Load libraries and read the full dataset (N = 3 431). We remove entries from dams for which host preference was not recorded.
## Cowpea Mung
## Larval survival rate 0.889 0.93
## 'data.frame': 3146 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/ 249 levels "d101","d102",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ IDm : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 18 18 18 18 18 18 ...
## $ ord.f : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C : int 8 8 8 8 8 8 8 8 8 8 ...
## $ pref.tot : int 13 13 13 13 13 13 13 13 13 13 ...
## $ host : Factor w/ 2 levels "C","M": 1 2 1 2 1 2 1 1 1 1 ...
## $ Whost : num 355 70.9 357.2 77.9 293.4 ...
## $ IDo : int 1 1 2 2 3 3 4 5 6 7 ...
## $ code : Factor w/ 3146 levels "C-101-1","C-101-10",..: 1 1728 3 1729 4 1730 5 6 7 8 ...
## $ state : Factor w/ 2 levels "dead","emerged": 2 2 2 2 2 2 2 1 2 2 ...
## $ day.em : Factor w/ 23 levels "","1.5.18","10.4.18",..: 16 6 9 4 8 5 8 1 9 7 ...
## $ dev.dur.o : int 40 31 34 29 33 30 33 NA 34 32 ...
## $ Wo : num 3.53 7.98 3.21 3.9 4.36 ...
## $ sex : Factor w/ 3 levels "","f","m": 3 2 3 3 3 2 3 1 2 2 ...
## $ mated : Factor w/ 4 levels "","not","succ",..: 2 3 2 2 2 3 2 1 2 3 ...
## $ pref.C.o : int NA 0 NA NA NA 10 NA NA NA 15 ...
## $ pref.tot.o: int NA 1 NA NA NA 19 NA NA NA 31 ...
## $ day.dead : Factor w/ 45 levels "","1.5.18","10.5.18",..: 30 21 34 2 5 8 5 1 11 17 ...
## $ adsurv.o : int 4 38 12 20 27 32 27 NA 30 18 ...
## $ rel.pref : num 0.615 0.615 0.615 0.615 0.615 ...
## $ rel.pref.o: num NA 0 NA NA NA ...
## $ y : Factor w/ 2 levels "dead","emerged": 2 2 2 2 2 2 2 1 2 2 ...
## $ WH : num 1.36933 -0.16654 1.41634 0.76934 0.00367 ...
## $ PREF : num -0.408 -0.408 -0.408 -0.408 -0.408 ...
## $ date : num 3 3 3 3 3 3 3 3 3 3 ...
## $ DATE : num -0.511 -0.511 -0.511 -0.511 -0.511 ...
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 3146 249 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). Note that in the binomial model, residual variance is fixed to 1 (see priors), so the model becomes estimable.
Below, we provide outcome for the best-selected model structure in the continuous traits (Gcov) and for comparison also the estimates from the most complex saturated model (Gcov + Mcov).
Here, we specify both separate variance per host type and cross-environmental covariance for additive genetic (animal
). Maternal effects are ignored. Residual variance (units
) is set to 1 (fix=1
).
## Time difference of 8.303483 hours
## [1] 1 6 11 16 26 31 41 51 61 76 81 91 121
## [1] 1 6 11 26 31 36 41 51 56 61 66 81 86 91
##
## Iterations = 500001:5490001
## Thinning interval = 5000
## Sample size = 999
##
## DIC: 1839.752
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 1.2854 6.402e-02 2.722 999.0
## hostM:hostC.animal 0.2958 -6.094e-01 1.195 936.7
## hostC:hostM.animal 0.2958 -6.094e-01 1.195 936.7
## hostM:hostM.animal 1.3671 7.282e-06 3.534 835.0
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 1 1 1 0
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 2.871323 2.347545 3.377522 1115 <0.001 **
## hostM 0.608837 -0.110407 1.398235 999 0.0821 .
## WH -0.168751 -0.311231 -0.001735 999 0.0280 *
## ord.f -0.028113 -0.188128 0.126334 999 0.7508
## DATE 0.081407 -0.098633 0.259491 999 0.3864
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Copy-friendly output of the ‘minimal’ model:
## Par Est 95% CredI
## 1 hostC:hostC.animal 0.916 0.064,2.722
## 2 hostM:hostC.animal 0.002 -0.609,1.195
## 3 hostC:hostM.animal 0.002 -0.609,1.195
## 4 hostM:hostM.animal 0.804 0,3.534
## 5 units 1 1,1
## 6 (Intercept) 2.782 2.348,3.378
## 7 hostM 0.631 -0.11,1.398
## 8 WH -0.159 -0.311,-0.002
## 9 ord.f -0.071 -0.188,0.126
## 10 DATE 0.095 -0.099,0.259
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 0.916 0.064,2.722
## Vres 1.000 1,1
## Vtot 1.916 1.064,3.722
## h2 0.608 0.222,0.794
## CVa 1.401 0.524,2.004
## emu 1.159 0.081,3.444
## [1] "Raw scale estimates (QGparams):"
## [1] "Computing observed mean..."
## [1] "Computing variances..."
## [1] "Computing Psi..."
## Est
## mean 0.894
## Vtot 0.094
## Vadd 0.006
## h2 0.060
## CVa 0.084
## emu 0.007
and in the novel (Mung)
## Est CredI
## Vadd 0.804 0,3.534
## Vres 1.000 1,1
## Vtot 1.804 1,4.534
## h2 0.624 0.06,0.821
## CVa 1.072 0.189,2.149
## emu 0.929 0,4.086
## [1] "Raw scale estimates (QGparams):"
## [1] "Computing observed mean..."
## [1] "Computing variances..."
## [1] "Computing Psi..."
## Est
## mean 0.930
## Vtot 0.065
## Vadd 0.003
## h2 0.040
## CVa 0.055
## emu 0.003
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): 0.286 -0.469,0.985
Here, we specify both separate variance per host type and the cross-environmental covariance for both additive genetic (animal
) and maternal effects (dam
). Residual variance (units
) is set to 1 (fix=1
).
## Time difference of 8.757259 hours
## [1] 1 6 16 26 31 41 61 76 81 91 96 116 121
## [1] 1 6 11 21 26 31 46 51 56 61 66 71 76 81 91 96 101 106 111
## [20] 116 121 126 141 146 151 161 166 171 181 186 191 201 206 211 226 231 236 241
## [39] 246 251 256 261 271 276 281 286 291 296 301 306 321 326 331 341 346 351
##
## Iterations = 500001:5490001
## Thinning interval = 5000
## Sample size = 999
##
## DIC: 1844.241
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 0.6477 1.719e-06 1.9181 999
## hostM:hostC.animal 0.1164 -4.693e-01 0.9724 999
## hostC:hostM.animal 0.1164 -4.693e-01 0.9724 999
## hostM:hostM.animal 1.0430 6.940e-05 2.8938 999
##
## ~us(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.dam 0.39513 1.497e-06 0.9036 999.0
## hostM:hostC.dam 0.09348 -1.735e-01 0.4480 999.0
## hostC:hostM.dam 0.09348 -1.735e-01 0.4480 999.0
## hostM:hostM.dam 0.24102 1.196e-08 0.8159 908.1
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 1 1 1 0
##
## Location effects: y ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 2.80187 2.29494 3.32137 999.0 <0.001 **
## hostM 0.64095 0.02194 1.44672 999.0 0.046 *
## WH -0.16596 -0.31633 -0.01136 999.0 0.042 *
## ord.f -0.02278 -0.19663 0.14358 781.4 0.791
## DATE 0.08889 -0.09198 0.26299 1069.1 0.350
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Copy-friendly output of the ‘minimal’ model:
## Par Est 95% CredI
## 1 hostC:hostC.animal 0.01 0,1.918
## 2 hostM:hostC.animal 0.002 -0.469,0.972
## 3 hostC:hostM.animal 0.002 -0.469,0.972
## 4 hostM:hostM.animal 0.012 0,2.894
## 5 hostC:hostC.dam 0.006 0,0.904
## 6 hostM:hostC.dam -0.001 -0.174,0.448
## 7 hostC:hostM.dam -0.001 -0.174,0.448
## 8 hostM:hostM.dam 0.006 0,0.816
## 9 units 1 1,1
## 10 (Intercept) 2.776 2.295,3.321
## 11 hostM 0.612 0.022,1.447
## 12 WH -0.208 -0.316,-0.011
## 13 ord.f -0.038 -0.197,0.144
## 14 DATE 0.102 -0.092,0.263
We calculate heritability, evolvability and maternal effects 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: \(V_{A} = V_{animal}\)
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 0.010 0,1.918
## Vmat 0.006 0,0.904
## Vres 1.000 1,1
## Vtot 1.524 1.152,3.262
## m2 0.002 0,0.443
## h2 0.004 0,0.631
## CVa 0.466 0.004,1.559
## emu 0.012 0,2.427
## [1] "Raw scale estimates (QGparams):"
## [1] "Computing observed mean..."
## [1] "Computing variances..."
## [1] "Computing Psi..."
## Est
## mean 0.903
## Vtot 0.087
## Vadd 0.000
## h2 0.001
## CVa 0.008
## emu 0.000
and in the novel (Mung)
## Est CredI
## Vadd 0.012 0,2.894
## Vmat 0.006 0,0.816
## Vres 1.000 1,1
## Vtot 1.448 1.01,4.054
## m2 0.002 0,0.368
## h2 0.003 0,0.722
## CVa 1.109 0.009,1.829
## emu 0.014 0,3.346
## [1] "Raw scale estimates (QGparams):"
## [1] "Computing observed mean..."
## [1] "Computing variances..."
## [1] "Computing Psi..."
## Est
## mean 0.943
## Vtot 0.054
## Vadd 0.000
## h2 0.001
## CVa 0.006
## emu 0.000
Using the additive genetic covariance between the two hosts, we estimate
genetic correlation: \(r_{G} = COV_{A(novel-original)}/\sqrt{(V_{A(novel)}V_{A(orignal)})}\)
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): 0.505 -0.825,1
## Est CredI
## dam-related covariance novel-original -0.001 -0.174,0.448
In the full model, we test the effect of novel host type (Prediction 3) and dam host preference on offspring performance (Prediction 4). The full model includes all the terms from the minimal model: host type (host
, original/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). We added dam host preference (PREF
, the relative preference ratio of cowpea: 0-1) along with its interaction with host type dam host preference:host (PREF:host
). This interaction tested if effect of the strength of preference for the original host on offspring traits differs depending on the host type. We also included interactions between host type and bean mass bean mass:host (WH:host
), as well as host type and day mated day mated:host (DATE:host
), as fixed effects to test for potential host-specific influences.
The random effects structure follows that of the best-selected minimal model for all the continuous traits (Gcov) and omitted maternal effects as they proved to be negligible in the traits we study (see also the Gcov + Mcov model above). Additive genetic variance is specified using the pedigree and the identity of the offspring as animal
in the random-effects part of the model. We defined random effects for each host separately as interaction with host
- animal (us(host):animal
) where ‘us’ - unstructured
also modeled additive genetic covariance to estimate the correlation (\(r_{G}\)). Residual variation was was fixed to 1.
## Time difference of 10.04946 hours
## [1] 1 6 11 16 26 46 51 76 91 101 121 136 151 201 216 226 251 266 276
## [20] 281 301 336 351 386 401
## [1] 1 6 11 26 31 36 41 51 56 61 66 81 86 91
##
## Iterations = 500001:5490001
## Thinning interval = 5000
## Sample size = 999
##
## DIC: 1840.441
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 1.3832 0.002722 2.918 999.0
## hostM:hostC.animal 0.3271 -0.527271 1.329 869.1
## hostC:hostM.animal 0.3271 -0.527271 1.329 869.1
## hostM:hostM.animal 1.3372 0.000031 3.497 906.3
##
## R-structure: ~units
##
## post.mean l-95% CI u-95% CI eff.samp
## units 1 1 1 0
##
## Location effects: y ~ host + WH + ord.f + DATE + PREF + WH:host + DATE:host + PREF:host
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) 2.90516 2.34052 3.44057 999.0 <0.001 **
## hostM 0.60032 -0.09438 1.44721 999.0 0.0901 .
## WH -0.14395 -0.35315 0.04967 941.5 0.1682
## ord.f -0.02821 -0.20611 0.12442 999.0 0.7568
## DATE 0.13502 -0.15314 0.35020 999.0 0.2583
## PREF -0.04355 -0.25807 0.18346 999.0 0.7107
## hostM:WH -0.06797 -0.37605 0.22138 1096.5 0.6787
## hostM:DATE -0.14829 -0.50116 0.24034 999.0 0.4044
## hostM:PREF 0.20597 -0.10636 0.54910 999.0 0.2202
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Copy-friendly output of the ‘full’ model:
## Par Est 95% CredI
## 1 hostC:hostC.animal 0.693 0.003,2.918
## 2 hostM:hostC.animal 0.011 -0.527,1.329
## 3 hostC:hostM.animal 0.011 -0.527,1.329
## 4 hostM:hostM.animal 0.007 0,3.497
## 5 units 1 1,1
## 6 (Intercept) 2.868 2.341,3.441
## 7 hostM 0.512 -0.094,1.447
## 8 WH -0.161 -0.353,0.05
## 9 ord.f -0.021 -0.206,0.124
## 10 DATE 0.095 -0.153,0.35
## 11 PREF -0.042 -0.258,0.183
## 12 hostM:WH -0.035 -0.376,0.221
## 13 hostM:DATE -0.122 -0.501,0.24
## 14 hostM:PREF 0.242 -0.106,0.549
Session info:
## Time difference of 27.1102 hours
## 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