![[Stable]](figures/lifecycle-stable.svg)
Analysis of genotypes in single experiments using mixed-effect models with estimation of genetic parameters.
Arguments
- .data
The dataset containing the columns related to, Genotypes, replication/block and response variable(s).
- gen
The name of the column that contains the levels of the genotypes, that will be treated as random effect.
- rep
The name of the column that contains the levels of the replications (assumed to be fixed).
- resp
The response variable(s). To analyze multiple variables in a single procedure a vector of variables may be used. For example
resp = c(var1, var2, var3). Select helpers are also allowed.- block
Defaults to
NULL. In this case, a randomized complete block design is considered. If block is informed, then an alpha-lattice design is employed considering block as random to make use of inter-block information, whereas the complete replicate effect is always taken as fixed, as no inter-replicate information was to be recovered (Mohring et al., 2015).- by
One variable (factor) to compute the function by. It is a shortcut to
dplyr::group_by().This is especially useful, for example, when the researcher want to fit a mixed-effect model for each environment. In this case, an object of class gamem_grouped is returned.mgidi()can then be used to compute the mgidi index within each environment.- prob
The probability for estimating confidence interval for BLUP's prediction.
- verbose
Logical argument. If
verbose = FALSEthe code are run silently.
Value
An object of class gamem or gamem_grouped, which is a
list with the following items for each element (variable):
fixed: Test for fixed effects.
random: Variance components for random effects.
LRT: The Likelihood Ratio Test for the random effects.
BLUPgen: The estimated BLUPS for genotypes
ranef: The random effects of the model
modellme The mixed-effect model of class
lmerMod.residuals The residuals of the mixed-effect model.
model_lm The fixed-effect model of class
lm.residuals_lm The residuals of the fixed-effect model.
Details: A tibble with the following data:
Ngen, the number of genotypes;OVmean, the grand mean;Min, the minimum observed (returning the genotype and replication/block);Maxthe maximum observed,MinGENthe winner genotype,MaxGEN, the loser genotype.ESTIMATES: A tibble with the values:
Gen_var, the genotypic variance and ;rep:block_varblock-within-replicate variance (if an alpha-lattice design is used by informing the block inblock);Res_var, the residual variance;Gen (%), rep:block (%), and Res (%)the respective contribution of variance components to the phenotypic variance;H2, broad-sense heritability;h2mg, heritability on the entry-mean basis;Accuracy, the accuracy of selection (square root ofh2mg);CVg, genotypic coefficient of variation;CVr, residual coefficient of variation;CV ratio, the ratio between genotypic and residual coefficient of variation.
formula The formula used to fit the mixed-model.
Details
gamem analyses data from a one-way genotype testing experiment.
By default, a randomized complete block design is used according to the following model:
\[Y_{ij} = m + g_i + r_j + e_{ij}\]
where \(Y_{ij}\) is the response variable of the ith genotype in the jth block;
m is the grand mean (fixed); \(g_i\) is the effect of the ith genotype
(assumed to be random); \(r_j\) is the effect of the jth replicate (assumed to be fixed);
and \(e_{ij}\) is the random error.
When block is informed, then a resolvable alpha design is implemented, according to the following model:
\[Y_{ijk} = m + g_i + r_j + b_{jk} + e_{ijk}\] where where \(y_{ijk}\) is the response variable of the ith genotype in the kth block of the jth replicate; m is the intercept, \(t_i\) is the effect for the ith genotype \(r_j\) is the effect of the jth replicate, \(b_{jk}\) is the effect of the kth incomplete block of the jth replicate, and \(e_{ijk}\) is the plot error effect corresponding to \(y_{ijk}\).
References
Mohring, J., E. Williams, and H.-P. Piepho. 2015. Inter-block information: to recover or not to recover it? TAG. Theor. Appl. Genet. 128:1541-54. doi:10.1007/s00122-015-2530-0
Author
Tiago Olivoto tiagoolivoto@gmail.com
Examples
# \donttest{
library(metan)
# fitting the model considering an RCBD
# Genotype as random effects
rcbd <- gamem(data_g,
gen = GEN,
rep = REP,
resp = c(PH, ED, EL, CL, CW, KW, NR, TKW, NKE))
#> Evaluating trait PH |===== | 11% 00:00:00
Evaluating trait ED |========== | 22% 00:00:00
Evaluating trait EL |=============== | 33% 00:00:00
Evaluating trait CL |==================== | 44% 00:00:00
Evaluating trait CW |======================== | 56% 00:00:01
Evaluating trait KW |============================= | 67% 00:00:01
Evaluating trait NR |================================== | 78% 00:00:01
Evaluating trait TKW |====================================== | 89% 00:00:01
Evaluating trait NKE |===========================================| 100% 00:00:01
#> Method: REML/BLUP
#> Random effects: GEN
#> Fixed effects: REP
#> Denominador DF: Satterthwaite's method
#> ---------------------------------------------------------------------------
#> P-values for Likelihood Ratio Test of the analyzed traits
#> ---------------------------------------------------------------------------
#> model PH ED EL CL CW KW NR TKW NKE
#> Complete NA NA NA NA NA NA NA NA NA
#> Genotype 0.051 2.73e-05 0.786 2.25e-06 1.24e-05 0.0253 0.0056 0.00955 0.00952
#> ---------------------------------------------------------------------------
#> Variables with nonsignificant Genotype effect
#> PH EL
#> ---------------------------------------------------------------------------
# Likelihood ratio test for random effects
get_model_data(rcbd, "lrt")
#> Class of the model: gamem
#> Variable extracted: lrt
#> # A tibble: 9 × 8
#> VAR model npar logLik AIC LRT Df `Pr(>Chisq)`
#> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 PH Genotype 4 -0.947 9.89 3.81 1 0.0510
#> 2 ED Genotype 4 -91.9 192. 17.6 1 0.0000273
#> 3 EL Genotype 4 -55.5 119. 0.0735 1 0.786
#> 4 CL Genotype 4 -86.2 180. 22.4 1 0.00000225
#> 5 CW Genotype 4 -114. 235. 19.1 1 0.0000124
#> 6 KW Genotype 4 -165. 339. 5.00 1 0.0253
#> 7 NR Genotype 4 -71.1 150. 7.67 1 0.00560
#> 8 TKW Genotype 4 -190. 389. 6.72 1 0.00955
#> 9 NKE Genotype 4 -206. 420. 6.72 1 0.00952
# Variance components
get_model_data(rcbd, "vcomp")
#> Class of the model: gamem
#> Variable extracted: vcomp
#> # A tibble: 2 × 10
#> Group PH ED EL CL CW KW NR TKW NKE
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 GEN 0.0171 5.37 0.0472 4.27 18.5 181. 1.18 841. 1982.
#> 2 Residual 0.0328 2.43 0.984 1.41 7.54 280. 1.27 1018. 2399.
# Genetic parameters
get_model_data(rcbd, "genpar")
#> Class of the model: gamem
#> Variable extracted: genpar
#> # A tibble: 11 × 10
#> Paramet…¹ PH ED EL CL CW KW NR TKW NKE
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Gen_var 0.0171 5.37 0.0472 4.27 18.5 181. 1.18 8.41e+2 1.98e+3
#> 2 Gen (%) 34.3 68.8 4.58 75.1 71.0 39.2 48.2 4.52e+1 4.52e+1
#> 3 Res_var 0.0328 2.43 0.984 1.41 7.54 280. 1.27 1.02e+3 2.40e+3
#> 4 Res (%) 65.7 31.2 95.4 24.9 29.0 60.8 51.8 5.48e+1 5.48e+1
#> 5 Phen_var 0.0498 7.80 1.03 5.68 26.0 461. 2.45 1.86e+3 4.38e+3
#> 6 H2 0.343 0.688 0.0458 0.751 0.710 0.392 0.482 4.52e-1 4.52e-1
#> 7 h2mg 0.610 0.869 0.126 0.901 0.880 0.659 0.736 7.12e-1 7.13e-1
#> 8 Accuracy 0.781 0.932 0.355 0.949 0.938 0.812 0.858 8.44e-1 8.44e-1
#> 9 CVg 6.03 4.84 1.48 7.26 20.7 9.16 6.88 9.13e+0 9.52e+0
#> 10 CVr 8.35 3.26 6.76 4.18 13.2 11.4 7.14 1.00e+1 1.05e+1
#> 11 CV ratio 0.722 1.49 0.219 1.74 1.56 0.803 0.964 9.09e-1 9.09e-1
#> # … with abbreviated variable name ¹Parameters
# random effects
get_model_data(rcbd, "ranef")
#> Class of the model: gamem
#> Variable extracted: ranef
#> $GEN
#> GEN PH ED EL CL CW KW
#> 1 H1 0.018773415 2.3610811 0.020813796 2.2056449 5.3329442 6.597949
#> 2 H10 -0.078441587 -3.4773234 -0.085772984 -3.3060659 -7.4818217 -17.311524
#> 3 H11 -0.039799640 -0.7171292 -0.053041610 -1.8922680 -4.2006643 -4.019522
#> 4 H12 0.160731724 -0.1152736 -0.089465754 -2.3605323 -2.6282930 1.022669
#> 5 H13 0.263641328 2.4352270 0.090472873 -1.0499926 0.6731997 22.941732
#> 6 H2 -0.007665811 2.4004711 0.092151405 1.5266616 1.1173015 8.900057
#> 7 H3 -0.075187528 -0.6956964 0.008224807 0.1086613 -2.0755405 -5.159344
#> 8 H4 -0.071526712 -1.7847132 0.108936725 -0.6927910 -1.1569455 -2.213329
#> 9 H5 -0.043867214 1.9584925 0.003189211 1.6503314 5.2258693 9.434104
#> 10 H6 -0.008072569 1.8461152 -0.142843071 3.1109558 1.9916308 -6.425132
#> 11 H7 0.006570695 0.8086529 -0.016113907 1.5969013 5.7354166 5.832276
#> 12 H8 -0.040613155 -1.5286784 0.004867743 0.5270975 1.1054193 -3.547764
#> 13 H9 -0.084542947 -3.4912257 0.058580766 -1.4246040 -3.6385165 -16.052173
#> NR TKW NKE
#> 1 0.06038462 36.368389 -30.472599
#> 2 -0.33211539 -50.194254 14.894629
#> 3 0.35475962 -20.721892 14.134550
#> 4 0.35475962 -24.282196 34.894214
#> 5 2.02288464 1.360088 79.073819
#> 6 -0.03774039 20.096643 -1.114539
#> 7 -0.72461539 13.062513 -33.417906
#> 8 -1.41149040 -7.828821 4.491045
#> 9 1.23788463 -8.706006 48.860670
#> 10 0.45288462 7.352279 -34.463015
#> 11 -0.13586539 28.730081 -19.403946
#> 12 -0.92086539 21.404122 -43.156422
#> 13 -0.92086539 -16.640945 -34.320501
#>
# Predicted values
predict(rcbd)
#> # A tibble: 39 × 11
#> GEN REP PH ED EL CL CW KW NR TKW NKE
#> <chr> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 H1 1 2.12 50.5 14.9 31.5 26.9 156. 15.8 360. 436.
#> 2 H1 2 2.20 49.5 14.5 29.9 24.4 146. 16.1 343. 428.
#> 3 H1 3 2.24 50.7 14.6 30.6 27.1 159. 15.7 359. 449.
#> 4 H10 1 2.02 44.6 14.8 26.0 14.0 132. 15.4 274. 481.
#> 5 H10 2 2.10 43.7 14.4 24.4 11.6 122. 15.7 257. 473.
#> 6 H10 3 2.14 44.9 14.5 25.1 14.2 135. 15.3 272. 494.
#> 7 H11 1 2.06 47.4 14.9 27.4 17.3 145. 16.1 303. 481.
#> 8 H11 2 2.14 46.4 14.5 25.8 14.9 135. 16.4 286. 472.
#> 9 H11 3 2.18 47.6 14.5 26.5 17.5 148. 16.0 302. 493.
#> 10 H12 1 2.26 48.0 14.8 26.9 18.9 150. 16.1 300. 501.
#> # … with 29 more rows
# fitting the model considering an alpha-lattice design
# Genotype and block-within-replicate as random effects
# Note that block effect was now informed.
alpha <- gamem(data_alpha,
gen = GEN,
rep = REP,
block = BLOCK,
resp = YIELD)
#> Evaluating trait YIELD |=========================================| 100% 00:00:00
#> Method: REML/BLUP
#> Random effects: GEN, BLOCK(REP)
#> Fixed effects: REP
#> Denominador DF: Satterthwaite's method
#> ---------------------------------------------------------------------------
#> P-values for Likelihood Ratio Test of the analyzed traits
#> ---------------------------------------------------------------------------
#> model YIELD
#> Complete NA
#> Genotype 1.18e-06
#> rep:block 3.35e-03
#> ---------------------------------------------------------------------------
#> All variables with significant (p < 0.05) genotype effect
# Genetic parameters
get_model_data(alpha, "genpar")
#> Class of the model: gamem
#> Variable extracted: genpar
#> # A tibble: 13 × 2
#> Parameters YIELD
#> <chr> <dbl>
#> 1 Gen_var 0.143
#> 2 Gen (%) 48.5
#> 3 rep:block_var 0.0702
#> 4 rep:block (%) 23.8
#> 5 Res_var 0.0816
#> 6 Res (%) 27.7
#> 7 Phen_var 0.295
#> 8 H2 0.485
#> 9 h2mg 0.798
#> 10 Accuracy 0.893
#> 11 CVg 8.44
#> 12 CVr 6.38
#> 13 CV ratio 1.32
# Random effects
get_model_data(alpha, "ranef")
#> Class of the model: gamem
#> Variable extracted: ranef
#> $GEN
#> GEN YIELD
#> 1 G01 0.501183769
#> 2 G02 0.004962705
#> 3 G03 -0.784562783
#> 4 G04 0.006125660
#> 5 G05 0.474950041
#> 6 G06 0.044640383
#> 7 G07 -0.308947691
#> 8 G08 0.062229524
#> 9 G09 -0.809931603
#> 10 G10 -0.089373059
#> 11 G11 -0.196434546
#> 12 G12 0.225758446
#> 13 G13 0.231664921
#> 14 G14 0.243399964
#> 15 G15 0.424699859
#> 16 G16 0.200964673
#> 17 G17 0.078077967
#> 18 G18 -0.110180929
#> 19 G19 0.289576067
#> 20 G20 -0.338969056
#> 21 G21 0.256132122
#> 22 G22 0.024088815
#> 23 G23 -0.176997620
#> 24 G24 -0.253057630
#>
#> $REP_BLOCK
#> REP BLOCK YIELD
#> 1 R1 B1 0.123136175
#> 2 R1 B2 -0.141225413
#> 3 R1 B3 -0.150394401
#> 4 R1 B4 -0.106755541
#> 5 R1 B5 0.073704281
#> 6 R1 B6 0.201534899
#> 7 R2 B1 -0.532640774
#> 8 R2 B2 -0.301232978
#> 9 R2 B3 0.243239346
#> 10 R2 B4 0.134878440
#> 11 R2 B5 0.275336937
#> 12 R2 B6 0.180419028
#> 13 R3 B1 0.050569780
#> 14 R3 B2 -0.047784038
#> 15 R3 B3 0.151079007
#> 16 R3 B4 0.053760694
#> 17 R3 B5 -0.008047649
#> 18 R3 B6 -0.199577794
#>
#> $GEN_REP_BLOCK
#> GEN REP BLOCK YIELD
#> 1 G01 R1 B5 0.57488805
#> 2 G01 R2 B4 0.63606221
#> 3 G01 R3 B1 0.55175355
#> 4 G02 R1 B2 -0.13626271
#> 5 G02 R2 B5 0.28029964
#> 6 G02 R3 B2 -0.04282133
#> 7 G03 R1 B4 -0.89131832
#> 8 G03 R2 B2 -1.08579576
#> 9 G03 R3 B6 -0.98414058
#> 10 G04 R1 B1 0.12926184
#> 11 G04 R2 B1 -0.52651511
#> 12 G04 R3 B3 0.15720467
#> 13 G05 R1 B1 0.59808622
#> 14 G05 R2 B4 0.60982848
#> 15 G05 R3 B6 0.27537225
#> 16 G06 R1 B6 0.24617528
#> 17 G06 R2 B6 0.22505941
#> 18 G06 R3 B3 0.19571939
#> 19 G07 R1 B5 -0.23524341
#> 20 G07 R2 B6 -0.12852866
#> 21 G07 R3 B6 -0.50852549
#> 22 G08 R1 B4 -0.04452602
#> 23 G08 R2 B1 -0.47041125
#> 24 G08 R3 B2 0.01444549
#> 25 G09 R1 B6 -0.60839670
#> 26 G09 R2 B4 -0.67505316
#> 27 G09 R3 B2 -0.85771564
#> 28 G10 R1 B2 -0.23059847
#> 29 G10 R2 B4 0.04550538
#> 30 G10 R3 B4 -0.03561236
#> 31 G11 R1 B1 -0.07329837
#> 32 G11 R2 B3 0.04680480
#> 33 G11 R3 B1 -0.14586477
#> 34 G12 R1 B6 0.42729335
#> 35 G12 R2 B3 0.46899779
#> 36 G12 R3 B4 0.27951914
#> 37 G13 R1 B4 0.12490938
#> 38 G13 R2 B5 0.50700186
#> 39 G13 R3 B4 0.28542562
#> 40 G14 R1 B3 0.09300556
#> 41 G14 R2 B1 -0.28924081
#> 42 G14 R3 B1 0.29396974
#> 43 G15 R1 B5 0.49840414
#> 44 G15 R2 B2 0.12346688
#> 45 G15 R3 B2 0.37691582
#> 46 G16 R1 B3 0.05057027
#> 47 G16 R2 B6 0.38138370
#> 48 G16 R3 B5 0.19291702
#> 49 G17 R1 B5 0.15178225
#> 50 G17 R2 B3 0.32131731
#> 51 G17 R3 B3 0.22915697
#> 52 G18 R1 B3 -0.26057533
#> 53 G18 R2 B5 0.16515601
#> 54 G18 R3 B3 0.04089808
#> 55 G19 R1 B4 0.18282053
#> 56 G19 R2 B6 0.46999510
#> 57 G19 R3 B1 0.34014585
#> 58 G20 R1 B2 -0.48019447
#> 59 G20 R2 B1 -0.87160983
#> 60 G20 R3 B6 -0.53854685
#> 61 G21 R1 B2 0.11490671
#> 62 G21 R2 B3 0.49937147
#> 63 G21 R3 B5 0.24808447
#> 64 G22 R1 B1 0.14722499
#> 65 G22 R2 B5 0.29942575
#> 66 G22 R3 B5 0.01604117
#> 67 G23 R1 B3 -0.32739202
#> 68 G23 R2 B2 -0.47823060
#> 69 G23 R3 B4 -0.12323693
#> 70 G24 R1 B6 -0.05152273
#> 71 G24 R2 B2 -0.55429061
#> 72 G24 R3 B5 -0.26110528
#>
# }