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 male offspring (sons)

## [1] "The number of removed missing and outlier values:"
## [1] 27
##      Cowpea   Mung
## mean 31.526 30.456
## SD    1.481  1.102
## SE    0.044  0.042
## 'data.frame':    1384 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 2 2 2 2 ...
##  $ IDm       : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 18 18 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 8 3 3 3 3 ...
##  $ pref.tot  : int  13 13 13 13 13 13 10 10 10 10 ...
##  $ host      : Factor w/ 2 levels "C","M": 1 2 1 1 1 1 2 1 1 2 ...
##  $ Whost     : num  357.2 77.9 293.4 327.4 266.9 ...
##  $ IDo       : int  2 2 3 4 9 10 1 2 4 4 ...
##  $ code      : Factor w/ 1384 levels "C-101-10","C-101-2",..: 2 758 3 4 5 1 759 6 7 760 ...
##  $ state     : Factor w/ 1 level "emerged": 1 1 1 1 1 1 1 1 1 1 ...
##  $ day.em    : Factor w/ 13 levels "10.4.18","11.4.18",..: 7 2 6 6 7 5 2 3 4 2 ...
##  $ dev.dur.o : int  34 29 33 33 34 32 29 30 31 29 ...
##  $ Wo        : num  3.21 3.9 4.36 3.55 3.34 ...
##  $ 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",..: 25 2 5 5 34 28 33 3 28 29 ...
##  $ adsurv.o  : int  12 20 27 27 23 16 27 28 17 23 ...
##  $ 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  34 29 33 33 34 32 29 30 31 29 ...
##  $ WH        : num  1.379 0.8039 -0.0229 0.7236 -0.606 ...
##  $ 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  -0.568 -0.568 -0.568 -0.568 -0.568 ...
Creating pedigree for the animal model approach

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

##   offspring dams sires
## 1      1384  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  21  26  31  41  51  56  61  66  71  76  81  86  89  91  96 101
## [20] 106 111 116 121 126 131 136 139 141 146 156 161 166 176 181 186 196 201 206
## [39] 211 221 226 231 236 241 251 256 261 266 271 276 281 286 296 301 306 311 316
## [58] 321 326 331 336 346 356 361 366 371 376 381 386 396 401 406 411 421 441 456
## [77] 461 466 476 481 486 496
## 
##  Iterations = 50001:549501
##  Thinning interval  = 500
##  Sample size  = 1000 
## 
##  DIC: 4398.772 
## 
##  G-structure:  ~us(host):animal
## 
##                    post.mean   l-95% CI u-95% CI eff.samp
## hostC:hostC.animal   0.31160  2.910e-07   0.6994     1000
## hostM:hostC.animal   0.03225 -1.700e-01   0.2803     1000
## hostC:hostM.animal   0.03225 -1.700e-01   0.2803     1000
## hostM:hostM.animal   0.49062  1.454e-01   0.8263     1000
## 
##                ~us(host):dam
## 
##                 post.mean   l-95% CI u-95% CI eff.samp
## hostC:hostC.dam   0.12984  1.861e-06  0.34109    890.1
## hostM:hostC.dam   0.01312 -6.329e-02  0.09951   1204.1
## hostC:hostM.dam   0.01312 -6.329e-02  0.09951   1204.1
## hostM:hostM.dam   0.05826  2.507e-08  0.19521   1000.0
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    1.7574   1.4357   2.0631     1000
## hostM.units    0.6217   0.3962   0.8288     1000
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean l-95% CI u-95% CI eff.samp  pMCMC    
## (Intercept)  31.41730 31.19141 31.62771   1000.0 <0.001 ***
## hostM        -1.11532 -1.28839 -0.92352   1000.0 <0.001 ***
## WH            0.08914  0.02418  0.14991   1000.0  0.006 ** 
## ord.f         0.06472 -0.01040  0.14329    895.3  0.100    
## DATE          0.23018  0.13701  0.32544   1000.0 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 22.55621 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 0.004     0,0.699
## Vmat 0.002     0,0.341
## Vres 1.850 1.436,2.063
## Vtot 2.166 1.964,2.433
## m2   0.001     0,0.154
## h2   0.002      0,0.31
## CVa  0.021 0.001,0.027
## emu  0.000     0,0.001

and in the novel host type (Mung)

##        Est       CredI
## Vadd 0.490 0.145,0.826
## Vmat 0.001     0,0.195
## Vres 0.629 0.396,0.829
## Vtot 1.153 1.039,1.338
## m2   0.001      0,0.17
## h2   0.459 0.147,0.677
## CVa  0.025 0.014,0.031
## emu  0.001     0,0.001
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): 0.111 -0.588,0.84
##                                       Est      CredI
## dam-related covariance novel-original   0 -0.063,0.1

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  21  31  41  46  51  61  81  86  91 101 136 146 156 161 166 171
## [20] 181 191 216 226 236 241 261 271 296 306 316
## 
##  Iterations = 60001:359701
##  Thinning interval  = 300
##  Sample size  = 1000 
## 
##  DIC: 4400.969 
## 
##  G-structure:  ~us(host):animal
## 
##                    post.mean   l-95% CI u-95% CI eff.samp
## hostC:hostC.animal   0.29197  1.926e-06   0.6693    816.3
## hostM:hostC.animal   0.04024 -1.705e-01   0.2305   1000.0
## hostC:hostM.animal   0.04024 -1.705e-01   0.2305   1000.0
## hostM:hostM.animal   0.47752  9.081e-02   0.8262   1000.0
## 
##                ~idh(host):dam
## 
##           post.mean  l-95% CI u-95% CI eff.samp
## hostC.dam   0.13338 1.489e-05   0.3309    696.6
## hostM.dam   0.06364 1.722e-08   0.1955   1000.0
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    1.7695   1.4202   2.0646     1000
## hostM.units    0.6277   0.3873   0.8413     1221
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean l-95% CI u-95% CI eff.samp  pMCMC    
## (Intercept)  31.42069 31.21299 31.62834     1000 <0.001 ***
## hostM        -1.11737 -1.28771 -0.94591     1000 <0.001 ***
## WH            0.09001  0.02990  0.15719     1000  0.008 ** 
## ord.f         0.06405 -0.01273  0.14575     1000  0.126    
## DATE          0.22781  0.12748  0.32218     1000 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 14.56577 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 0.003    0,0.669
## Vmat 0.003    0,0.331
## Vres 1.739 1.42,2.065
## Vtot 2.175 1.972,2.44
## m2   0.001    0,0.151
## h2   0.001    0,0.304
## CVa  0.021    0,0.026
## emu  0.000    0,0.001

and in the novel (Mung)

##        Est       CredI
## Vadd 0.459 0.091,0.826
## Vmat 0.001     0,0.196
## Vres 0.673 0.387,0.841
## Vtot 1.143 1.034,1.336
## m2   0.001     0,0.172
## h2   0.374 0.116,0.685
## CVa  0.022 0.013,0.032
## emu  0.000     0,0.001
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): 0.099 -0.606,0.828

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  34  61  76  91 121
##  [1]   1   6  11  21  26  31  36  46  56  61  71  81  96 106 116 121 131 141 146
## [20] 151 156 166 171 176
## 
##  Iterations = 60001:359701
##  Thinning interval  = 300
##  Sample size  = 1000 
## 
##  DIC: 4397.015 
## 
##  G-structure:  ~idh(host):animal
## 
##              post.mean  l-95% CI u-95% CI eff.samp
## hostC.animal    0.3521 1.048e-05   0.7205     1100
## hostM.animal    0.4886 1.360e-01   0.8389     1000
## 
##                ~idh(host):dam
## 
##           post.mean  l-95% CI u-95% CI eff.samp
## hostC.dam    0.1131 5.795e-09   0.3006     1136
## hostM.dam    0.0588 2.324e-07   0.1865     1000
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    1.7292   1.3817   2.0151     1000
## hostM.units    0.6233   0.4223   0.8407     1095
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
## (Intercept) 31.420945 31.194684 31.620351     1000 <0.001 ***
## hostM       -1.119755 -1.309285 -0.941378     1391 <0.001 ***
## WH           0.088682  0.028203  0.152620     1000  0.008 ** 
## ord.f        0.064036 -0.009447  0.150456     1000  0.110    
## DATE         0.229559  0.142160  0.327636     1000 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 11.58047 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 0.004     0,0.721
## Vmat 0.002     0,0.301
## Vres 1.678 1.382,2.015
## Vtot 2.123 1.972,2.424
## m2   0.001     0,0.138
## h2   0.002     0,0.313
## CVa  0.020 0.003,0.029
## emu  0.000     0,0.001

and in the novel (Mung)

##        Est       CredI
## Vadd 0.429 0.136,0.839
## Vmat 0.001     0,0.186
## Vres 0.626 0.422,0.841
## Vtot 1.155 1.029,1.322
## m2   0.001      0,0.16
## h2   0.494 0.142,0.686
## CVa  0.024 0.013,0.031
## emu  0.000     0,0.001

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  46  61  76  91 106 121
##  [1]   1   6  11  21  31  36  41  46  56  61  66  71  76  86  96 101 106 116 121
## [20] 141 156 161 166 176
## 
##  Iterations = 60001:359701
##  Thinning interval  = 300
##  Sample size  = 1000 
## 
##  DIC: 4367.834 
## 
##  G-structure:  ~us(host):animal
## 
##                    post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal   0.50483   0.2076   0.8760   1000.0
## hostM:hostC.animal   0.07062  -0.1672   0.3008    979.9
## hostC:hostM.animal   0.07062  -0.1672   0.3008    979.9
## hostM:hostM.animal   0.61450   0.3553   0.8921   1000.0
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    1.6799   1.3109    1.963    948.4
## hostM.units    0.5619   0.3761    0.763   1000.0
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
## (Intercept) 31.411726 31.207303 31.625600     1000 <0.001 ***
## hostM       -1.117266 -1.289804 -0.910574     1000 <0.001 ***
## WH           0.089429  0.032003  0.149813     1000 <0.001 ***
## ord.f        0.067413 -0.006392  0.138501     1000  0.060 .  
## DATE         0.228242  0.140211  0.328966     1147  0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 12.47464 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 0.448 0.208,0.876
## Vres 1.677 1.311,1.963
## Vtot 2.167 1.979,2.409
## h2   0.210 0.082,0.374
## CVa  0.021  0.014,0.03
## emu  0.000     0,0.001

and in the novel (Mung)

##        Est       CredI
## Vadd 0.527 0.355,0.892
## Vres 0.578 0.376,0.763
## Vtot 1.154 1.028,1.339
## h2   0.495 0.348,0.708
## CVa  0.026  0.02,0.031
## emu  0.001     0,0.001
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): 0.147 -0.279,0.533

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: 4367.461 
## 
##  G-structure:  ~idh(host):animal
## 
##              post.mean l-95% CI u-95% CI eff.samp
## hostC.animal    0.5119   0.1879   0.8415    676.6
## hostM.animal    0.5998   0.3334   0.8875   1000.0
## 
##  R-structure:  ~idh(host):units
## 
##             post.mean l-95% CI u-95% CI eff.samp
## hostC.units    1.6731   1.3654   2.0053     1388
## hostM.units    0.5717   0.3741   0.7962     1000
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean  l-95% CI  u-95% CI eff.samp  pMCMC    
## (Intercept) 31.412981 31.180449 31.642023   1000.0 <0.001 ***
## hostM       -1.110506 -1.295914 -0.914312   1000.0 <0.001 ***
## WH           0.088099  0.028591  0.150004   1000.0  0.002 ** 
## ord.f        0.065891 -0.009468  0.145278    712.9  0.086 .  
## DATE         0.230699  0.146624  0.320451   1000.0 <0.001 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 5.630001 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 0.494 0.188,0.842
## Vres 1.643 1.365,2.005
## Vtot 2.167 1.973,2.422
## h2   0.208 0.095,0.384
## CVa  0.022 0.014,0.029
## emu  0.000     0,0.001

and in the novel (Mung)

##        Est       CredI
## Vadd 0.594 0.333,0.888
## Vres 0.561 0.374,0.796
## Vtot 1.198  1.03,1.327
## h2   0.492 0.319,0.707
## CVa  0.025 0.019,0.031
## emu  0.001     0,0.001

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   4   6  16  21  26  31  61  76  91  96 101 116 121
## [1]  1  6 11 16 21 26 31 36 41
## 
##  Iterations = 20001:219801
##  Thinning interval  = 200
##  Sample size  = 1000 
## 
##  DIC: 4600.783 
## 
##  G-structure:  ~animal
## 
##        post.mean  l-95% CI u-95% CI eff.samp
## animal    0.2362 0.0008574    0.447    788.6
## 
##                ~dam
## 
##     post.mean  l-95% CI u-95% CI eff.samp
## dam   0.06444 7.829e-07   0.1698    898.7
## 
##  R-structure:  ~units
## 
##       post.mean l-95% CI u-95% CI eff.samp
## units     1.416    1.242    1.599     1000
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean l-95% CI u-95% CI eff.samp  pMCMC    
## (Intercept)  31.42035 31.20378 31.64154   1000.0 <0.001 ***
## hostM        -1.14446 -1.27457 -1.01345   1000.0 <0.001 ***
## WH            0.09329  0.01879  0.15615   1294.9  0.010 *  
## ord.f         0.06102 -0.02682  0.14242    893.4  0.190    
## DATE          0.20096  0.10729  0.30678   1000.0  0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 4.774898 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 0.210 0.001,0.447
## Vmat 0.001      0,0.17
## Vres 1.436 1.242,1.599
## Vtot 1.727 1.586,1.833
## m2   0.001     0,0.098
## h2   0.123     0,0.252
## CVa  0.017 0.005,0.022
## emu  0.000         0,0

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  91 106 121
## [1]  1  6 11 16
## 
##  Iterations = 20001:219601
##  Thinning interval  = 200
##  Sample size  = 999 
## 
##  DIC: 4592.872 
## 
##  G-structure:  ~animal
## 
##        post.mean l-95% CI u-95% CI eff.samp
## animal    0.3457   0.1745   0.5418      999
## 
##  R-structure:  ~units
## 
##       post.mean l-95% CI u-95% CI eff.samp
## units     1.375    1.181     1.55    925.2
## 
##  Location effects: y ~ host + WH + ord.f + DATE 
## 
##             post.mean l-95% CI u-95% CI eff.samp   pMCMC   
## (Intercept)  31.41562 31.22125 31.62819      516 < 0.001 **
## hostM        -1.14142 -1.27501 -0.99670      999 < 0.001 **
## WH            0.09436  0.02686  0.15997      999 0.00601 **
## ord.f         0.06337 -0.02282  0.13379      999 0.12412   
## DATE          0.20527  0.10852  0.30497      999 < 0.001 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 3.958119 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 0.351 0.175,0.542
## Vres 1.408  1.181,1.55
## Vtot 1.729 1.568,1.851
## h2   0.197 0.097,0.299
## CVa  0.019 0.014,0.024
## emu  0.000     0,0.001

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 4398.772  31.3
## Gcov + Msep 4400.969  33.5
## Gsep + Msep 4397.015  29.6
## Gcov        4367.834   0.4
## Gsep        4367.461   0.0
## G + M       4600.783 233.3
## G           4592.872 225.4

Session info:

## Time difference of 75.54011 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