R script for ‘The role of maternal effects on offspring performance in familiar and novel environments’
M. Vrtilek
20 November 2020
PART 1: ‘Minimal’ models (testing maternal effects - Predictions 1 & 2)
Default code for minimal models for ALL the continuous traits
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.
Data preparation
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.
Development duration of female offspring (daughters)
## [1] "The number of removed missing and outlier values:"## [1] 24## Cowpea Mung
## mean 32.025 30.770
## SD 1.355 1.009
## SE 0.043 0.038## 'data.frame': 1420 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/ 246 levels "d101","d102",..: 1 1 1 1 1 2 2 2 2 2 ...
## $ IDm : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 18 20 20 20 20 20 ...
## $ ord.f : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C : int 8 8 8 8 8 3 3 3 3 3 ...
## $ pref.tot : int 13 13 13 13 13 10 10 10 10 10 ...
## $ host : Factor w/ 2 levels "C","M": 2 2 1 1 1 1 2 1 2 2 ...
## $ Whost : num 70.9 62.6 328.4 310.1 210.4 ...
## $ IDo : int 1 3 6 7 8 1 2 3 3 5 ...
## $ code : Factor w/ 1420 levels "C-101-6","C-101-7",..: 735 736 1 2 3 4 737 5 738 739 ...
## $ state : Factor w/ 1 level "emerged": 1 1 1 1 1 1 1 1 1 1 ...
## $ day.em : Factor w/ 12 levels "10.4.18","11.4.18",..: 4 3 7 5 3 4 3 4 3 3 ...
## $ dev.dur.o : int 31 30 34 32 30 31 30 31 30 30 ...
## $ Wo : num 7.98 7.79 5.99 5.55 7.03 ...
## $ sex : Factor w/ 1 level "f": 1 1 1 1 1 1 1 1 1 1 ...
## $ mated : Factor w/ 3 levels "not","succ","unsucc": 2 2 1 2 2 2 1 2 1 2 ...
## $ pref.C.o : int 0 10 NA 15 9 15 NA 18 NA 10 ...
## $ pref.tot.o: int 1 19 NA 31 13 21 NA 20 NA 19 ...
## $ day.dead : Factor w/ 43 levels "","1.5.18","10.5.18",..: 19 7 10 15 15 33 3 39 17 40 ...
## $ adsurv.o : int 38 32 30 18 20 16 28 22 38 24 ...
## $ rel.pref : num 0.615 0.615 0.615 0.615 0.615 ...
## $ rel.pref.o: num 0 0.526 NA 0.484 0.692 ...
## $ y : int 31 30 34 32 30 31 30 31 30 30 ...
## $ WH : num -0.149 -1.224 0.848 0.445 -1.751 ...
## $ PREF : num -0.403 -0.403 -0.403 -0.403 -0.403 ...
## $ date : num 3 3 3 3 3 3 3 3 3 3 ...
## $ DATE : num -0.482 -0.482 -0.482 -0.482 -0.482 ...Creating pedigree for the animal model approach
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 1420 246 82Bayesian ‘animal’ model approach to comparison of minimal models (DIC) and phenotypic variance partitioning
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.
The Gcov + Mcov model
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 96 116 121## [1] 1 6 11 16 21 26 31 36 41 46 51 56 57 61 62 66 71 76
## [19] 77 81 82 86 91 96 101 106 107 111 112 116 121 126 127 131 132 136
## [37] 141 146 151 156 161 166 171 176 181 186 191 196 201 206 211 216 221 226
## [55] 231 236 241 246 251 256 257 261 262 266 271 276 281 286 291 296 301 306
## [73] 307 311 312 316 321 326 331 336 341 346 351 356 361 366 371 376 381 386
## [91] 396 401 406 411 416 421 426 431 441 446 451 456 461 466 471 476 481 486
## [109] 491 496##
## Iterations = 50001:549501
## Thinning interval = 500
## Sample size = 1000
##
## DIC: 4246.116
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.2274 2.069e-06 0.5084 1000.0
## hostM:hostC.animal 0.1361 -3.057e-02 0.3363 596.8
## hostC:hostM.animal 0.1361 -3.057e-02 0.3363 596.8
## hostM:hostM.animal 0.2414 6.120e-11 0.4878 1000.0
##
## ~us(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.dam 0.11564 1.069e-08 0.2684 1000.0
## hostM:hostC.dam 0.03845 -4.109e-02 0.1432 856.1
## hostC:hostM.dam 0.03845 -4.109e-02 0.1432 856.1
## hostM:hostM.dam 0.09147 5.631e-07 0.2146 1000.0
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 1.4211 1.1716 1.6579 855.9
## hostM.units 0.6234 0.4574 0.7793 1000.0
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.903302 31.712664 32.093242 1000 <0.001 ***
## hostM -1.271594 -1.428602 -1.133245 1034 <0.001 ***
## WH 0.083572 0.026540 0.136681 1000 0.002 **
## ord.f 0.064657 -0.004386 0.140582 1000 0.080 .
## DATE 0.317853 0.238624 0.410327 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 22.46152 minsEstimating heritability, evolvability and maternal effects
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 0.002 0,0.508
## Vmat 0.002 0,0.268
## Vres 1.425 1.172,1.658
## Vtot 1.743 1.585,1.946
## m2 0.001 0,0.151
## h2 0.002 0,0.282
## CVa 0.015 0.001,0.023
## emu 0.000 0,0and in the novel host type (Mung)
## Est CredI
## Vadd 0.251 0,0.488
## Vmat 0.002 0,0.215
## Vres 0.672 0.457,0.779
## Vtot 0.948 0.851,1.069
## m2 0.001 0,0.222
## h2 0.267 0,0.494
## CVa 0.016 0.003,0.024
## emu 0.000 0,0.001Estimating the cross-environmental additive genetic correlation and maternal effects covariance
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): 0.99 -0.315,1## Est CredI
## dam-related covariance novel-original 0 -0.041,0.143The Gcov + Msep model
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 21 31 41 46 51 56 61 66 71 76 81 86 91 96 101 106
## [20] 111 116 122 126 131 136 146 156 161 166 171 181 191 206 211 216 226 236 241
## [39] 246 251 261 271 286 291 296 306 316##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 4239.748
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.2733 1.612e-05 0.5304 1000.0
## hostM:hostC.animal 0.1760 -2.063e-03 0.3495 569.8
## hostC:hostM.animal 0.1760 -2.063e-03 0.3495 569.8
## hostM:hostM.animal 0.2806 6.269e-02 0.5418 1000.0
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.09182 4.230e-06 0.2247 1000
## hostM.dam 0.07293 1.489e-06 0.1842 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 1.3963 1.156 1.6584 1000
## hostM.units 0.6047 0.451 0.7428 1165
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.898934 31.718699 32.110322 1000 <0.001 ***
## hostM -1.263861 -1.403436 -1.116246 1000 <0.001 ***
## WH 0.081006 0.025212 0.133477 1000 0.006 **
## ord.f 0.065112 -0.002199 0.137288 1116 0.066 .
## DATE 0.321488 0.234017 0.403636 1248 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 14.48759 minsEstimating heritability, evolvability and maternal effects
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 0.239 0,0.53
## Vmat 0.001 0,0.225
## Vres 1.424 1.156,1.658
## Vtot 1.778 1.576,1.931
## m2 0.001 0,0.126
## h2 0.099 0,0.297
## CVa 0.018 0.004,0.024
## emu 0.000 0,0.001and in the novel (Mung)
## Est CredI
## Vadd 0.265 0.063,0.542
## Vmat 0.001 0,0.184
## Vres 0.605 0.451,0.743
## Vtot 0.966 0.863,1.083
## m2 0.001 0,0.19
## h2 0.226 0.058,0.533
## CVa 0.020 0.009,0.025
## emu 0.000 0,0.001Estimating cross-environmental additive genetic correlation
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): 0.741 0.25,0.996The Gsep + Msep model
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 91 121## [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: 4258.497
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 0.1962 7.341e-07 0.5167 1000
## hostM.animal 0.2292 6.484e-06 0.4818 1000
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.12792 5.481e-06 0.2934 1000
## hostM.dam 0.09448 7.009e-06 0.2157 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 1.4407 1.1879 1.7000 627
## hostM.units 0.6267 0.4524 0.7769 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.91107 31.73451 32.09660 944.5 <0.001 ***
## hostM -1.27112 -1.42710 -1.12781 813.7 <0.001 ***
## WH 0.08147 0.02577 0.13459 1000.0 0.014 *
## ord.f 0.06267 -0.01194 0.12508 964.5 0.080 .
## DATE 0.31662 0.23501 0.40072 1000.0 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 11.79666 minsEstimating heritability, evolvability and maternal effects
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 0.003 0,0.517
## Vmat 0.002 0,0.293
## Vres 1.486 1.188,1.7
## Vtot 1.744 1.595,1.966
## m2 0.001 0,0.166
## h2 0.002 0,0.288
## CVa 0.014 0,0.022
## emu 0.000 0,0.001and in the novel (Mung)
## Est CredI
## Vadd 0.187 0,0.482
## Vmat 0.002 0,0.216
## Vres 0.613 0.452,0.777
## Vtot 0.949 0.842,1.055
## m2 0.001 0,0.222
## h2 0.137 0,0.476
## CVa 0.017 0.003,0.024
## emu 0.000 0,0.001The Gcov model
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 31 36 37 41 42 46 51 56 61 66 67 71 72 76
## [20] 81 86 91 96 101 106 116 121 126 131 141 156 161 166 176##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 4216
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.4006 0.10527 0.6785 1000.0
## hostM:hostC.animal 0.2444 0.06815 0.4244 723.7
## hostC:hostM.animal 0.2444 0.06815 0.4244 723.7
## hostM:hostM.animal 0.4102 0.21345 0.6217 1000.0
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 1.3631 1.0872 1.6263 1000
## hostM.units 0.5504 0.3883 0.7061 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.892883 31.677250 32.071015 1000 <0.001 ***
## hostM -1.259718 -1.402130 -1.119797 1000 <0.001 ***
## WH 0.081114 0.021384 0.134785 1000 0.002 **
## ord.f 0.065998 -0.001734 0.136490 1000 0.070 .
## DATE 0.319121 0.228076 0.420056 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 12.66418 minsEstimating heritability and evolvability
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 0.430 0.105,0.678
## Vres 1.467 1.087,1.626
## Vtot 1.768 1.578,1.948
## h2 0.229 0.084,0.387
## CVa 0.020 0.012,0.027
## emu 0.000 0,0.001and in the novel (Mung)
## Est CredI
## Vadd 0.349 0.213,0.622
## Vres 0.599 0.388,0.706
## Vtot 0.956 0.853,1.083
## h2 0.365 0.241,0.606
## CVa 0.020 0.016,0.026
## emu 0.000 0,0.001Estimating cross-environmental genetic correlation
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): 0.706 0.277,0.981The Gsep model
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 36 41 51 66 76##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 4226.449
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 0.3917 0.1293 0.7011 1000
## hostM.animal 0.3913 0.2116 0.5925 1113
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 1.3690 1.1029 1.6827 1000
## hostM.units 0.5611 0.3874 0.6941 1011
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.9094048 31.7269174 32.0888203 1000 <0.001 ***
## hostM -1.2629744 -1.4296661 -1.0981124 1000 <0.001 ***
## WH 0.0797128 0.0220312 0.1362517 963 0.012 *
## ord.f 0.0613216 0.0009565 0.1254774 1000 0.060 .
## DATE 0.3163742 0.2333964 0.4069813 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 5.802438 minsEstimating heritability and evolvability
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 0.437 0.129,0.701
## Vres 1.331 1.103,1.683
## Vtot 1.739 1.585,1.947
## h2 0.235 0.053,0.366
## CVa 0.021 0.011,0.026
## emu 0.000 0,0.001and in the novel (Mung)
## Est CredI
## Vadd 0.370 0.212,0.592
## Vres 0.574 0.387,0.694
## Vtot 0.941 0.843,1.056
## h2 0.390 0.229,0.579
## CVa 0.020 0.015,0.025
## emu 0.000 0,0.001The G + M model
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 61 76 91 121## [1] 1 6 11 16 21 26 31 36 41##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 4367.753
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 0.1766 7.396e-07 0.3765 1001
##
## ~dam
##
## post.mean l-95% CI u-95% CI eff.samp
## dam 0.08837 4.2e-08 0.1898 1000
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 1.103 0.9553 1.251 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.90738 31.70164 32.08002 1109 <0.001 ***
## hostM -1.28010 -1.38954 -1.15084 1000 <0.001 ***
## WH 0.09366 0.03452 0.15342 1163 0.002 **
## ord.f 0.06322 -0.01313 0.14045 1116 0.106
## DATE 0.31673 0.22835 0.40373 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 5.0086 minsEstimating heritability, evolvability and maternal effects
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 0.002 0,0.377
## Vmat 0.001 0,0.19
## Vres 1.091 0.955,1.251
## Vtot 1.358 1.255,1.479
## m2 0.001 0,0.14
## h2 0.002 0,0.27
## CVa 0.016 0.002,0.02
## emu 0.000 0,0The G model
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 21 26 31 61 76 91 96 101 116 121## [1] 1 6 11 16##
## Iterations = 20001:219601
## Thinning interval = 200
## Sample size = 999
##
## DIC: 4353.634
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## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 0.3408 0.1725 0.4893 999
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 1.027 0.8914 1.174 999
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 31.89352 31.71678 32.08539 999 <0.001 **
## hostM -1.26720 -1.38553 -1.14875 999 <0.001 **
## WH 0.09341 0.03695 0.15322 999 0.0020 **
## ord.f 0.06463 -0.01402 0.12997 999 0.0921 .
## DATE 0.32040 0.22774 0.41964 999 <0.001 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Time difference of 4.091943 minsEstimating heritability and evolvability
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 0.351 0.172,0.489
## Vres 1.056 0.891,1.174
## Vtot 1.361 1.265,1.474
## h2 0.259 0.147,0.361
## CVa 0.018 0.014,0.022
## emu 0.000 0,0Model comparison
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 4246.116 30.1
## Gcov + Msep 4239.748 23.7
## Gsep + Msep 4258.497 42.5
## Gcov 4216.000 0.0
## Gsep 4226.449 10.4
## G + M 4367.753 151.8
## G 4353.634 137.6Session info:
## Time difference of 76.31293 mins## 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_0.5.0END