This file is to be used with the continuous life-history traits from the study (duration of larval development, body mass and adult lifespan). We alternate between analyses of respective traits through assigning them into the response variable y
.
Load libraries and read the full dataset (N = 3 431). We analyse data on female and male offspring separately due to the profound sexual dimorphism in seed beetle life history. We remove offspring of dams for which host preference was not recorded. We also exclude outliers in the response variable that are larger than 3-times trait SD.
## [1] "The number of removed missing and outlier values:"
## [1] 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 ...
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 1384 245 82
The minimal model contains only fixed effects stemming from our experimental design. The fixed effects are: host type (host
, “C” (original)/“M” (novel)), bean mass (WH
, standardized within each host type), dam mating order (ord.f
, mating sequence, 1 to 4), and day mated (DATE
, 1-6). Additive genetic variance is specified using the pedigree and the identity of the offspring as animal
in the random-effect part. Maternal effects above the additive genetic variance (including non-genetic and genetic maternal effects, but also genetic dominance) is specified with calling dam
in the random-effect part of the model. We defined the random effects for each host separately as interaction with host
- animal (host:animal
) and dam (host:dam
). We extracted additive genetic (proxy of GxE) and maternal effects covariance (MxE) between novel and original host using term us
(unstructured). We called host-specific variance only (with idh
) in the models where we ignore covariance between the additive genetic (or maternal) effects in different host types. Residual variance was allowed to be estimated separately per host type (rcov=~idh(host):units
).
Below, we provide outcome for each of the alternative models that estimate additive genetic variance and maternal effects differently per host. They include/exclude specific variance per host type and the cross-host covariance.
Here, we specify both separate variance per host type and the cross-environmental covariance for both additive genetic (animal
) and maternal effects (dam
). We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 121
## [1] 1 6 11 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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