Analysis of genotypes in single experiments using mixed-effect models with estimation of genetic parameters.

gamem(.data, gen, rep, resp, block = NULL, prob = 0.05, verbose = TRUE)

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).

prob

The probability for estimating confidence interval for BLUP's prediction.

verbose

Logical argument. If verbose = FALSE the code are run silently.

Value

An object of class gamem, 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

  • 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); Max the maximum observed, MinGEN the winner genotype, MaxGEN, the loser genotype.

  • ESTIMATES: A tibble with the values for the genotypic variance, block-within-replicate variance (if an alpha-lattice design is used by informing the block in block), the residual variance and their respective contribution to the phenotypic variance; broad-sence heritability, heritability on the entry-mean basis, genotypic coefficient of variation residual coefficient of variation and ratio between genotypic and residual coefficient of variation.

  • residuals: The residuals of the model.

  • formula The formula used to fit the 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

See also

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))
#> 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 x 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 x 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 x 10 #> Parameters PH ED EL CL CW KW NR TKW #> <chr> <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 #> 2 Gen (%) 34.3 68.8 4.58 75.1 71.0 39.2 48.2 4.52e+1 #> 3 Res_var 0.0328 2.43 0.984 1.41 7.54 280. 1.27 1.02e+3 #> 4 Res (%) 65.7 31.2 95.4 24.9 29.0 60.8 51.8 5.48e+1 #> 5 Phen_var 0.0498 7.80 1.03 5.68 26.0 461. 2.45 1.86e+3 #> 6 H2 0.343 0.688 0.0458 0.751 0.710 0.392 0.482 4.52e-1 #> 7 h2mg 0.610 0.869 0.126 0.901 0.880 0.659 0.736 7.12e-1 #> 8 Accuracy 0.781 0.932 0.355 0.949 0.938 0.812 0.858 8.44e-1 #> 9 CVg 6.03 4.84 1.48 7.26 20.7 9.16 6.88 9.13e+0 #> 10 CVr 8.35 3.26 6.76 4.18 13.2 11.4 7.14 1.00e+1 #> 11 CV ratio 0.722 1.49 0.219 1.74 1.56 0.803 0.964 9.09e-1 #> # ... with 1 more variable: NKE <dbl>
# 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 x 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)
#> 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 x 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 #>
# }