This file is to be used with the continuous life-history traits from the study (duration of larval development, body mass and adult lifespan). We alternate between analyses of respective traits through assigning them into the response variable y
.
Load libraries and read the full dataset (N = 3 431). We analyse data on female and male offspring separately due to the profound sexual dimorphism in seed beetle life history. We remove offspring of dams for which host preference was not recorded. We also exclude outliers in the response variable that are larger than 3-times trait SD.
## [1] "The number of removed missing and outlier values:"
## [1] 55
## Cowpea Mung
## mean 16.913 19.366
## SD 5.367 5.164
## SE 0.084 0.091
## 'data.frame': 1389 obs. of 27 variables:
## $ day.mated : Factor w/ 6 levels "11.3.18","12.3.18",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ IDf : Factor w/ 245 levels "d101","d102",..: 1 1 1 1 1 1 1 2 2 2 ...
## $ IDm : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 18 18 18 20 20 20 ...
## $ ord.f : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C : int 8 8 8 8 8 8 8 3 3 3 ...
## $ pref.tot : int 13 13 13 13 13 13 13 10 10 10 ...
## $ host : Factor w/ 2 levels "C","M": 1 1 2 1 1 1 1 2 1 1 ...
## $ Whost : num 355 357.2 77.9 293.4 327.4 ...
## $ IDo : int 1 2 2 3 4 9 10 1 2 4 ...
## $ code : Factor w/ 1389 levels "C-101-1","C-101-10",..: 1 3 769 4 5 6 2 770 7 8 ...
## $ state : Factor w/ 1 level "emerged": 1 1 1 1 1 1 1 1 1 1 ...
## $ day.em : Factor w/ 18 levels "10.4.18","11.4.18",..: 13 7 2 6 6 7 5 2 3 4 ...
## $ dev.dur.o : int 40 34 29 33 33 34 32 29 30 31 ...
## $ Wo : num 3.53 3.21 3.9 4.36 3.55 ...
## $ sex : Factor w/ 1 level "m": 1 1 1 1 1 1 1 1 1 1 ...
## $ mated : Factor w/ 2 levels "not","unsucc": 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C.o : logi NA NA NA NA NA NA ...
## $ pref.tot.o: logi NA NA NA NA NA NA ...
## $ day.dead : Factor w/ 33 levels "1.5.18","10.5.18",..: 22 24 1 4 4 33 27 32 2 27 ...
## $ adsurv.o : int 4 12 20 27 27 23 16 27 28 17 ...
## $ rel.pref : num 0.615 0.615 0.615 0.615 0.615 ...
## $ rel.pref.o: num NA NA NA NA NA NA NA NA NA NA ...
## $ y : int 4 12 20 27 27 23 16 27 28 17 ...
## $ WH : num 1.3359 1.3832 0.8069 -0.0377 0.7189 ...
## $ PREF : num -0.421 -0.421 -0.421 -0.421 -0.421 ...
## $ date : num 3 3 3 3 3 3 3 3 3 3 ...
## $ DATE : num -0.562 -0.562 -0.562 -0.562 -0.562 ...
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 1389 245 82
The minimal model contains only fixed effects stemming from our experimental design. The fixed effects are: host type (host
, “C” (original)/“M” (novel)), bean mass (WH
, standardized within each host type), dam mating order (ord.f
, mating sequence, 1 to 4), and day mated (DATE
, 1-6). Additive genetic variance is specified using the pedigree and the identity of the offspring as animal
in the random-effect part. Maternal effects above the additive genetic variance (including non-genetic and genetic maternal effects, but also genetic dominance) is specified with calling dam
in the random-effect part of the model. We defined the random effects for each host separately as interaction with host
- animal (host:animal
) and dam (host:dam
). We extracted additive genetic (proxy of GxE) and maternal effects covariance (MxE) between novel and original host using term us
(unstructured). We called host-specific variance only (with idh
) in the models where we ignore covariance between the additive genetic (or maternal) effects in different host types. Residual variance was allowed to be estimated separately per host type (rcov=~idh(host):units
).
Below, we provide outcome for each of the alternative models that estimate additive genetic variance and maternal effects differently per host. They include/exclude specific variance per host type and the cross-host covariance.
Here, we specify both separate variance per host type and the cross-environmental covariance for both additive genetic (animal
) and maternal effects (dam
). We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 121
## [1] 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86
## [19] 91 96 101 106 111 116 121 126 131 136 141 146 151 156 161 166 171 176
## [37] 181 186 191 196 201 206 211 216 221 226 231 236 241 246 251 256 261 266
## [55] 271 276 277 281 282 286 291 296 301 306 311 316 321 326 327 331 332 336
## [73] 341 346 351 356 361 366 371 376 381 386 391 396 401 406 411 416 421 426
## [91] 431 436 441 446 451 456 461 466 471 476 481 486 491 496
##
## Iterations = 50001:549501
## Thinning interval = 500
## Sample size = 1000
##
## DIC: 8104.504
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 8.82 3.368 14.43 1000.0
## hostM:hostC.animal 10.79 5.829 16.16 790.8
## hostC:hostM.animal 10.79 5.829 16.16 790.8
## hostM:hostM.animal 15.95 7.860 23.20 864.2
##
## ~us(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.dam 1.0245 2.051e-06 3.145 1000.0
## hostM:hostC.dam 0.2884 -6.234e-01 1.722 776.2
## hostC:hostM.dam 0.2884 -6.234e-01 1.722 776.2
## hostM:hostM.dam 0.8496 1.152e-05 3.031 1000.0
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 18.42 14.251 22.52 1000.0
## hostM.units 10.26 5.455 15.09 901.4
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.33440 15.42571 17.30156 883.7 <0.001 ***
## hostM 2.32015 1.71929 2.88267 1000.0 <0.001 ***
## WH -0.37071 -0.63517 -0.12856 910.5 0.006 **
## ord.f 0.25065 -0.09268 0.59302 912.6 0.170
## DATE 0.71293 0.20771 1.23117 847.4 0.008 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 25.72237 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
and maternal effects variance by dam
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 8.457 3.368,14.428
## Vmat 0.018 0,3.145
## Vres 19.101 14.251,22.521
## Vtot 28.594 25.057,31.324
## m2 0.000 0,0.11
## h2 0.331 0.125,0.49
## CVa 0.172 0.119,0.234
## emu 0.030 0.012,0.05
and in the novel host type (Mung)
## Est CredI
## Vadd 15.644 7.86,23.204
## Vmat 0.024 0,3.031
## Vres 10.652 5.455,15.087
## Vtot 26.028 23.802,31.088
## m2 0.001 0,0.109
## h2 0.561 0.348,0.811
## CVa 0.204 0.157,0.259
## emu 0.042 0.021,0.062
additive genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
dam-related covariance between offspring in the original and novel host: \(COV_{dam(novel-original)}\) (Due to low maternal effects variance in both hosts and potential computational problems - dividing by zero; we do not estimate maternal effects correlation (\(r_{M}\)). The covariance estimate is unreliable because of the low variance too.)
## Est CredI
## genetic correlation (rG): 0.996 0.79,1
## Est CredI
## dam-related covariance novel-original 0.01 -0.623,1.722
Here, we specify both separate variance per host type and the cross-environmental covariance for additive genetic (animal
) effects and separate maternal effects variance per host type without the covariance. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 96 116 121
## [1] 1 6 11 16 21 31 36 41 46 51 56 61 66 71 76 81 86 91 96
## [20] 101 106 111 116 121 126 131 136 146 151 156 161 166 171 181 206 211 216 226
## [39] 236 241 246 251 256 271 281 286 291 296 306 316
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 8087.493
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 9.424 4.522 14.28 1000.0
## hostM:hostC.animal 11.510 6.675 16.15 797.4
## hostC:hostM.animal 11.510 6.675 16.15 797.4
## hostM:hostM.animal 16.656 9.026 24.22 1000.0
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.7916 1.320e-07 2.421 1000
## hostM.dam 0.6496 2.348e-08 2.316 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 18.13 14.636 21.87 1000
## hostM.units 9.98 5.389 15.34 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.32483 15.41971 17.29588 1000.0 <0.001 ***
## hostM 2.32062 1.64984 2.86815 1000.0 <0.001 ***
## WH -0.36163 -0.61089 -0.11485 1000.0 0.006 **
## ord.f 0.25803 -0.08843 0.63254 1000.0 0.164
## DATE 0.70151 0.22346 1.17682 804.3 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 16.77966 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
and maternal effects variance by dam
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 8.645 4.522,14.281
## Vmat 0.012 0,2.421
## Vres 17.348 14.636,21.865
## Vtot 28.721 25.488,31.512
## m2 0.001 0,0.085
## h2 0.320 0.181,0.489
## CVa 0.174 0.13,0.227
## emu 0.030 0.016,0.05
and in the novel (Mung)
## Est CredI
## Vadd 16.604 9.026,24.217
## Vmat 0.014 0,2.316
## Vres 10.470 5.389,15.344
## Vtot 27.339 23.549,30.779
## m2 0.000 0,0.084
## h2 0.578 0.363,0.808
## CVa 0.211 0.161,0.258
## emu 0.044 0.024,0.065
Using the additive genetic covariance between the two hosts, we estimate
genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
## Est CredI
## genetic correlation (rG): 0.997 0.796,1
Here, we specify separate variance per host type for both additive genetic (animal
) and maternal effects (dam
), but ignore potential cross-environmental covariances. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 96 116 121
## [1] 1 11 21 36 46 56 61 71 81 96 106 116 121 131 141 156 166 176
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 8202.995
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 4.957 1.638e-08 10.79 1000
## hostM.animal 13.616 3.887e+00 22.38 1000
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 2.719 8.244e-06 5.758 1000
## hostM.dam 1.543 5.087e-06 5.054 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 20.53 15.369 24.38 950.8
## hostM.units 11.61 6.205 17.23 1000.0
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.30985 15.43725 17.16829 1000.0 <0.001 ***
## hostM 2.22832 1.36382 2.95957 778.6 <0.001 ***
## WH -0.34651 -0.60371 -0.08092 1000.0 0.004 **
## ord.f 0.28385 -0.03374 0.58442 1092.7 0.078 .
## DATE 0.68291 0.30482 1.07533 1000.0 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 12.05191 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
and maternal effects variance by dam
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 0.049 0,10.794
## Vmat 0.038 0,5.758
## Vres 22.226 15.369,24.385
## Vtot 28.131 25.489,31.573
## m2 0.001 0,0.2
## h2 0.001 0,0.381
## CVa 0.152 0,0.194
## emu 0.000 0,0.038
and in the novel (Mung)
## Est CredI
## Vadd 11.704 3.887,22.379
## Vmat 0.041 0,5.054
## Vres 13.914 6.205,17.227
## Vtot 27.201 23.324,30.823
## m2 0.001 0,0.194
## h2 0.484 0.219,0.814
## CVa 0.185 0.124,0.258
## emu 0.031 0.01,0.06
Here, we specify both separate variance per host type and cross-environmental covariance for additive genetic (animal
). Maternal effects are ignored. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 121
## [1] 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91
## [20] 96 101 106 111 116 121 126 131 136 141 146 151 156 161 166 171 176
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 8069.9
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 10.12 5.578 14.84 1101.0
## hostM:hostC.animal 12.15 7.934 16.93 693.2
## hostC:hostM.animal 12.15 7.934 16.93 693.2
## hostM:hostM.animal 17.64 11.261 24.82 1000.0
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 18.049 14.073 21.61 1000.0
## hostM.units 9.517 4.744 14.06 909.2
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.3378 15.4315 17.2460 1000.0 <0.001 ***
## hostM 2.3406 1.7616 2.9172 1000.0 <0.001 ***
## WH -0.3729 -0.6443 -0.1256 1000.0 0.002 **
## ord.f 0.2470 -0.1127 0.5686 902.6 0.176
## DATE 0.6829 0.1756 1.1875 1000.0 0.012 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 15.20231 mins
We calculate heritability and evolvability based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
. Maternal effects variance is ignored.
Additive genetic variance: \(V_{A} = V_{animal}\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 9.694 5.578,14.841
## Vres 17.821 14.073,21.612
## Vtot 28.298 24.908,31.138
## h2 0.333 0.218,0.505
## CVa 0.184 0.146,0.234
## emu 0.034 0.02,0.052
and in the novel (Mung)
## Est CredI
## Vadd 16.304 11.261,24.817
## Vres 9.100 4.744,14.057
## Vtot 26.675 23.763,31.265
## h2 0.627 0.48,0.854
## CVa 0.208 0.176,0.26
## emu 0.043 0.03,0.066
Using the additive genetic covariance between the two hosts, we estimate
genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
## Est CredI
## genetic correlation (rG): 0.967 0.777,0.999
Here, we specify separate variance per host type for additive genetic (animal
) effects only, but ignore potential cross-environmental covariance. Maternal effects were also ignored. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 96 116 121
## [1] 1 11 26 27 36 41 51 66 67 76 77
##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 8142.712
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 9.74 5.472 15.07 903.3
## hostM.animal 16.71 10.004 23.75 864.9
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 18.68 15.079 23.46 1000
## hostM.units 10.25 5.417 15.12 1004
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.29431 15.43250 17.17217 1000.0 <0.001 ***
## hostM 2.29978 1.47297 3.18790 924.8 <0.001 ***
## WH -0.35852 -0.62154 -0.11308 1217.1 0.010 **
## ord.f 0.26758 -0.04591 0.58500 1103.8 0.086 .
## DATE 0.67050 0.22951 1.07554 1000.0 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 5.906577 mins
We calculate heritability and evolvability based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 9.093 5.472,15.066
## Vres 17.599 15.079,23.464
## Vtot 28.346 25.458,31.388
## h2 0.319 0.188,0.488
## CVa 0.178 0.138,0.229
## emu 0.032 0.019,0.053
and in the novel (Mung)
## Est CredI
## Vadd 18.513 10.004,23.75
## Vres 10.099 5.417,15.118
## Vtot 26.105 23.732,31.38
## h2 0.614 0.415,0.811
## CVa 0.222 0.163,0.252
## emu 0.049 0.027,0.063
Here, we estimate variance for both additive genetic (animal
) and maternal effects (dam
), but ignore their potential host-specificity and the cross-environmental covariances. We estimate residual variance (units
) across host types.
## [1] 1 6 16 26 31 46 61 76 91 106 121
## [1] 1 6 11 16 21 26 31 36 41
##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 8223.135
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 10.58 4.416 15.65 942.8
##
## ~dam
##
## post.mean l-95% CI u-95% CI eff.samp
## dam 0.9652 8.173e-09 3.062 1000
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 15.91 12.87 19.5 895.8
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.25745 15.27633 17.17015 1000.0 <0.001 ***
## hostM 2.38679 1.89041 2.93520 866.6 <0.001 ***
## WH -0.37819 -0.63629 -0.14297 891.0 0.002 **
## ord.f 0.27581 -0.08983 0.61432 825.6 0.136
## DATE 0.67974 0.10202 1.14104 936.0 0.010 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 4.917072 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
. Maternal effects variance is ignored.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates across the two host types
## Est CredI
## Vadd 11.508 4.416,15.649
## Vmat 0.017 0,3.062
## Vres 15.721 12.866,19.505
## Vtot 27.341 25.186,30.022
## m2 0.001 0,0.112
## h2 0.403 0.183,0.553
## CVa 0.201 0.132,0.24
## emu 0.040 0.015,0.055
Here, we specify additive genetic (animal
) effects only, ignore maternal effects or host-specificity. We estimate residual variance (units
) across host types.
## [1] 1 6 16 26 31 46 61 76 91 96 106 116 121
## [1] 1 6 11 16
##
## Iterations = 20001:219601
## Thinning interval = 200
## Sample size = 999
##
## DIC: 8195.484
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 12.59 8.525 16.55 999
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 15 12.25 17.88 999
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 16.26930 15.40986 17.17386 988.6 < 0.001 **
## hostM 2.39899 1.91143 2.97477 882.4 < 0.001 **
## WH -0.38358 -0.67390 -0.15329 843.2 0.00601 **
## ord.f 0.27156 -0.07973 0.59165 999.0 0.12012
## DATE 0.66349 0.12139 1.12643 999.0 0.00801 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 3.95651 mins
We calculate heritability and evolvability based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
. Maternal effects variance is ignored.
Additive genetic variance: \(V_{A} = V_{animal}\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates across both host types
## Est CredI
## Vadd 12.328 8.525,16.55
## Vres 14.653 12.255,17.88
## Vtot 27.102 25.161,30.124
## h2 0.460 0.336,0.571
## CVa 0.207 0.174,0.242
## emu 0.043 0.03,0.058
The DIC of the alternative models. We base our inference on the best-selected models (lowest AIC within 2 unit difference).
## DIC delta
## Gcov + Mcov 8104.504 34.6
## Gcov + Msep 8087.493 17.6
## Gsep + Msep 8202.995 133.1
## Gcov 8069.900 0.0
## Gsep 8142.712 72.8
## G + M 8223.135 153.2
## G 8195.484 125.6
## Time difference of 84.53641 mins
Session info:
## R version 4.0.0 (2020-04-24)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
##
## Matrix products: default
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] QGglmm_0.7.4 MCMCglmm_2.29 ape_5.3 coda_0.19-3 scales_1.1.1
## [6] MuMIn_1.43.17 lme4_1.1-23 Matrix_1.2-18
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.4.6 compiler_4.0.0 nloptr_1.2.2.1 tools_4.0.0
## [5] boot_1.3-24 digest_0.6.25 statmod_1.4.34 evaluate_0.14
## [9] lifecycle_0.2.0 nlme_3.1-147 lattice_0.20-41 rlang_0.4.6
## [13] yaml_2.2.1 parallel_4.0.0 xfun_0.14 stringr_1.4.0
## [17] knitr_1.28 stats4_4.0.0 grid_4.0.0 R6_2.4.1
## [21] rmarkdown_2.2 tensorA_0.36.1 minqa_1.2.4 corpcor_1.6.9
## [25] magrittr_1.5 htmltools_0.4.0 MASS_7.3-51.5 splines_4.0.0
## [29] colorspace_1.4-1 cubature_2.0.4 stringi_1.4.6 munsell_0.5.0
END