4.2 Multivariate genetic effects

We can simulate genetic effects affecting multiple phenotypes and the covariance between them, by specifying the number of response variables, and a covariance matrix, instead of only a variance.

squid_data <- simulate_population(
  data_structure = ped,
  pedigree = list(animal = ped),
  n_response=2,
  parameters = list(
    animal = list(
      vcov = diag(2)

    ),
    residual = list(
      vcov = diag(2)
    )
  )
)

data <- get_population_data(squid_data)
head(data)

##           y1          y2 animal_effect1 animal_effect2  residual1  residual2
## 1  0.6642658  0.83471076     0.46407220     0.22094082  0.2001936  0.6137699
## 2 -0.7466087  0.14747280     0.54421651     0.52761540 -1.2908253 -0.3801426
## 3  1.6963890 -0.40456141     0.39385325    -0.30347849  1.3025357 -0.1010829
## 4  1.9764612  0.85993234     0.08271504     0.26908060  1.8937461  0.5908517
## 5 -0.8080648 -0.09793586    -1.85489445     0.07503407  1.0468296 -0.1729699
## 6  3.0311582  0.96837367     2.32009932     0.25440902  0.7110589  0.7139646
##   animal  dam sire squid_pop
## 1    204 <NA> <NA>         1
## 2    205 <NA> <NA>         1
## 3    206 <NA> <NA>         1
## 4    207 <NA> <NA>         1
## 5    208 <NA> <NA>         1
## 6    209 <NA> <NA>         1

library(MCMCglmm)
Ainv<-inverseA(ped)$Ainv
mod <- MCMCglmm(cbind(y1,y2)~1,
  random=~us(trait):animal, 
  rcov=~us(trait):units,
  data=data,
  ginverse=list(animal=Ainv),
  family=rep("gaussian",2),
  verbose=FALSE)
summary(mod)

## 
##  Iterations = 3001:12991
##  Thinning interval  = 10
##  Sample size  = 1000 
## 
##  DIC: 32469.06 
## 
##  G-structure:  ~us(trait):animal
## 
##                        post.mean l-95% CI u-95% CI eff.samp
## traity1:traity1.animal   0.99346  0.82773   1.1631    162.4
## traity2:traity1.animal   0.01649 -0.09408   0.1259    211.7
## traity1:traity2.animal   0.01649 -0.09408   0.1259    211.7
## traity2:traity2.animal   1.06973  0.87654   1.2265    202.6
## 
##  R-structure:  ~us(trait):units
## 
##                       post.mean l-95% CI u-95% CI eff.samp
## traity1:traity1.units   1.06566   0.9433  1.21635    206.0
## traity2:traity1.units  -0.05158  -0.1421  0.04004    209.5
## traity1:traity2.units  -0.05158  -0.1421  0.04004    209.5
## traity2:traity2.units   0.97807   0.8336  1.10499    211.3
## 
##  Location effects: cbind(y1, y2) ~ 1 
## 
##             post.mean l-95% CI u-95% CI eff.samp pMCMC
## (Intercept)  -0.02171 -0.05669  0.01237    893.3 0.242