Comstock RE, Harvey PH (1955). “Genetic variances in open pollinated varieties of corn.” Genetics, 40(1), 45–60. Robinson HF (1966). “Quantitative genetics in relation to breeding on centennial of Mendelism.” Indian Journal of Genetics and Plant Breeding, 171. Dudley JW, Moll RH (1969). “Interpretation and use of estimates of heritability and genetic variances in plant breeding.” Crop Science, 9(3), 257–262. Sivasubramaniam S, Madhavamenon P (1973). “Genotypic and phenotypic variability in rice.” The Madras Agricultural Journal, 60(9-13), 1093–1096. Federer WT, Searle SR (1976). “Model Considerations and Variance Component Estimation in Augmented Completely Randomized and Randomized Complete Blocks Designs-Preliminary Version.” Technical Report BU-592-M, Cornell University, New York. Falconer DS, Mackay TFC (1996). Introduction to Quantitative Genetics. Pearson/Prenctice Hall, New York, NY. ### See Also augmentedRCBD ### Examples # 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)


[Package augmentedRCBD version 0.1.5 Index]