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.

Adult lifespan of male offspring (sons)

## [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 ...
Creating pedigree for the animal model approach

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

##   offspring dams sires
## 1      1389  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  91 121
##   [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
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  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
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): 0.996 0.79,1
##                                        Est        CredI
## dam-related covariance novel-original 0.01 -0.623,1.722

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  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
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  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
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): 0.997 0.796,1

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: 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
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  0.049      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

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  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
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  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
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): 0.967 0.777,0.999

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  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
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  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

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  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
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 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

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  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
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 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

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 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