Load libraries and read the full dataset (N = 3 431) of which we recorded host preference for 665 daughters. We remove offspring of dams for which host preference was not recorded.
## Cowpea Mung
## Daughter preference of Cowpea 0.681 0.517
## 'data.frame': 665 obs. of 26 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/ 239 levels "d101","d102",..: 1 1 1 1 2 2 2 2 3 3 ...
## $ IDm : Factor w/ 82 levels "s11","s12","s13",..: 18 18 18 18 20 20 20 20 21 21 ...
## $ ord.f : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C : int 8 8 8 8 3 3 3 3 13 13 ...
## $ pref.tot : int 13 13 13 13 10 10 10 10 14 14 ...
## $ host : Factor w/ 2 levels "C","M": 2 2 1 1 1 1 2 2 1 1 ...
## $ Whost : num 70.9 62.6 310.1 210.4 332 ...
## $ IDo : int 1 3 7 8 1 3 5 6 2 5 ...
## $ code : Factor w/ 665 levels "C-101-7","C-101-8",..: 365 366 1 2 3 4 367 368 5 6 ...
## $ 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",..: 4 3 5 3 4 4 3 3 3 4 ...
## $ dev.dur.o : int 31 30 32 30 31 31 30 30 30 31 ...
## $ Wo : num 7.98 7.79 5.55 7.03 4.32 ...
## $ sex : Factor w/ 1 level "f": 1 1 1 1 1 1 1 1 1 1 ...
## $ mated : Factor w/ 1 level "succ": 1 1 1 1 1 1 1 1 1 1 ...
## $ pref.C.o : int 0 10 15 9 15 18 10 3 7 13 ...
## $ pref.tot.o: int 1 19 31 13 21 20 19 12 13 24 ...
## $ day.dead : Factor w/ 35 levels "","1.5.18","10.5.18",..: 17 7 13 13 27 31 32 30 31 26 ...
## $ adsurv.o : int 38 32 18 20 16 22 24 22 23 15 ...
## $ rel.pref : num 0.615 0.615 0.615 0.615 0.3 ...
## $ rel.pref.o: num 0 0.526 0.484 0.692 0.714 ...
## $ WH : num -0.113 -1.168 0.48 -1.75 0.97 ...
## $ PREF : num -0.38 -0.38 -0.38 -0.38 -1.63 ...
## $ date : num 3 3 3 3 3 3 3 3 3 3 ...
## $ DATE : num -0.489 -0.489 -0.489 -0.489 -0.489 ...
We have dams, sires and their offspring, i.e. parental and offspring generation.
## offspring dams sires
## 1 665 239 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). Residual variance was allowed to be estimated separately per host type (rcov=~idh(host):units
).
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. We estimate residual variance (units
) separately per each host type.
## [1] 1 6 16 26 31 61 76 91 96 116 121
## [1] 1 36 41 46 66 71 76 96 101 106 141 176
##
## Iterations = 60001:359701
## Thinning interval = 300
## Sample size = 1000
##
## DIC: 19846.32
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 1.056e-03 3.146e-09 0.003833 1000
## hostM:hostC.animal 2.498e-05 -1.386e-03 0.001191 1000
## hostC:hostM.animal 2.498e-05 -1.386e-03 0.001191 1000
## hostM:hostM.animal 1.244e-03 2.775e-09 0.004807 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.02983 0.02030 0.04032 1160
## hostM.units 0.03480 0.02322 0.04848 1000
##
## Location effects: cbind(pref.C.o, pref.tot.o) ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) -0.434883 -0.527074 -0.351040 1000 <0.001 ***
## hostM -0.247735 -0.330321 -0.181139 1000 <0.001 ***
## WH 0.005534 -0.029727 0.042473 1000 0.778
## ord.f 0.008708 -0.022501 0.049018 1000 0.640
## DATE -0.049622 -0.088381 -0.013052 1185 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 7.456047 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 0.000 0,0.004
## Vres 0.029 0.02,0.04
## Vtot 0.030 0.021,0.043
## h2 0.001 0,0.119
## CVa 0.010 0,0.12
## emu 0.000 0,0.014
## [1] "Raw scale estimates (QGparams):"
## [1] "Using the closed forms for a Poisson - log model."
## mean.obs var.obs var.a.obs h2.obs
## 1 0.6574141 0.6709698 0.0004565064 0.000680368
and in the novel (Mung)
## Est CredI
## Vadd 0.000 0,0.005
## Vres 0.035 0.023,0.048
## Vtot 0.036 0.024,0.05
## h2 0.001 0,0.126
## CVa 0.008 0,0.134
## emu 0.000 0,0.018
## [1] "Raw scale estimates (QGparams):"
## [1] "Using the closed forms for a Poisson - log model."
## mean.obs var.obs var.a.obs h2.obs
## 1 0.5144804 0.5241939 0.001317166 0.002512746
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): -0.046 -0.905,0.948
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 11 16 21 26 31 51 61 66 76 86 91 96 101 107 116 121
## [1] 1 6 11 51 56 61 66 101 106 111 116 156 161 166 221 276 281 326 331
## [20] 386 441 496
##
## Iterations = 50001:549501
## Thinning interval = 500
## Sample size = 1000
##
## DIC: 19849.88
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 9.572e-04 5.566e-10 0.003374 1000
## hostM:hostC.animal 2.797e-05 -1.358e-03 0.001604 1153
## hostC:hostM.animal 2.797e-05 -1.358e-03 0.001604 1153
## hostM:hostM.animal 1.335e-03 3.947e-08 0.005335 1000
##
## ~us(host):dam
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.dam 9.455e-04 5.859e-11 0.003675 1000
## hostM:hostC.dam 1.356e-05 -1.402e-03 0.001443 1146
## hostC:hostM.dam 1.356e-05 -1.402e-03 0.001443 1146
## hostM:hostM.dam 1.250e-03 8.811e-10 0.004600 1000
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.02966 0.02064 0.03986 924.3
## hostM.units 0.03446 0.02189 0.04787 1000.0
##
## Location effects: cbind(pref.C.o, pref.tot.o) ~ host + WH + ord.f + DATE
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) -0.435620 -0.525712 -0.337571 1000 <0.001 ***
## hostM -0.248258 -0.323750 -0.182367 1000 <0.001 ***
## WH 0.005825 -0.032325 0.042212 1000 0.770
## ord.f 0.008673 -0.029079 0.043008 1000 0.638
## DATE -0.048329 -0.080627 -0.007699 1000 0.020 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Time difference of 13.7619 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
.
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 in the original host type (Cowpea)
## Est CredI
## Vadd 0.000 0,0.003
## Vmat 0.000 0,0.004
## Vres 0.027 0.021,0.04
## Vtot 0.028 0.022,0.042
## m2 0.000 0,0.111
## h2 0.000 0,0.107
## CVa 0.016 0,0.113
## emu 0.000 0,0.013
## [1] "Raw scale estimates (QGparams):"
## [1] "Using the closed forms for a Poisson - log model."
## mean.obs var.obs var.a.obs h2.obs
## 1 0.6571536 0.6710023 0.0004133827 0.0006160675
and in the novel (Mung)
## Est CredI
## Vadd 0.000 0,0.005
## Vmat 0.000 0,0.005
## Vres 0.032 0.022,0.048
## Vtot 0.033 0.025,0.053
## m2 0.001 0,0.116
## h2 0.001 0,0.141
## CVa 0.010 0,0.141
## emu 0.000 0,0.02
## [1] "Raw scale estimates (QGparams):"
## [1] "Using the closed forms for a Poisson - log model."
## mean.obs var.obs var.a.obs h2.obs
## 1 0.5140896 0.5240625 0.001410833 0.002692108
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): -0.022 -0.898,0.999
## Est CredI
## dam-related covariance novel-original 0 -0.001,0.001
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 allowed to be estimated separately per host type (rcov=~idh(host):units
).
## Time difference of 12.50469 mins
## [1] 1 6 16 46 51 101 121 136 151 156 196 201 206 216 246 251 266 281 301
## [20] 336 351 386 401
## [1] 1 36 41 66 71 106 141 176
##
## Iterations = 50001:549501
## Thinning interval = 500
## Sample size = 1000
##
## DIC: 19853.27
##
## G-structure: ~us(host):animal
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC:hostC.animal 9.256e-04 1.446e-10 0.003368 1000.0
## hostM:hostC.animal 3.521e-05 -1.317e-03 0.001385 1157.4
## hostC:hostM.animal 3.521e-05 -1.317e-03 0.001385 1157.4
## hostM:hostM.animal 1.298e-03 2.496e-09 0.005600 904.4
##
## R-structure: ~idh(host):units
##
## post.mean l-95% CI u-95% CI eff.samp
## hostC.units 0.02959 0.01960 0.04022 1000.0
## hostM.units 0.03421 0.02225 0.04594 906.5
##
## Location effects: cbind(pref.C.o, pref.tot.o) ~ host + WH + ord.f + DATE + PREF + WH:host + DATE:host + PREF:host
##
## post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept) -0.4333866 -0.5277276 -0.3381198 1592 <0.001 ***
## hostM -0.2491236 -0.3241015 -0.1802623 1000 <0.001 ***
## WH 0.0003389 -0.0463467 0.0491787 1000 0.980
## ord.f 0.0080676 -0.0270372 0.0470594 1000 0.690
## DATE -0.0507864 -0.0936524 0.0035481 1000 0.048 *
## PREF 0.0084391 -0.0414349 0.0571935 1000 0.732
## hostM:WH 0.0108014 -0.0748511 0.0761709 1000 0.760
## hostM:DATE 0.0035927 -0.0661617 0.0831093 1000 0.942
## hostM:PREF -0.0258098 -0.0956927 0.0494892 1000 0.502
## ---
## 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 0,0.003
## 2 hostM:hostC.animal 0 -0.001,0.001
## 3 hostC:hostM.animal 0 -0.001,0.001
## 4 hostM:hostM.animal 0 0,0.006
## 5 hostC.units 0.029 0.02,0.04
## 6 hostM.units 0.032 0.022,0.046
## 7 (Intercept) -0.409 -0.528,-0.338
## 8 hostM -0.247 -0.324,-0.18
## 9 WH 0.01 -0.046,0.049
## 10 ord.f -0.001 -0.027,0.047
## 11 DATE -0.053 -0.094,0.004
## 12 PREF 0.014 -0.041,0.057
## 13 hostM:WH 0.017 -0.075,0.076
## 14 hostM:DATE -0.016 -0.066,0.083
## 15 hostM:PREF -0.037 -0.096,0.049
Session info:
## Time difference of 33.72263 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