gva.augmentedRCBD: Perform Genetic Variability Analysis on 'augmentedRCBD'...

Description Usage Arguments Details Value Note References See Also Examples

View source: R/gva.augmentedRCBD.R

Description

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

Usage

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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:

\mjsdeqn

GCV = \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:

\mjsdeqn

H^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:

\mjsdeqn

GA = 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.

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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:

\mjsdeqn

GAM = \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

\insertRef

lush_intra-sire_1940augmentedRCBD

\insertRef

burton_quantitative_1951augmentedRCBD

\insertRef

burton_qualitative_1952augmentedRCBD

\insertRef

johnson_estimates_1955augmentedRCBD

\insertRef

robinson_genetic_1955augmentedRCBD

\insertRef

robinson_quantitative_1966augmentedRCBD

\insertRef

dudley_interpretation_1969augmentedRCBD

\insertRef

sivasubramaniam_genotypic_1973augmentedRCBD

\insertRef

federerModelConsiderationsVariance1976augmentedRCBD

\insertRef

falconer_introduction_1996augmentedRCBD

See Also

augmentedRCBD

Examples

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# 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)

Example output

--------------------------------------------------------------------------------
Welcome to augmentedRCBD version 0.1.3


# To know how to use this package type:
  browseVignettes(package = 'augmentedRCBD')
  for the package vignette.

# To know whats new in this version type:
  news(package='augmentedRCBD')
  for the NEWS file.

# To cite the methods in the package type:
  citation(package='augmentedRCBD')

# To suppress this message use:
  suppressPackageStartupMessages(library(augmentedRCBD))
--------------------------------------------------------------------------------


Augmented Design Details
========================
                                       
Number of blocks           "3"         
Number of treatments       "12"        
Number of check treatments "4"         
Number of test treatments  "8"         
Check treatments           "1, 2, 3, 4"

ANOVA, Treatment Adjusted
=========================
                                     Df Sum Sq Mean Sq F value Pr(>F)  
Block (ignoring Treatments)           2  360.1  180.04   6.675 0.0298 *
Treatment (eliminating Blocks)       11  285.1   25.92   0.961 0.5499  
  Treatment: Check                    3   52.9   17.64   0.654 0.6092  
  Treatment: Test and Test vs. Check  8  232.2   29.02   1.076 0.4779  
Residuals                             6  161.8   26.97                 
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1

ANOVA, Block Adjusted
=====================
                               Df Sum Sq Mean Sq F value Pr(>F)
Treatment (ignoring Blocks)    11  575.7   52.33   1.940  0.215
  Treatment: Check              3   52.9   17.64   0.654  0.609
  Treatment: Test               7  505.9   72.27   2.679  0.125
  Treatment: Test vs. Check     1   16.9   16.87   0.626  0.459
Block (eliminating Treatments)  2   69.5   34.75   1.288  0.342
Residuals                       6  161.8   26.97               

Treatment Means
===============
   Treatment Block    Means       SE r Min Max Adjusted Means
1          1       84.66667 3.844188 3  79  92       84.66667
2         10     3 74.00000       NA 1  74  74       77.25000
3         11     1 89.00000       NA 1  89  89       86.50000
4         12     1 82.00000       NA 1  82  82       79.50000
5          2       79.00000 1.154701 3  77  81       79.00000
6          3       82.00000 2.645751 3  78  87       82.00000
7          4       83.33333 3.929942 3  78  91       83.33333
8          5     2 79.00000       NA 1  79  79       78.25000
9          6     3 75.00000       NA 1  75  75       78.25000
10         7     1 96.00000       NA 1  96  96       93.50000
11         8     3 70.00000       NA 1  70  70       73.25000
12         9     2 78.00000       NA 1  78  78       77.25000

Coefficient of Variation
========================
6.372367

Overall Adjusted Mean
=====================
81.0625

Standard Errors
===================
                                         Std. Error of Diff.  CD (5%)
Control Treatment Means                             4.240458 10.37603
Two Test Treatments (Same Block)                    7.344688 17.97180
Two Test Treatments (Different Blocks)              8.211611 20.09309
A Test Treatment and a Control Treatment            6.704752 16.40594

Treatment Groups
==================

Method : lsd

   Treatment Adjusted Means       SE df lower.CL  upper.CL Group
8          8       73.25000 5.609598  6 59.52381  86.97619    1 
9          9       77.25000 5.609598  6 63.52381  90.97619    12
10        10       77.25000 5.609598  6 63.52381  90.97619    12
5          5       78.25000 5.609598  6 64.52381  91.97619    12
6          6       78.25000 5.609598  6 64.52381  91.97619    12
2          2       79.00000 2.998456  6 71.66304  86.33696    12
12        12       79.50000 5.609598  6 65.77381  93.22619    12
3          3       82.00000 2.998456  6 74.66304  89.33696    12
4          4       83.33333 2.998456  6 75.99637  90.67029    12
1          1       84.66667 2.998456  6 77.32971  92.00363    12
11        11       86.50000 5.609598  6 72.77381 100.22619    12
7          7       93.50000 5.609598  6 79.77381 107.22619     2

Augmented Design Details
========================
                                       
Number of blocks           "3"         
Number of treatments       "12"        
Number of check treatments "4"         
Number of test treatments  "8"         
Check treatments           "1, 2, 3, 4"

ANOVA, Treatment Adjusted
=========================
                                     Df Sum Sq Mean Sq F value   Pr(>F)    
Block (ignoring Treatments)           2   7019    3510  12.261 0.007597 ** 
Treatment (eliminating Blocks)       11  58965    5360  18.727 0.000920 ***
  Treatment: Check                    3   2150     717   2.504 0.156116    
  Treatment: Test and Test vs. Check  8  56815    7102  24.810 0.000473 ***
Residuals                             6   1717     286                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

ANOVA, Block Adjusted
=====================
                               Df Sum Sq Mean Sq F value   Pr(>F)    
Treatment (ignoring Blocks)    11  64708    5883  20.550 0.000707 ***
  Treatment: Check              3   2150     717   2.504 0.156116    
  Treatment: Test               7  34863    4980  17.399 0.001366 ** 
  Treatment: Test vs. Check     1  27694   27694  96.749 6.36e-05 ***
Block (eliminating Treatments)  2   1277     639   2.231 0.188645    
Residuals                       6   1718     286                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Treatment Means
===============
   Treatment Block    Means        SE r Min Max Adjusted Means
1          1       256.0000  3.055050 3 250 260       256.0000
2         10     3 450.0000        NA 1 450 450       437.6667
3         11     1 300.0000        NA 1 300 300       299.4167
4         12     1 289.0000        NA 1 289 289       288.4167
5          2       228.0000  6.110101 3 220 240       228.0000
6          3       247.6667 10.170764 3 237 268       247.6667
7          4       264.0000 18.681542 3 227 287       264.0000
8          5     2 281.0000        NA 1 281 281       293.9167
9          6     3 395.0000        NA 1 395 395       382.6667
10         7     1 347.0000        NA 1 347 347       346.4167
11         8     3 226.0000        NA 1 226 226       213.6667
12         9     2 311.0000        NA 1 311 311       323.9167

Coefficient of Variation
========================
6.057617

Overall Adjusted Mean
=====================
298.4792

Standard Errors
===================
                                         Std. Error of Diff.  CD (5%)
Control Treatment Means                             13.81424 33.80224
Two Test Treatments (Same Block)                    23.92697 58.54719
Two Test Treatments (Different Blocks)              26.75117 65.45775
A Test Treatment and a Control Treatment            21.84224 53.44603

Treatment Groups
==================

Method : lsd

   Treatment Adjusted Means        SE df lower.CL upper.CL    Group
8          8       213.6667 18.274527  6 168.9505 258.3828  12     
2          2       228.0000  9.768146  6 204.0982 251.9018  1      
3          3       247.6667  9.768146  6 223.7649 271.5685  123    
1          1       256.0000  9.768146  6 232.0982 279.9018  1234   
4          4       264.0000  9.768146  6 240.0982 287.9018   234   
12        12       288.4167 18.274527  6 243.7005 333.1328    345  
5          5       293.9167 18.274527  6 249.2005 338.6328    345  
11        11       299.4167 18.274527  6 254.7005 344.1328     45  
9          9       323.9167 18.274527  6 279.2005 368.6328      56 
7          7       346.4167 18.274527  6 301.7005 391.1328      56 
6          6       382.6667 18.274527  6 337.9505 427.3828       67
10        10       437.6667 18.274527  6 392.9505 482.3828        7
$Mean
[1] 81.0625

$PV
[1] 72.26786

$GV
[1] 45.29563

$EV
[1] 26.97222

$GCV
[1] 8.302487

$`GCV category`
[1] "Low"

$PCV
[1] 10.48703

$`PCV category`
[1] "Medium"

$ECV
[1] 6.406759

$hBS
[1] 62.67743

$`hBS category`
[1] "High"

$GA
[1] 10.99216

$GAM
[1] 13.5601

$`GAM category`
[1] "Medium"

$Mean
[1] 298.4792

$PV
[1] 4980.411

$GV
[1] 4694.161

$EV
[1] 286.25

$GCV
[1] 22.95435

$`GCV category`
[1] "High"

$PCV
[1] 23.64387

$`PCV category`
[1] "High"

$ECV
[1] 5.668377

$hBS
[1] 94.25248

$`hBS category`
[1] "High"

$GA
[1] 137.2223

$GAM
[1] 45.97382

$`GAM category`
[1] "High"

augmentedRCBD documentation built on June 12, 2021, 9:06 a.m.