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.

Body mass of male offspring (sons)

## [1] "The number of removed missing and outlier values:"
## [1] 12
##      Cowpea  Mung
## mean  3.527 3.885
## SD    0.564 0.459
## SE    0.027 0.027
## 'data.frame':    1399 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/ 1399 levels "C-101-1","C-101-10",..: 1 3 776 4 5 6 2 777 7 8 ...
##  $ state     : Factor w/ 1 level "emerged": 1 1 1 1 1 1 1 1 1 1 ...
##  $ day.em    : Factor w/ 17 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/ 34 levels "","1.5.18","10.5.18",..: 23 25 2 5 5 34 28 33 3 28 ...
##  $ 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         : num  3.53 3.21 3.9 4.36 3.55 ...
##  $ WH        : num  1.3273 1.3741 0.8086 -0.0316 0.7169 ...
##  $ PREF      : num  -0.425 -0.425 -0.425 -0.425 -0.425 ...
##  $ date      : num  3 3 3 3 3 3 3 3 3 3 ...
##  $ DATE      : num  -0.557 -0.557 -0.557 -0.557 -0.557 ...
Creating pedigree for the animal model approach

We have dams, sires and their offspring, i.e. parental and offspring generation.

##   offspring dams sires
## 1      1399  245    82

Bayesian ‘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   2   6   7  11  12  16  17  21  22  26  27  31  32  36  41  42  46
##  [19]  51  52  56  57  61  62  66  67  71  72  76  77  81  82  86  87  91  92
##  [37]  96  97 101 102 106 107 111 112 116 117 121 122 126 127 131 132 136 137
##  [55] 141 142 146 147 151 152 156 157 161 162 166 171 172 176 177 181 182 186
##  [73] 191 196 201 202 206 207 211 212 216 221 226 227 231 232 236 241 246 251
##  [91] 252 256 257 261 262 266 267 271 272 276 277 281 282 286 287 291 292 296
## [109] 301 302 306 307 311 312 316 317 321 322 326 327 331 332 336 337 341 342
## [127] 346 351 352 356 357 361 362 366 367 371 372 376 377 381 382 386 387 391
## [145] 396 401 402 406 407 411 412 416 421 426 427 431 432 436 441 446 451 452
## [163] 456 457 461 462 466 471 476 477 481 482 486 491 496
## 
##  Iterations = 50001:549501
##  Thinning interval  = 500
##  Sample size  = 1000 
## 
##  DIC: 1888.152 
## 
##  G-structure:  ~us(host):animal
## 
##                    post.mean   l-95% CI u-95% CI eff.samp
## hostC:hostC.animal   0.03430  7.113e-08  0.08811    589.4
## hostM:hostC.animal   0.02913 -4.283e-03  0.08103    370.3
## hostC:hostM.animal   0.02913 -4.283e-03  0.08103    370.3
## hostM:hostM.animal   0.03966  6.381e-09  0.10089    698.8
## 
##                ~us(host):dam
## 
##                 post.mean   l-95% CI u-95% CI eff.samp
## hostC:hostC.dam   0.02412  1.036e-07  0.05068    831.1
## hostM:hostC.dam   0.02362 -1.346e-03  0.04799    565.7
## hostC:hostM.dam   0.02362 -1.346e-03  0.04799    565.7
## hostM:hostM.dam   0.03709  3.481e-06  0.06499    725.8
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    0.2544  0.21359   0.2963    820.6
## hostM.units    0.1323  0.09483   0.1660   1000.0
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
## (Intercept)  3.493330  3.403382  3.589270     1000 <0.001 ***
## hostM        0.349294  0.289110  0.408559     1000 <0.001 ***
## WH          -0.024455 -0.051627 -0.001475     1000  0.062 .  
## ord.f        0.015277 -0.019217  0.050446     1000  0.396    
## DATE         0.077971  0.039694  0.119903     1081 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 27.25003 mins
Estimating 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 0.001     0,0.088
## Vmat 0.000     0,0.051
## Vres 0.254 0.214,0.296
## Vtot 0.306 0.282,0.343
## m2   0.001     0,0.159
## h2   0.002      0,0.28
## CVa  0.063     0,0.084
## emu  0.000     0,0.007

and in the novel host type (Mung)

##        Est       CredI
## Vadd 0.001     0,0.101
## Vmat 0.039     0,0.065
## Vres 0.141 0.095,0.166
## Vtot 0.207 0.184,0.235
## m2   0.238     0,0.301
## h2   0.003     0,0.471
## CVa  0.050 0.002,0.083
## emu  0.000     0,0.007
Estimating 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): 0.994 -0.398,1
##                                       Est        CredI
## dam-related covariance novel-original   0 -0.001,0.048

The 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  16  18  21  31  41  46  51  56  61  66  71  76  81  86  91  96
## [20] 101 106 111 116 121 126 131 136 146 156 161 166 171 181 206 211 216 226 236
## [39] 241 246 251 271 286 291 296 306 316
## 
##  Iterations = 60001:359701
##  Thinning interval  = 300
##  Sample size  = 1000 
## 
##  DIC: 1846.674 
## 
##  G-structure:  ~us(host):animal
## 
##                    post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal   0.07335  0.03392   0.1159     1000
## hostM:hostC.animal   0.07006  0.03527   0.1064     1000
## hostC:hostM.animal   0.07006  0.03527   0.1064     1000
## hostM:hostM.animal   0.08458  0.03519   0.1327     1000
## 
##                ~idh(host):dam
## 
##           post.mean  l-95% CI u-95% CI eff.samp
## hostC.dam  0.005151 1.224e-08  0.01928     1145
## hostM.dam  0.013937 1.815e-08  0.03502     1000
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    0.2354  0.19999   0.2774     1267
## hostM.units    0.1115  0.07991   0.1439     1000
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
## (Intercept)  3.499134  3.405698  3.581250     1000 <0.001 ***
## hostM        0.349914  0.292890  0.406401     1000 <0.001 ***
## WH          -0.025260 -0.050919 -0.001453     1000  0.040 *  
## ord.f        0.012556 -0.017473  0.047740     1000  0.462    
## DATE         0.077544  0.031708  0.119848     1000 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 14.49925 mins
Estimating 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 0.074 0.034,0.116
## Vmat 0.000     0,0.019
## Vres 0.234   0.2,0.277
## Vtot 0.324  0.28,0.343
## m2   0.000      0,0.06
## h2   0.216  0.11,0.361
## CVa  0.077 0.052,0.097
## emu  0.006 0.003,0.009

and in the novel (Mung)

##        Est       CredI
## Vadd 0.077 0.035,0.133
## Vmat 0.000     0,0.035
## Vres 0.113  0.08,0.144
## Vtot 0.208 0.185,0.235
## m2   0.001     0,0.167
## h2   0.391 0.168,0.596
## CVa  0.081 0.049,0.094
## emu  0.005 0.002,0.009
Estimating 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): 0.968 0.743,0.998

The 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  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: 1933.455 
## 
##  G-structure:  ~idh(host):animal
## 
##              post.mean  l-95% CI u-95% CI eff.samp
## hostC.animal   0.03264 6.939e-07  0.08216     1000
## hostM.animal   0.02590 3.784e-07  0.07850     1000
## 
##                ~idh(host):dam
## 
##           post.mean  l-95% CI u-95% CI eff.samp
## hostC.dam    0.0216 5.016e-08  0.04912     1115
## hostM.dam    0.0436 1.249e-02  0.07041     1000
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    0.2585   0.2127   0.2960   1000.0
## hostM.units    0.1405   0.1059   0.1656    980.4
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##              post.mean   l-95% CI   u-95% CI eff.samp  pMCMC    
## (Intercept)  3.5036689  3.4200419  3.5856675     1106 <0.001 ***
## hostM        0.3391408  0.2684447  0.4068880     1432 <0.001 ***
## WH          -0.0248635 -0.0504194 -0.0009484     1000  0.046 *  
## ord.f        0.0124326 -0.0185429  0.0424433     1097  0.450    
## DATE         0.0786300  0.0428712  0.1130780     1000 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 11.62689 mins
Estimating 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 0.001     0,0.082
## Vmat 0.000     0,0.049
## Vres 0.259 0.213,0.296
## Vtot 0.316 0.279,0.343
## m2   0.001     0,0.154
## h2   0.002     0,0.261
## CVa  0.067     0,0.081
## emu  0.000     0,0.007

and in the novel (Mung)

##        Est       CredI
## Vadd 0.000     0,0.079
## Vmat 0.049  0.012,0.07
## Vres 0.136 0.106,0.166
## Vtot 0.203 0.185,0.235
## m2   0.253 0.077,0.335
## h2   0.003     0,0.373
## CVa  0.041     0,0.072
## emu  0.000     0,0.005

The 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: 1824.573 
## 
##  G-structure:  ~us(host):animal
## 
##                    post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal   0.07695  0.03384   0.1139   1000.0
## hostM:hostC.animal   0.08130  0.05282   0.1136    638.1
## hostC:hostM.animal   0.08130  0.05282   0.1136    638.1
## hostM:hostM.animal   0.10710  0.06830   0.1479   1000.0
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    0.2360  0.19756   0.2720     1000
## hostM.units    0.1042  0.07395   0.1355     1000
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##              post.mean   l-95% CI   u-95% CI eff.samp  pMCMC    
## (Intercept)  3.4985515  3.4089176  3.5838330     1000 <0.001 ***
## hostM        0.3545428  0.2985594  0.4081838     1000 <0.001 ***
## WH          -0.0259423 -0.0493593 -0.0007006     1279  0.032 *  
## ord.f        0.0124301 -0.0178987  0.0455109     1000  0.440    
## DATE         0.0769923  0.0284104  0.1186582     1096  0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 12.4481 mins
Estimating 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 0.070 0.034,0.114
## Vres 0.231 0.198,0.272
## Vtot 0.310 0.282,0.343
## h2   0.225 0.122,0.358
## CVa  0.075   0.058,0.1
## emu  0.006 0.003,0.009

and in the novel (Mung)

##        Est       CredI
## Vadd 0.103 0.068,0.148
## Vres 0.100 0.074,0.136
## Vtot 0.211 0.186,0.236
## h2   0.513 0.355,0.669
## CVa  0.082 0.067,0.099
## emu  0.007  0.005,0.01
Estimating 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): 0.996 0.75,1

The 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  91 121
## [1]  1 11 26 36 41 51 66 76
## 
##  Iterations = 20001:219801
##  Thinning interval  = 200
##  Sample size  = 1000 
## 
##  DIC: 1870.876 
## 
##  G-structure:  ~idh(host):animal
## 
##              post.mean l-95% CI u-95% CI eff.samp
## hostC.animal   0.06443  0.02200   0.1135     1000
## hostM.animal   0.10458  0.06315   0.1509     1000
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    0.2484  0.20493   0.2957   1000.0
## hostM.units    0.1073  0.07716   0.1417    829.1
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##              post.mean   l-95% CI   u-95% CI eff.samp  pMCMC    
## (Intercept)  3.504e+00  3.424e+00  3.588e+00    905.2 <0.001 ***
## hostM        3.455e-01  2.654e-01  4.250e-01   1000.0 <0.001 ***
## WH          -2.637e-02 -5.039e-02  4.011e-05    913.0  0.044 *  
## ord.f        1.228e-02 -1.842e-02  3.978e-02   1000.0  0.418    
## DATE         7.800e-02  4.462e-02  1.179e-01   1000.0 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 5.782449 mins
Estimating 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 0.053 0.022,0.114
## Vres 0.256 0.205,0.296
## Vtot 0.319 0.283,0.348
## h2   0.189 0.082,0.359
## CVa  0.076 0.045,0.097
## emu  0.004 0.002,0.009

and in the novel (Mung)

##        Est       CredI
## Vadd 0.102 0.063,0.151
## Vres 0.110 0.077,0.142
## Vtot 0.207 0.183,0.237
## h2   0.504 0.314,0.653
## CVa  0.082   0.065,0.1
## emu  0.007  0.004,0.01

The 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: 1940.508 
## 
##  G-structure:  ~animal
## 
##        post.mean  l-95% CI u-95% CI eff.samp
## animal   0.04356 9.221e-07  0.09282     1161
## 
##                ~dam
## 
##     post.mean  l-95% CI u-95% CI eff.samp
## dam   0.02458 6.056e-07  0.04619     1170
## 
##  R-structure:  ~units
## 
##       post.mean l-95% CI u-95% CI eff.samp
## units    0.1963   0.1635   0.2252     1000
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
## (Intercept)  3.499216  3.414120  3.595284     1000 <0.001 ***
## hostM        0.353252  0.297721  0.398446     1000 <0.001 ***
## WH          -0.032475 -0.057759 -0.008173     1000  0.010 ** 
## ord.f        0.012576 -0.017704  0.052700     1000  0.474    
## DATE         0.078664  0.038758  0.123447     1000 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 4.834484 mins
Estimating 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 0.041     0,0.093
## Vmat 0.024     0,0.046
## Vres 0.197 0.164,0.225
## Vtot 0.264 0.244,0.286
## m2   0.088     0,0.172
## h2   0.113      0,0.34
## CVa  0.058 0.012,0.091
## emu  0.003     0,0.007

The 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  26  31  46  61  66  76  86  91  96 106 116 121
## [1]  1  6 11 16
## 
##  Iterations = 20001:219601
##  Thinning interval  = 200
##  Sample size  = 999 
## 
##  DIC: 1903.341 
## 
##  G-structure:  ~animal
## 
##        post.mean l-95% CI u-95% CI eff.samp
## animal    0.0931  0.06136    0.129      999
## 
##  R-structure:  ~units
## 
##       post.mean l-95% CI u-95% CI eff.samp
## units    0.1738   0.1468   0.2015     1038
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean l-95% CI u-95% CI eff.samp  pMCMC   
## (Intercept)   3.50177  3.41333  3.59193      999 <0.001 **
## hostM         0.35537  0.30649  0.41029      999 <0.001 **
## WH           -0.03147 -0.05745 -0.00642     1205  0.018 * 
## ord.f         0.01042 -0.02360  0.04374      999  0.535   
## DATE          0.07770  0.02790  0.11974      999  0.004 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 3.937672 mins
Estimating 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 0.089 0.061,0.129
## Vres 0.168 0.147,0.202
## Vtot 0.264 0.246,0.289
## h2   0.341 0.234,0.458
## CVa  0.087  0.07,0.102
## emu  0.007  0.005,0.01

Model 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 1888.152  63.6
## Gcov + Msep 1846.674  22.1
## Gsep + Msep 1933.455 108.9
## Gcov        1824.573   0.0
## Gsep        1870.876  46.3
## G + M       1940.508 115.9
## G           1903.341  78.8

Session info:

## Time difference of 80.37887 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_0.5.0

END