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] 12
## Cowpea Mung
## mean 3.527 3.885
## SD 0.564 0.459
## SE 0.027 0.027
## 'data.frame': 1399 obs. of 27 variables:
## $ day.mated : Factor w/ 6 levels "11.3.18","12.3.18",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ IDf : Factor w/ 245 levels "d101","d102",..: 1 1 1 1 1 1 1 2 2 2 ...
## $ IDm : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 18 18 18 20 20 20 ...
## $ ord.f : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C : int 8 8 8 8 8 8 8 3 3 3 ...
## $ pref.tot : int 13 13 13 13 13 13 13 10 10 10 ...
## $ host : Factor w/ 2 levels "C","M": 1 1 2 1 1 1 1 2 1 1 ...
## $ Whost : num 355 357.2 77.9 293.4 327.4 ...
## $ IDo : int 1 2 2 3 4 9 10 1 2 4 ...
## $ code : Factor w/ 1399 levels "C-101-1","C-101-10",..: 1 3 776 4 5 6 2 777 7 8 ...
## $ state : Factor w/ 1 level "emerged": 1 1 1 1 1 1 1 1 1 1 ...
## $ day.em : Factor w/ 17 levels "10.4.18","11.4.18",..: 13 7 2 6 6 7 5 2 3 4 ...
## $ dev.dur.o : int 40 34 29 33 33 34 32 29 30 31 ...
## $ Wo : num 3.53 3.21 3.9 4.36 3.55 ...
## $ sex : Factor w/ 1 level "m": 1 1 1 1 1 1 1 1 1 1 ...
## $ mated : Factor w/ 2 levels "not","unsucc": 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C.o : logi NA NA NA NA NA NA ...
## $ pref.tot.o: logi NA NA NA NA NA NA ...
## $ day.dead : Factor w/ 34 levels "","1.5.18","10.5.18",..: 23 25 2 5 5 34 28 33 3 28 ...
## $ adsurv.o : int 4 12 20 27 27 23 16 27 28 17 ...
## $ rel.pref : num 0.615 0.615 0.615 0.615 0.615 ...
## $ rel.pref.o: num NA NA NA NA NA NA NA NA NA NA ...
## $ y : num 3.53 3.21 3.9 4.36 3.55 ...
## $ WH : num 1.3273 1.3741 0.8086 -0.0316 0.7169 ...
## $ PREF : num -0.425 -0.425 -0.425 -0.425 -0.425 ...
## $ date : num 3 3 3 3 3 3 3 3 3 3 ...
## $ DATE : num -0.557 -0.557 -0.557 -0.557 -0.557 ...
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 1399 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 96 116 121
## [1] 1 2 6 7 11 12 16 17 21 22 26 27 31 32 36 41 42 46
## [19] 51 52 56 57 61 62 66 67 71 72 76 77 81 82 86 87 91 92
## [37] 96 97 101 102 106 107 111 112 116 117 121 122 126 127 131 132 136 137
## [55] 141 142 146 147 151 152 156 157 161 162 166 171 172 176 177 181 182 186
## [73] 191 196 201 202 206 207 211 212 216 221 226 227 231 232 236 241 246 251
## [91] 252 256 257 261 262 266 267 271 272 276 277 281 282 286 287 291 292 296
## [109] 301 302 306 307 311 312 316 317 321 322 326 327 331 332 336 337 341 342
## [127] 346 351 352 356 357 361 362 366 367 371 372 376 377 381 382 386 387 391
## [145] 396 401 402 406 407 411 412 416 421 426 427 431 432 436 441 446 451 452
## [163] 456 457 461 462 466 471 476 477 481 482 486 491 496
##
## Iterations = 50001:549501
## Thinning interval = 500
## Sample size = 1000
##
## DIC: 1888.152
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.03430 7.113e-08 0.08811 589.4
## hostM:hostC.animal 0.02913 -4.283e-03 0.08103 370.3
## hostC:hostM.animal 0.02913 -4.283e-03 0.08103 370.3
## hostM:hostM.animal 0.03966 6.381e-09 0.10089 698.8
##
## ~us(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.dam 0.02412 1.036e-07 0.05068 831.1
## hostM:hostC.dam 0.02362 -1.346e-03 0.04799 565.7
## hostC:hostM.dam 0.02362 -1.346e-03 0.04799 565.7
## hostM:hostM.dam 0.03709 3.481e-06 0.06499 725.8
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2544 0.21359 0.2963 820.6
## hostM.units 0.1323 0.09483 0.1660 1000.0
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.493330 3.403382 3.589270 1000 <0.001 ***
## hostM 0.349294 0.289110 0.408559 1000 <0.001 ***
## WH -0.024455 -0.051627 -0.001475 1000 0.062 .
## ord.f 0.015277 -0.019217 0.050446 1000 0.396
## DATE 0.077971 0.039694 0.119903 1081 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 27.25003 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
and maternal effects variance by dam
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 0.001 0,0.088
## Vmat 0.000 0,0.051
## Vres 0.254 0.214,0.296
## Vtot 0.306 0.282,0.343
## m2 0.001 0,0.159
## h2 0.002 0,0.28
## CVa 0.063 0,0.084
## emu 0.000 0,0.007
and in the novel host type (Mung)
## Est CredI
## Vadd 0.001 0,0.101
## Vmat 0.039 0,0.065
## Vres 0.141 0.095,0.166
## Vtot 0.207 0.184,0.235
## m2 0.238 0,0.301
## h2 0.003 0,0.471
## CVa 0.050 0.002,0.083
## emu 0.000 0,0.007
additive genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
dam-related covariance between offspring in the original and novel host: \(COV_{dam(novel-original)}\) (Due to low maternal effects variance in both hosts and potential computational problems - dividing by zero; we do not estimate maternal effects correlation (\(r_{M}\)). The covariance estimate is unreliable because of the low variance too.)
## Est CredI
## genetic correlation (rG): 0.994 -0.398,1
## Est CredI
## dam-related covariance novel-original 0 -0.001,0.048
Here, we specify both separate variance per host type and the cross-environmental covariance for additive genetic (animal
) effects and separate maternal effects variance per host type without the covariance. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 96 116 121
## [1] 1 6 11 16 18 21 31 41 46 51 56 61 66 71 76 81 86 91 96
## [20] 101 106 111 116 121 126 131 136 146 156 161 166 171 181 206 211 216 226 236
## [39] 241 246 251 271 286 291 296 306 316
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 1846.674
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.07335 0.03392 0.1159 1000
## hostM:hostC.animal 0.07006 0.03527 0.1064 1000
## hostC:hostM.animal 0.07006 0.03527 0.1064 1000
## hostM:hostM.animal 0.08458 0.03519 0.1327 1000
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.005151 1.224e-08 0.01928 1145
## hostM.dam 0.013937 1.815e-08 0.03502 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2354 0.19999 0.2774 1267
## hostM.units 0.1115 0.07991 0.1439 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.499134 3.405698 3.581250 1000 <0.001 ***
## hostM 0.349914 0.292890 0.406401 1000 <0.001 ***
## WH -0.025260 -0.050919 -0.001453 1000 0.040 *
## ord.f 0.012556 -0.017473 0.047740 1000 0.462
## DATE 0.077544 0.031708 0.119848 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 14.49925 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
and maternal effects variance by dam
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 0.074 0.034,0.116
## Vmat 0.000 0,0.019
## Vres 0.234 0.2,0.277
## Vtot 0.324 0.28,0.343
## m2 0.000 0,0.06
## h2 0.216 0.11,0.361
## CVa 0.077 0.052,0.097
## emu 0.006 0.003,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.077 0.035,0.133
## Vmat 0.000 0,0.035
## Vres 0.113 0.08,0.144
## Vtot 0.208 0.185,0.235
## m2 0.001 0,0.167
## h2 0.391 0.168,0.596
## CVa 0.081 0.049,0.094
## emu 0.005 0.002,0.009
Using the additive genetic covariance between the two hosts, we estimate
genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
## Est CredI
## genetic correlation (rG): 0.968 0.743,0.998
Here, we specify separate variance per host type for both additive genetic (animal
) and maternal effects (dam
), but ignore potential cross-environmental covariances. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 96 116 121
## [1] 1 11 21 36 46 56 61 71 81 96 106 116 121 131 141 156 166 176
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 1933.455
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 0.03264 6.939e-07 0.08216 1000
## hostM.animal 0.02590 3.784e-07 0.07850 1000
##
## ~idh(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.dam 0.0216 5.016e-08 0.04912 1115
## hostM.dam 0.0436 1.249e-02 0.07041 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2585 0.2127 0.2960 1000.0
## hostM.units 0.1405 0.1059 0.1656 980.4
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.5036689 3.4200419 3.5856675 1106 <0.001 ***
## hostM 0.3391408 0.2684447 0.4068880 1432 <0.001 ***
## WH -0.0248635 -0.0504194 -0.0009484 1000 0.046 *
## ord.f 0.0124326 -0.0185429 0.0424433 1097 0.450
## DATE 0.0786300 0.0428712 0.1130780 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 11.62689 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
and maternal effects variance by dam
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 0.001 0,0.082
## Vmat 0.000 0,0.049
## Vres 0.259 0.213,0.296
## Vtot 0.316 0.279,0.343
## m2 0.001 0,0.154
## h2 0.002 0,0.261
## CVa 0.067 0,0.081
## emu 0.000 0,0.007
and in the novel (Mung)
## Est CredI
## Vadd 0.000 0,0.079
## Vmat 0.049 0.012,0.07
## Vres 0.136 0.106,0.166
## Vtot 0.203 0.185,0.235
## m2 0.253 0.077,0.335
## h2 0.003 0,0.373
## CVa 0.041 0,0.072
## emu 0.000 0,0.005
Here, we specify both separate variance per host type and cross-environmental covariance for additive genetic (animal
). Maternal effects are ignored. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 121
## [1] 1 6 11 16 21 31 36 37 41 42 46 51 56 61 66 67 71 72 76
## [20] 81 86 91 96 101 106 116 121 126 131 141 156 161 166 176
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 1824.573
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.07695 0.03384 0.1139 1000.0
## hostM:hostC.animal 0.08130 0.05282 0.1136 638.1
## hostC:hostM.animal 0.08130 0.05282 0.1136 638.1
## hostM:hostM.animal 0.10710 0.06830 0.1479 1000.0
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2360 0.19756 0.2720 1000
## hostM.units 0.1042 0.07395 0.1355 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.4985515 3.4089176 3.5838330 1000 <0.001 ***
## hostM 0.3545428 0.2985594 0.4081838 1000 <0.001 ***
## WH -0.0259423 -0.0493593 -0.0007006 1279 0.032 *
## ord.f 0.0124301 -0.0178987 0.0455109 1000 0.440
## DATE 0.0769923 0.0284104 0.1186582 1096 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 12.4481 mins
We calculate heritability and evolvability based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
. Maternal effects variance is ignored.
Additive genetic variance: \(V_{A} = V_{animal}\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 0.070 0.034,0.114
## Vres 0.231 0.198,0.272
## Vtot 0.310 0.282,0.343
## h2 0.225 0.122,0.358
## CVa 0.075 0.058,0.1
## emu 0.006 0.003,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.103 0.068,0.148
## Vres 0.100 0.074,0.136
## Vtot 0.211 0.186,0.236
## h2 0.513 0.355,0.669
## CVa 0.082 0.067,0.099
## emu 0.007 0.005,0.01
Using the additive genetic covariance between the two hosts, we estimate
genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
## Est CredI
## genetic correlation (rG): 0.996 0.75,1
Here, we specify separate variance per host type for additive genetic (animal
) effects only, but ignore potential cross-environmental covariance. Maternal effects were also ignored. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 121
## [1] 1 11 26 36 41 51 66 76
##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 1870.876
##
## G-structure: ~idh(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.animal 0.06443 0.02200 0.1135 1000
## hostM.animal 0.10458 0.06315 0.1509 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.2484 0.20493 0.2957 1000.0
## hostM.units 0.1073 0.07716 0.1417 829.1
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.504e+00 3.424e+00 3.588e+00 905.2 <0.001 ***
## hostM 3.455e-01 2.654e-01 4.250e-01 1000.0 <0.001 ***
## WH -2.637e-02 -5.039e-02 4.011e-05 913.0 0.044 *
## ord.f 1.228e-02 -1.842e-02 3.978e-02 1000.0 0.418
## DATE 7.800e-02 4.462e-02 1.179e-01 1000.0 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 5.782449 mins
We calculate heritability and evolvability based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
.
Additive genetic variance: \(V_{A} = V_{animal}\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{M} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates in the original host type (Cowpea)
## Est CredI
## Vadd 0.053 0.022,0.114
## Vres 0.256 0.205,0.296
## Vtot 0.319 0.283,0.348
## h2 0.189 0.082,0.359
## CVa 0.076 0.045,0.097
## emu 0.004 0.002,0.009
and in the novel (Mung)
## Est CredI
## Vadd 0.102 0.063,0.151
## Vres 0.110 0.077,0.142
## Vtot 0.207 0.183,0.237
## h2 0.504 0.314,0.653
## CVa 0.082 0.065,0.1
## emu 0.007 0.004,0.01
Here, we estimate variance for both additive genetic (animal
) and maternal effects (dam
), but ignore their potential host-specificity and the cross-environmental covariances. We estimate residual variance (units
) across host types.
## [1] 1 6 16 26 31 61 76 91 121
## [1] 1 6 11 16 21 26 31 36 41
##
## Iterations = 20001:219801
## Thinning interval = 200
## Sample size = 1000
##
## DIC: 1940.508
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 0.04356 9.221e-07 0.09282 1161
##
## ~dam
##
## post.mean l-95% CI u-95% CI eff.samp
## dam 0.02458 6.056e-07 0.04619 1170
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 0.1963 0.1635 0.2252 1000
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.499216 3.414120 3.595284 1000 <0.001 ***
## hostM 0.353252 0.297721 0.398446 1000 <0.001 ***
## WH -0.032475 -0.057759 -0.008173 1000 0.010 **
## ord.f 0.012576 -0.017704 0.052700 1000 0.474
## DATE 0.078664 0.038758 0.123447 1000 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 4.834484 mins
We calculate heritability, evolvability and maternal effects proportion based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
. Maternal effects variance is ignored.
Additive genetic variance: \(V_{A} = V_{animal}\)
Maternal effects above the additive genetic effects: \(V_M = V_{dam}\)
Maternal effects proportion: \(m^2 = V_{M}/(V_{A} + V_{M} + V_{residual})\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates across the two host types
## Est CredI
## Vadd 0.041 0,0.093
## Vmat 0.024 0,0.046
## Vres 0.197 0.164,0.225
## Vtot 0.264 0.244,0.286
## m2 0.088 0,0.172
## h2 0.113 0,0.34
## CVa 0.058 0.012,0.091
## emu 0.003 0,0.007
Here, we specify additive genetic (animal
) effects only, ignore maternal effects or host-specificity. We estimate residual variance (units
) across host types.
## [1] 1 6 16 26 31 46 61 66 76 86 91 96 106 116 121
## [1] 1 6 11 16
##
## Iterations = 20001:219601
## Thinning interval = 200
## Sample size = 999
##
## DIC: 1903.341
##
## G-structure: ~animal
##
## post.mean l-95% CI u-95% CI eff.samp
## animal 0.0931 0.06136 0.129 999
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 0.1738 0.1468 0.2015 1038
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 3.50177 3.41333 3.59193 999 <0.001 **
## hostM 0.35537 0.30649 0.41029 999 <0.001 **
## WH -0.03147 -0.05745 -0.00642 1205 0.018 *
## ord.f 0.01042 -0.02360 0.04374 999 0.535
## DATE 0.07770 0.02790 0.11974 999 0.004 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 3.937672 mins
We calculate heritability and evolvability based on the minimal model, i.e. after accounting for the design effects (bean mass, dam mating order, day mated). Additive genetic variance is given by animal
. Maternal effects variance is ignored.
Additive genetic variance: \(V_{A} = V_{animal}\)
Heritability: \(h^{2} = V_{A}/(V_{A} + V_{residual})\)
Coef. of add. gen. variation: \(CV_{A} = \sqrt{V_{A}}/\overline{y}\)
Evolvability: \(e_{\mu} = V_{A}/\overline{y}^2\), or \(e_{\mu} = CV_{A}^2\)
Parameter estimates across both host types
## Est CredI
## Vadd 0.089 0.061,0.129
## Vres 0.168 0.147,0.202
## Vtot 0.264 0.246,0.289
## h2 0.341 0.234,0.458
## CVa 0.087 0.07,0.102
## emu 0.007 0.005,0.01
The DIC of the alternative models. We base our inference on the best-selected models (lowest AIC within 2 unit difference).
## DIC delta
## Gcov + Mcov 1888.152 63.6
## Gcov + Msep 1846.674 22.1
## Gsep + Msep 1933.455 108.9
## Gcov 1824.573 0.0
## Gsep 1870.876 46.3
## G + M 1940.508 115.9
## G 1903.341 78.8
Session info:
## Time difference of 80.37887 mins
## R version 4.0.0 (2020-04-24)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
##
## Matrix products: default
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] QGglmm_0.7.4 MCMCglmm_2.29 ape_5.3 coda_0.19-3 scales_1.1.1
## [6] MuMIn_1.43.17 lme4_1.1-23 Matrix_1.2-18
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.4.6 compiler_4.0.0 nloptr_1.2.2.1 tools_4.0.0
## [5] boot_1.3-24 digest_0.6.25 statmod_1.4.34 evaluate_0.14
## [9] lifecycle_0.2.0 nlme_3.1-147 lattice_0.20-41 rlang_0.4.6
## [13] yaml_2.2.1 parallel_4.0.0 xfun_0.14 stringr_1.4.0
## [17] knitr_1.28 stats4_4.0.0 grid_4.0.0 R6_2.4.1
## [21] rmarkdown_2.2 tensorA_0.36.1 minqa_1.2.4 corpcor_1.6.9
## [25] magrittr_1.5 htmltools_0.4.0 MASS_7.3-51.5 splines_4.0.0
## [29] colorspace_1.4-1 cubature_2.0.4 stringi_1.4.6 munsell_0.5.0
END