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)
.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 |
block | Defaults to |
prob | The probability for estimating confidence interval for BLUP's prediction. |
verbose | Logical argument. If |
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.
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 \(y_{ijk}\).
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
Tiago Olivoto tiagoolivoto@gmail.com
# \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))#>#>#>#>#> --------------------------------------------------------------------------- #> 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 #> ---------------------------------------------------------------------------#>#>#> # 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#>#>#> # 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.#>#>#> # 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>#>#>#> $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 #>#> # 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)#>#>#>#>#> --------------------------------------------------------------------------- #> 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#>#>#> # 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#>#>#> $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 #># }