gva.augmentedRCBD: Perform Genetic Variability Analysis on 'augmentedRCBD'...
In augmentedRCBD: Analysis of Augmented Randomised Complete Block Designs
View source: R/gva.augmentedRCBD.R
gva.augmentedRCBD R Documentation
Perform Genetic Variability Analysis on augmentedRCBD Output
Description
gva.augmentedRCBD performs genetic variability analysis on an object of
class augmentedRCBD. \loadmathjax
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 (\mjseqn\sigma^2_p,
\mjseqn\sigma^2_g and \mjseqn\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:
\mjsdeqn\sigma^2_g = \sigma^2_p - \sigma^2_e
Phenotypic and genotypic coefficients of variation (\mjseqnPCV and
\mjseqnGCV) are estimated according to Burton (1951, 1952) as follows:
\mjsdeqnGCV = \frac\sigma^2_g\sqrt\overlinex \times 100
Where \mjseqn\overlinex is the mean.
The estimates of \mjseqnPCV and \mjseqnGCV are categorised according to
Sivasubramanian and Madhavamenon (1978) as follows:
CV (%) Category
x \mjseqn <
10 Low
10 \mjseqn\le x \mjseqn < 20 Medium
\mjseqn\ge 20 High
The broad-sense heritability (\mjseqnH^2) is calculated according to
method of Lush (1940) as follows:
\mjsdeqnH^2 = \frac\sigma^2_g\sigma^2_p
The estimates of broad-sense heritability (\mjseqnH^2) are categorised
according to Robinson (1966) as follows:
\mjseqnH^2 Category
x \mjseqn <
30 Low
30 \mjseqn\le x \mjseqn < 60 Medium
\mjseqn\ge 60 High
Genetic advance (\mjseqnGA) is estimated and categorised according to
Johnson et al., (1955) as follows:
\mjsdeqnGA = k \times \sigma_g \times \fracH^2100
Where the constant \mjseqnk is the standardized selection differential or
selection intensity. The value of \mjseqnk at 5% proportion selected is
2.063. Values of \mjseqnk at other selected proportions are available in
Appendix Table A of Falconer and Mackay (1996).
Selection intensity (\mjseqnk) 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 (\mjseqnGAM) are estimated and
categorised according to Johnson et al., (1955) as follows:
\mjsdeqnGAM = \fracGA\overlinex \times 100
GAM Category
x \mjseqn < 10
Low
10 \mjseqn\le x \mjseqn < 20 Medium
\mjseqn\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 \mjseqnGCV category according to
\insertCitesivasubramaniam_genotypic_1973;textualaugmentedRCBD.
PCV
Phenotypic coefficient of variation
PCV category
The
\mjseqnPCV category according to
\insertCitesivasubramaniam_genotypic_1973;textualaugmentedRCBD.
ECV
Environmental coefficient of variation
hBS
The
broad-sense heritability (\mjseqnH^2)
\insertCitelush_intra-sire_1940augmentedRCBD.
hBS category
The
\mjseqnH^2 category according to
\insertCiterobinson_quantitative_1966;textualaugmentedRCBD.
GA
Genetic advance
\insertCitejohnson_estimates_1955augmentedRCBD.
GAM
Genetic
advance as per cent of mean
\insertCitejohnson_estimates_1955augmentedRCBD.
GAM category
The
\mjseqnGAM category according to
\insertCitejohnson_estimates_1955;textualaugmentedRCBD.
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
\insertReflush_intra-sire_1940augmentedRCBD
\insertRefburton_quantitative_1951augmentedRCBD
\insertRefburton_qualitative_1952augmentedRCBD
\insertRefjohnson_estimates_1955augmentedRCBD
\insertRefrobinson_genetic_1955augmentedRCBD
\insertRefrobinson_quantitative_1966augmentedRCBD
\insertRefdudley_interpretation_1969augmentedRCBD
\insertRefsivasubramaniam_genotypic_1973augmentedRCBD
\insertReffedererModelConsiderationsVariance1976augmentedRCBD
\insertReffalconer_introduction_1996augmentedRCBD
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)
augmentedRCBD documentation built on Aug. 19, 2023, 1:06 a.m.
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View source: R/gva.augmentedRCBD.R
| gva.augmentedRCBD | R Documentation |
Perform Genetic Variability Analysis on augmentedRCBD Output
Description
gva.augmentedRCBD performs genetic variability analysis on an object of
class augmentedRCBD. \loadmathjax
Usage
gva.augmentedRCBD(aug, k = 2.063)
Arguments
aug |
An object of class |
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 (\mjseqn\sigma^2_p, \mjseqn\sigma^2_g and \mjseqn\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:
\mjsdeqn\sigma^2_g = \sigma^2_p - \sigma^2_e
Phenotypic and genotypic coefficients of variation (\mjseqnPCV and \mjseqnGCV) are estimated according to Burton (1951, 1952) as follows:
\mjsdeqnGCV = \frac\sigma^2_g\sqrt\overlinex \times 100
Where \mjseqn\overlinex is the mean.
The estimates of \mjseqnPCV and \mjseqnGCV are categorised according to Sivasubramanian and Madhavamenon (1978) as follows:
| CV (%) | Category |
| x \mjseqn < 10 | Low |
| 10 \mjseqn\le x \mjseqn < 20 | Medium |
| \mjseqn\ge 20 | High |
The broad-sense heritability (\mjseqnH^2) is calculated according to method of Lush (1940) as follows:
\mjsdeqnH^2 = \frac\sigma^2_g\sigma^2_p
The estimates of broad-sense heritability (\mjseqnH^2) are categorised according to Robinson (1966) as follows:
| \mjseqnH^2 | Category |
| x \mjseqn < 30 | Low |
| 30 \mjseqn\le x \mjseqn < 60 | Medium |
| \mjseqn\ge 60 | High |
Genetic advance (\mjseqnGA) is estimated and categorised according to Johnson et al., (1955) as follows:
\mjsdeqnGA = k \times \sigma_g \times \fracH^2100
Where the constant \mjseqnk is the standardized selection differential or selection intensity. The value of \mjseqnk at 5% proportion selected is 2.063. Values of \mjseqnk at other selected proportions are available in Appendix Table A of Falconer and Mackay (1996).
Selection intensity (\mjseqnk) 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 (\mjseqnGAM) are estimated and categorised according to Johnson et al., (1955) as follows:
\mjsdeqnGAM = \fracGA\overlinex \times 100
| GAM | Category |
| x \mjseqn < 10 | Low |
| 10 \mjseqn\le x \mjseqn < 20 | Medium |
| \mjseqn\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 \mjseqnGCV category according to \insertCitesivasubramaniam_genotypic_1973;textualaugmentedRCBD. |
PCV |
Phenotypic coefficient of variation |
PCV category |
The \mjseqnPCV category according to \insertCitesivasubramaniam_genotypic_1973;textualaugmentedRCBD. |
ECV |
Environmental coefficient of variation |
hBS |
The broad-sense heritability (\mjseqnH^2) \insertCitelush_intra-sire_1940augmentedRCBD. |
hBS category |
The \mjseqnH^2 category according to \insertCiterobinson_quantitative_1966;textualaugmentedRCBD. |
GA |
Genetic advance \insertCitejohnson_estimates_1955augmentedRCBD. |
GAM |
Genetic advance as per cent of mean \insertCitejohnson_estimates_1955augmentedRCBD. |
GAM category |
The \mjseqnGAM category according to \insertCitejohnson_estimates_1955;textualaugmentedRCBD. |
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
\insertReflush_intra-sire_1940augmentedRCBD
\insertRefburton_quantitative_1951augmentedRCBD
\insertRefburton_qualitative_1952augmentedRCBD
\insertRefjohnson_estimates_1955augmentedRCBD
\insertRefrobinson_genetic_1955augmentedRCBD
\insertRefrobinson_quantitative_1966augmentedRCBD
\insertRefdudley_interpretation_1969augmentedRCBD
\insertRefsivasubramaniam_genotypic_1973augmentedRCBD
\insertReffedererModelConsiderationsVariance1976augmentedRCBD
\insertReffalconer_introduction_1996augmentedRCBD
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)
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