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] 13
## Cowpea Mung
## mean 5.826 6.515
## SD 0.707 0.615
## SE 0.031 0.030
## 'data.frame': 1431 obs. of 27 variables:
## $ day.mated : Factor w/ 6 levels "11.3.18","12.3.18",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ IDf : Factor w/ 246 levels "d101","d102",..: 1 1 1 1 1 2 2 2 2 2 ...
## $ IDm : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 18 20 20 20 20 20 ...
## $ ord.f : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C : int 8 8 8 8 8 3 3 3 3 3 ...
## $ pref.tot : int 13 13 13 13 13 10 10 10 10 10 ...
## $ host : Factor w/ 2 levels "C","M": 2 2 1 1 1 1 2 1 2 2 ...
## $ Whost : num 70.9 62.6 328.4 310.1 210.4 ...
## $ IDo : int 1 3 6 7 8 1 2 3 3 5 ...
## $ code : Factor w/ 1431 levels "C-101-6","C-101-7",..: 744 745 1 2 3 4 746 5 747 748 ...
## $ state : Factor w/ 1 level "emerged": 1 1 1 1 1 1 1 1 1 1 ...
## $ day.em : Factor w/ 18 levels "1.5.18","10.4.18",..: 5 4 8 6 4 5 4 5 4 4 ...
## $ dev.dur.o : int 31 30 34 32 30 31 30 31 30 30 ...
## $ Wo : num 7.98 7.79 5.99 5.55 7.03 ...
## $ sex : Factor w/ 1 level "f": 1 1 1 1 1 1 1 1 1 1 ...
## $ mated : Factor w/ 3 levels "not","succ","unsucc": 2 2 1 2 2 2 1 2 1 2 ...
## $ pref.C.o : int 0 10 NA 15 9 15 NA 18 NA 10 ...
## $ pref.tot.o: int 1 19 NA 31 13 21 NA 20 NA 19 ...
## $ day.dead : Factor w/ 41 levels "","1.5.18","10.5.18",..: 17 7 9 13 13 31 3 37 15 38 ...
## $ adsurv.o : int 38 32 30 18 20 16 28 22 38 24 ...
## $ rel.pref : num 0.615 0.615 0.615 0.615 0.615 ...
## $ rel.pref.o: num 0 0.526 NA 0.484 0.692 ...
## $ y : num 7.98 7.79 5.99 5.55 7.03 ...
## $ WH : num -0.15 -1.223 0.843 0.438 -1.764 ...
## $ PREF : num -0.402 -0.402 -0.402 -0.402 -0.402 ...
## $ date : num 3 3 3 3 3 3 3 3 3 3 ...
## $ DATE : num -0.48 -0.48 -0.48 -0.48 -0.48 ...
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 1431 246 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 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] 271 276 281 286 291 296 301 306 311 316 321 326 331 336 341 346 351 356
## [73] 361 366 371 376 381 386 391 396 401 406 411 416 421 426 431 436 441 446
## [91] 451 456 461 466 471 476 481 486 491 496
##
## Iterations = 50001:549501
## Thinning interval = 500
## Sample size = 1000
##
## DIC: 2367.27
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.1944 0.08467 0.3044 1106.5
## hostM:hostC.animal 0.1695 0.07954 0.2566 1000.0
## hostC:hostM.animal 0.1695 0.07954 0.2566 1000.0
## hostM:hostM.animal 0.2056 0.10097 0.3026 894.3
##
## ~us(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.dam 0.02218 9.057e-11 0.06484 696.3
## hostM:hostC.dam 0.01117 -8.272e-03 0.04609 856.2
## hostC:hostM.dam 0.01117 -8.272e-03 0.04609 856.2
## hostM:hostM.dam 0.02303 1.839e-08 0.06917 1003.2
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2856 0.20435 0.3553 1000.0
## hostM.units 0.1497 0.09149 0.2062 906.7
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.799811 5.673932 5.919226 1000 <0.001 ***
## hostM 0.721695 0.650185 0.799659 1000 <0.001 ***
## WH -0.053186 -0.086329 -0.021534 1000 <0.001 ***
## ord.f 0.007654 -0.038302 0.051397 1000 0.750
## DATE 0.043882 -0.020244 0.121085 1000 0.246
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 22.67681 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 0.187 0.085,0.304
## Vmat 0.001 0,0.065
## Vres 0.300 0.204,0.355
## Vtot 0.508 0.449,0.565
## m2 0.001 0,0.127
## h2 0.364 0.166,0.575
## CVa 0.081 0.051,0.095
## emu 0.005 0.002,0.009
and in the novel host type (Mung)
## Est CredI
## Vadd 0.218 0.101,0.303
## Vmat 0.001 0,0.069
## Vres 0.156 0.091,0.206
## Vtot 0.383 0.338,0.426
## m2 0.001 0,0.183
## h2 0.563 0.286,0.758
## CVa 0.071 0.049,0.085
## emu 0.005 0.002,0.007
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): 0.909 0.668,0.999
## Est CredI
## dam-related covariance novel-original 0 -0.008,0.046
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 68 76 91 121
## [1] 1 6 11 16 21 31 41 46 51 56 61 66 71 76 77 81 86 91 96
## [20] 101 106 111 116 117 121 126 131 136 146 156 161 166 171 181 191 206 211 216
## [39] 226 236 241 246 251 261 271 286 291 296 306 316
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 2345.261
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.2114 0.1123 0.2991 1000
## hostM:hostC.animal 0.1900 0.1288 0.2578 1000
## hostC:hostM.animal 0.1900 0.1288 0.2578 1000
## hostM:hostM.animal 0.2244 0.1473 0.3197 1000
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.01390 1.931e-09 0.04248 1000
## hostM.dam 0.01454 1.950e-07 0.04537 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2765 0.20849 0.3431 1000
## hostM.units 0.1409 0.08387 0.1864 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.799042 5.676729 5.910622 1000 <0.001 ***
## hostM 0.722743 0.648817 0.795778 1000 <0.001 ***
## WH -0.052684 -0.081759 -0.022051 1000 0.002 **
## ord.f 0.007579 -0.040290 0.047969 1000 0.720
## DATE 0.044323 -0.023643 0.112856 1000 0.194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 16.38587 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 0.206 0.112,0.299
## Vmat 0.000 0,0.042
## Vres 0.288 0.208,0.343
## Vtot 0.510 0.451,0.555
## m2 0.001 0,0.086
## h2 0.435 0.26,0.58
## CVa 0.078 0.059,0.095
## emu 0.006 0.003,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.217 0.147,0.32
## Vmat 0.000 0,0.045
## Vres 0.135 0.084,0.186
## Vtot 0.370 0.332,0.425
## m2 0.001 0,0.117
## h2 0.605 0.398,0.763
## CVa 0.072 0.059,0.087
## emu 0.005 0.003,0.008
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): 0.976 0.706,1
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 21 26 31 61 76 91 96 101 116 121
## [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: 2411.449
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 0.1692 0.05143 0.2939 1000.0
## hostM.animal 0.1919 0.06834 0.2938 910.7
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.02690 4.451e-15 0.08030 1000
## hostM.dam 0.03683 1.395e-07 0.09281 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.3048 0.22633 0.3794 857.6
## hostM.units 0.1547 0.09552 0.2185 1072.1
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.8027260 5.6905698 5.9117718 1000.0 <0.001 ***
## hostM 0.7045693 0.6098177 0.8197041 869.3 <0.001 ***
## WH -0.0523235 -0.0821966 -0.0234061 1000.0 <0.001 ***
## ord.f 0.0098910 -0.0331403 0.0498538 1000.0 0.614
## DATE 0.0499203 -0.0003471 0.1094014 894.7 0.076 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 13.58653 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 0.193 0.051,0.294
## Vmat 0.000 0,0.08
## Vres 0.289 0.226,0.379
## Vtot 0.491 0.443,0.558
## m2 0.001 0,0.156
## h2 0.358 0.113,0.565
## CVa 0.075 0.039,0.093
## emu 0.006 0.002,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.191 0.068,0.294
## Vmat 0.000 0,0.093
## Vres 0.136 0.096,0.218
## Vtot 0.383 0.338,0.43
## m2 0.001 0,0.236
## h2 0.647 0.196,0.74
## CVa 0.073 0.045,0.086
## emu 0.004 0.002,0.007
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] 96 101 106 111 116 121 126 131 136 141 151 156 161 166 176
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 2313.943
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.2320 0.1467 0.3170 1000.0
## hostM:hostC.animal 0.1993 0.1314 0.2591 849.9
## hostC:hostM.animal 0.1993 0.1314 0.2591 849.9
## hostM:hostM.animal 0.2443 0.1764 0.3192 1000.0
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2700 0.20063 0.3359 1000
## hostM.units 0.1347 0.07988 0.1840 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.797251 5.670608 5.921223 1000 <0.001 ***
## hostM 0.722759 0.652262 0.797482 1000 <0.001 ***
## WH -0.054207 -0.083117 -0.020647 1000 0.002 **
## ord.f 0.008582 -0.035316 0.051548 1000 0.734
## DATE 0.044150 -0.024802 0.121567 1168 0.224
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 12.78856 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 0.215 0.147,0.317
## Vres 0.255 0.201,0.336
## Vtot 0.501 0.446,0.555
## h2 0.447 0.327,0.615
## CVa 0.084 0.066,0.097
## emu 0.006 0.004,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.250 0.176,0.319
## Vres 0.134 0.08,0.184
## Vtot 0.374 0.34,0.426
## h2 0.649 0.501,0.786
## CVa 0.077 0.065,0.087
## emu 0.006 0.004,0.008
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): 0.901 0.67,0.995
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 8 16 26 31 61 76 83 91 121
## [1] 1 11 26 36 41 51 66 76
##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 2332.051
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 0.2171 0.1316 0.3156 1094
## hostM.animal 0.2522 0.1759 0.3286 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2827 0.20897 0.3512 1000
## hostM.units 0.1288 0.07784 0.1779 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.801042 5.685652 5.915364 750.9 <0.001 ***
## hostM 0.703642 0.591959 0.819169 1000.0 <0.001 ***
## WH -0.051131 -0.082260 -0.021017 1000.0 <0.001 ***
## ord.f 0.009375 -0.031008 0.050397 1000.0 0.648
## DATE 0.050695 -0.007474 0.104201 900.9 0.074 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 5.906396 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 0.198 0.132,0.316
## Vres 0.296 0.209,0.351
## Vtot 0.493 0.449,0.558
## h2 0.468 0.288,0.6
## CVa 0.083 0.062,0.096
## emu 0.006 0.004,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.257 0.176,0.329
## Vres 0.121 0.078,0.178
## Vtot 0.385 0.332,0.422
## h2 0.661 0.514,0.805
## CVa 0.078 0.066,0.089
## emu 0.006 0.004,0.008
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 96 116 121
## [1] 1 6 11 16 21 26 31 36 41
##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 2450.216
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 0.1966 0.09837 0.2929 1000
##
## ~dam
##
## post.mean l-95% CI u-95% CI eff.samp
## dam 0.01932 1.784e-09 0.05541 1000
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 0.227 0.169 0.2826 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.801509 5.694583 5.944549 1000 <0.001 ***
## hostM 0.723228 0.652827 0.785273 1000 <0.001 ***
## WH -0.057895 -0.088795 -0.025914 1000 <0.001 ***
## ord.f 0.005896 -0.036765 0.053883 1000 0.800
## DATE 0.041755 -0.036570 0.100364 1000 0.242
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 5.03205 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 0.213 0.098,0.293
## Vmat 0.000 0,0.055
## Vres 0.225 0.169,0.283
## Vtot 0.440 0.404,0.483
## m2 0.001 0,0.125
## h2 0.478 0.242,0.631
## CVa 0.079 0.057,0.095
## emu 0.006 0.003,0.009
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 61 76 91 121
## [1] 1 6 11 16
##
## Iterations = 20001:219601
## Thinning interval = 200
## Sample size = 999
##
## DIC: 2395.971
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 0.2399 0.1689 0.3092 1182
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 0.2053 0.1597 0.2522 999
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 5.802593 5.692102 5.943290 999.0 <0.001 **
## hostM 0.723308 0.661809 0.790222 808.9 <0.001 **
## WH -0.056115 -0.086096 -0.025178 999.0 0.004 **
## ord.f 0.005906 -0.040904 0.049041 999.0 0.785
## DATE 0.043964 -0.027033 0.117458 999.0 0.214
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 4.126062 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 0.237 0.169,0.309
## Vres 0.201 0.16,0.252
## Vtot 0.445 0.406,0.488
## h2 0.534 0.408,0.658
## CVa 0.084 0.071,0.095
## emu 0.007 0.005,0.009
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 2367.270 53.3
## Gcov + Msep 2345.261 31.3
## Gsep + Msep 2411.449 97.5
## Gcov 2313.943 0.0
## Gsep 2332.051 18.1
## G + M 2450.216 136.3
## G 2395.971 82.0
Session info:
## Time difference of 80.50227 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