#Title:
#Authors: Mads F. Schou
#Date: 23/09/2020

#------- 1. Random regression models
# 1a. Egg laying
# 1b. Egg mass
# 1c. Chick hathcing
# 1d. Number of offspring
# 1e. Number of sperm
# 1f. Sperm viability

#------- 2. Random regression models with year-specific slopes
# 2a. Egg laying
# 2b. Egg mass
# 2c. Number of sperm
# 2d. Sperm viability
# 2e. Repeatabilitites
# 2f. PSlopeVar

#------- 3. Character-state models
# 3a. Egg laying
# 3b. Egg mass
# 3c. Chick hathcing
# 3d. Number of offspring
# 3e. Number of sperm
# 3f. Sperm viability

#------- 4. Bivariate (two-trait) models
# 4a. Egg laying vs Egg mass using character-state model
# 4b. Egg laying vs Egg mass using random regression model
# 4c. Number of sperm vs Sperm viability using character-state model
# 4d. Number of sperm vs Sperm viability using random regression model


#############################################################
# 1. Random regression models
#############################################################

Myprior <- list(
  R=list(V = diag(1), nu=0.002, fix = FALSE), 
  G=list(G1=list(V        = diag(3),
                 nu        = 2.002),
         G2=list(V        = diag(1),
                 nu        = 0.002),
         G3=list(V        = diag(1),   
                 nu        = 0.002)))

#------------- 1a. Egg laying ----------------#

RR.laying <- MCMCglmm(cbind(Neggs, NoEggsHalf) ~ TSIcon:Stress*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(1 + TSIcon:Stress):damid + enclosure + year,
         data   = temp,
         family = "multinomial2",
         prior  = Myprior,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)


#------------- 1b. Egg mass ----------------#

RR.mass <- MCMCglmm(mass ~ TSI:Stress*dam_subpop + sire_subpop + poly(days.since.prev.eggLOG_z,2) + dam_age_z,
         random = ~ us(1 + TSI:Stress):damid + enclosure + year,
         data   = temp,
         prior  = Myprior,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 1c. Chick hatching ----------------#

RR.hatching <- MCMCglmm(cbind(Nhatched, NotHatched) ~ TSIcon:Stress*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(1 + TSIcon:Stress):damid + enclosure + year,
         data   = eggC,
         family = "multinomial2",
         prior  = Myprior,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)


#------------- 1d. Number of offspring ----------------#

RR.offspring <- MCMCglmm(cbind(Nchicks, NoChicksHalf) ~ TSIcon:Stress*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(1 + TSIcon:Stress):damid + enclosure + year,
         data   = temp,
         family = "multinomial2",
         prior  = prior.m2,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 1e. Number of sperm ----------------#

Spermprior<-list(R=list(V = diag(1),nu=0.002),
            G=list(
              G1=list(V = diag(3),nu = 2.002),
              G2=list(V= diag(1),nu = 0.002)
            ))

RR.spermnum <- MCMCglmm(sperm_num5 ~ TSI:Stress + poly(age,2), 
         random= ~ us(1+TSI:Stress):name + year
         ,data=sperm_num, 
         nitt=3000000, thin=30000, burnin=3000, 
         prior=Spermprior,
         family = "poisson",pr = TRUE)

#------------- 1f. Sperm viability ----------------#

RR.spermlive <- MCMCglmm(cbind(sperm_live,sperm_notlive) ~ TSI:Stress + poly(age,2),
                   random= ~ us(1+TSI:Stress):name +  year
                   ,data=sperm_liv,
                   nitt=3000000, thin=30000, burnin=3000, 
                   prior=Spermprior,
                   family = "multinomial2")


#############################################################
# 2. Random regression models with year-specific slopes
#############################################################


prior.m2 <- list(
  R=list(V = diag(1), nu=0.002, fix = FALSE),  #Not fixed at one as binomial model!, inverse-Wishart prior with low beleif. 2.002 because 3 in diag!
  G=list(G1=list(V        = diag(3),
                 nu        = 2.002),
         G2=list(V        = diag(3),
                 nu        = 2.002),
         G3=list(V        = diag(1),
                 nu        = 0.002),
         G4=list(V        = diag(1),   
                 nu        = 0.002)))

#------------- 2a. Egg laying ----------------#

RRyear.laying <- MCMCglmm(cbind(Neggs, NoEggsHalf) ~ TSIcon:Stress*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(1 + TSIcon:Stress):damid + us(1 + TSIcon:Stress):year_damid + enclosure + year,
         data   = temp,
         family = "multinomial2",
         prior  = prior.m2,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 2b. Egg mass ----------------#

RRyear.mass <- MCMCglmm(mass ~ TSI:Stress*dam_subpop + sire_subpop + poly(days.since.prev.eggLOG_z,2) + dam_age_z,
         random = ~ us(1 + TSI:Stress):damid + us(1 + TSI:Stress):year_damid + enclosure + year,
         data   = temp,
         prior  = prior.m2,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 2c. Number of sperm ----------------#

Spermprior2 <-list(R=list(V = diag(1),nu=0.002),
            G=list(
              G1=list(V = diag(3),nu = 2.002),
              G2=list(V = diag(3),nu = 2.002),
              G3=list(V= diag(1),nu = 0.002)
            ))

RRyear.spermnum <- MCMCglmm(sperm_num5 ~ TSI:Stress + poly(age,2), 
                  random= ~ us(1+TSI:Stress):name + us(1+TSI:Stress):year_name + year
                  ,data=sperm_num, 
                  nitt=3000000, thin=30000, burnin=3000, 
                  prior=Spermprior2,
                  family = "poisson",pr = TRUE)

#------------- 2d. Sperm viability ----------------#

RRyear.spermvia <- MCMCglmm(cbind(sperm_live,sperm_notlive) ~ TSI:Stress + poly(age,2),
         random= ~ us(1+TSI:Stress):name + us(1+TSI:Stress):year_name + year
         ,data=sperm_liv,
         nitt=3000000, thin=30000, burnin=3000, 
         prior=Spermprior2,
         family = "multinomial2")

#------------- 2e. Repeatabilitites ----------------#
#Example egg-laying

#-- Intercept
rep_int<-(RRyear.laying$VCV[,'(Intercept):(Intercept).damid'])/rowSums(RRyear.laying$VCV[,c('(Intercept):(Intercept).damid',
                                                                      '(Intercept):(Intercept).year_damid',
                                                                      'year',
                                                                      'enclosure',
                                                                      'units')])
rep_int <- data.frame(t(c(posterior.mode(rep_int),HPDinterval(rep_int))))

#-- slope heat stress
rep_slope<- RRyear.laying$VCV[,'TSIcon:StressHeat:TSIcon:StressHeat.damid']/rowSums(RRyear.laying$VCV[,c('TSIcon:StressHeat:TSIcon:StressHeat.damid','TSIcon:StressHeat:TSIcon:StressHeat.year_damid')])
rep_slope <- data.frame(t(c(posterior.mode(rep_slope),HPDinterval(rep_slope))))

#-- slope cold stress
rep_slope_cold<- RRyear.laying$VCV[,'TSIcon:StressCold:TSIcon:StressCold.damid']/rowSums(RRyear.laying$VCV[,c('TSIcon:StressCold:TSIcon:StressCold.damid','TSIcon:StressCold:TSIcon:StressCold.year_damid')])
rep_slope_cold <- data.frame(t(c(posterior.mode(rep_slope_cold),HPDinterval(rep_slope_cold))))

#------------- 2f. PSlopeVar ----------------#
#Example egg-laying

PSlopeVar <-  (RRyear.laying$VCV[,'TSIcon:StressHeat:TSIcon:StressHeat.damid'] * var(temp$TSIcon[temp$Stress %in% "Heat"])+
                     RRyear.laying$VCV[,'TSIcon:StressHeat:TSIcon:StressHeat.year_damid'] * var(temp$TSIcon[temp$Stress %in% "Heat"])+
                     RRyear.laying$VCV[,'TSIcon:StressCold:TSIcon:StressCold.damid'] * var(temp$TSIcon[temp$Stress %in% "Cold"])+
                     RRyear.laying$VCV[,'TSIcon:StressCold:TSIcon:StressCold.year_damid'] * var(temp$TSIcon[temp$Stress %in% "Cold"]))/
  (
    RRyear.laying$VCV[,'TSIcon:StressHeat:TSIcon:StressHeat.damid'] * var(temp$TSIcon[temp$Stress %in% "Heat"])+
      RRyear.laying$VCV[,'TSIcon:StressHeat:TSIcon:StressHeat.year_damid'] * var(temp$TSIcon[temp$Stress %in% "Heat"])+ 
      RRyear.laying$VCV[,'TSIcon:StressCold:TSIcon:StressCold.damid'] * var(temp$TSIcon[temp$Stress %in% "Cold"])+
      RRyear.laying$VCV[,'TSIcon:StressCold:TSIcon:StressCold.year_damid'] * var(temp$TSIcon[temp$Stress %in% "Cold"])+
      RRyear.laying$VCV[,'(Intercept):(Intercept).damid']+
      RRyear.laying$VCV[,'(Intercept):(Intercept).year_damid'] +
      RRyear.laying$VCV[,'enclosure']+
      RRyear.laying$VCV[,'year']+
      RRyear.laying$VCV[,'units']
  )

PSlopeVarCI <- data.frame(t(c(posterior.mode(PSlopeVar),HPDinterval(PSlopeVar))))


#############################################################
# 3. Character-state models
#############################################################

prior.m2.char <- list(
  R=list(V = diag(3), nu=2.002, fix = FALSE),  #Not fixed at one as binomial model!, inverse-Wishart prior with low beleif. 3.002 because 3 in diag!
  G=list(G1=list(V        = diag(3),
                 n        = 2.002),
         G2=list(V        = diag(1),   
                 n        = 0.002),
         G3=list(V        = diag(1),   
                 n        = 0.002)))

#------------- 3a. Egg laying ----------------#

CS.laying <- MCMCglmm(cbind(Neggs, NoEggsHalf) ~ 1 + TSIcat*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(TSIcat):damid + enclosure + year,
         rcov = ~idh(TSIcat):units,
         data   = temp,
         family = "multinomial2",
         prior  = prior.m2.char,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 3b. Egg mass ----------------#

CS.mass <- MCMCglmm(mass ~ 1 + TSIcat*dam_subpop + sire_subpop + poly(days.since.prev.eggLOG_z,2) + dam_age_z,
         random = ~ us(TSIcat):damid + enclosure + year,
         rcov = ~idh(TSIcat):units,
         data   = temp,
         prior  = prior.m2.char,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 3c. Chick hathcing ----------------#

CS.hatching <- MCMCglmm(cbind(Nhatched, NotHatched) ~ 1 + TSIcat*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(TSIcat):damid + enclosure + year,
         rcov = ~idh(TSIcat):units,
         data   = eggC,
         family = "multinomial2",
         prior  = prior.m2.char,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 3d. Number of offspring ----------------#

CS.offspring <- MCMCglmm(cbind(Nchicks, NoChicksHalf) ~ 1 + TSIcat*dam_subpop + sire_subpop + dam_age_z,
         random = ~ us(TSIcat):damid + enclosure + year,
         rcov = ~idh(TSIcat):units,
         data   = temp,
         family = "multinomial2",
         prior  = prior.m2.char,
         thin   = 10000,burnin = 100000,nitt   = 10000000,
         verbose = TRUE)

#------------- 3e. Number of sperm ----------------#

priorspermCS<-list(R=list(V = diag(3), nu=2.002),
            G=list(
              G1=list(V = diag(3),nu = 2.002),
              G2=list(V= diag(1),nu = 0.002)
            ))

CS.spermnum <- MCMCglmm(sperm_num5 ~ TSIcat + poly(age,2), 
         random= ~ us(TSIcat):name + year
         ,rcov = ~idh(TSIcat):units
         ,data=sperm_num, 
         nitt=3000000, thin=30000, burnin=3000, 
         prior=priorspermCS,
         family = "poisson")

#------------- 3f. Sperm viability ----------------#

CS.spermvia <- MCMCglmm(cbind(sperm_live,sperm_notlive) ~ TSIcat + poly(age,2), 
         random= ~ us(TSIcat):name + year
         ,rcov = ~idh(TSIcat):units
         ,data=sperm_liv, 
         nitt=3000000, thin=30000, burnin=3000, 
         prior=priorspermCS,
         family = "multinomial2")


#############################################################
# 4. Bivariate (two-trait) models
#############################################################

#------------- 4a. Egg laying vs Egg mass using character-state model ----------------#

prior.cross.egg.cs <- list(
  R=list(
    R1 = list(V = diag(2), nu=1.002, fix = FALSE),
    R2 = list(V = diag(2), nu=1.002, fix = FALSE),
    R3 = list(V = diag(2), nu=1.002, fix = FALSE)), 
  G=list(
    G1=list(V=diag(2),nu= 1.002), 
    G2=list(V=diag(2),nu= 1.002),
    G3=list(V=diag(2),nu= 1.002),
    G4=list(V=diag(2),nu= 1.002),
    G5=list(V=diag(2),nu= 1.002)))

twotrait.egg.CS <- MCMCglmm(cbind(mass,cbind(Neggs, NoEggsHalf)) ~ trait-1 + dam_subpop*TSIcat*trait + trait*sire_subpop + dam_age_z*trait,
         random = ~ us(trait:at.level(TSIcat,"Cold")):damid + 
           us(trait:at.level(TSIcat,"Benign")):damid + 
           us(trait:at.level(TSIcat,"Hot")):damid + 
           idh(trait):enclosure + 
           idh(trait):year,
         rcov = ~ us(trait:at.level(TSIcat,"Cold")):units +
           us(trait:at.level(TSIcat,"Benign")):units + 
           us(trait:at.level(TSIcat,"Hot")):units ,
         data   = dat,
         family = c("gaussian","multinomial2"),
         prior  = prior.cross.egg.cs,
         thin   = 2000,burnin = 100000,nitt   = 5000000,
         verbose = TRUE,
         pr = TRUE)

#------------- 4b. Egg laying vs Egg mass using random regression model ----------------#

prior.cross.egg.RR <- list(
  R=list(V = diag(2), nu=1.002, fix = FALSE),
  G=list(G1=list(V        = diag(4),
                 nu        = 3.002),
         G2=list(V        = diag(4),
                 nu        = 3.002),
         G3=list(V        = diag(4),
                 nu        = 3.002),
         G4=list(V        = diag(4),
                 nu        = 3.002),
         G5=list(V        = diag(2),
                 nu        = 1.002),
         G6=list(V        = diag(2),
                 nu        = 1.002)))

twotrait.egg.RR <- MCMCglmm(cbind(mass,cbind(Neggs, NoEggsHalf)) ~ trait-1 + dam_subpop*trait:TSIcon:Stress + sire_subpop*trait + dam_age_z*trait,
         random = ~ us(trait-1+trait:TSIcon:at.level(Stress, "Heat")):damid + us(trait-1+trait:TSIcon:at.level(Stress, "Cold")):damid + us(trait-1+trait:TSIcon:at.level(Stress, "Heat")):year_damid + us(trait-1+trait:TSIcon:at.level(Stress, "Cold")):year_damid + idh(trait):enclosure + idh(trait):year,
         rcov = ~us(trait):units,
         data   = dat,
         family = c("gaussian","multinomial2"),
         prior  = prior.cross.egg.RR,
         thin   = 2000,burnin = 100000,nitt   = 5000000,
         verbose = TRUE,
         pr = FALSE)


#------------- 4c. Number of sperm vs Sperm viability using character-state model ----------------#

prior.cross.sperm.cs <- list(
  R=list(
    R1 = list(V = diag(2), nu=1.002, fix = FALSE),
    R2 = list(V = diag(2), nu=1.002, fix = FALSE),
    R3 = list(V = diag(2), nu=1.002, fix = FALSE)), 
  G=list(
    G1=list(V=diag(2),nu= 1.002), 
    G2=list(V=diag(2),nu= 1.002),
    G3=list(V=diag(2),nu= 1.002),
    G4=list(V=diag(2),nu= 1.002)))

twotrait.sperm.CS <- MCMCglmm(cbind(sperm_num5,cbind(sperm_live,sperm_notlive)) ~ trait-1 + trait:TSIcat + trait*poly(age,2),
         random = ~ us(trait:at.level(TSIcat,"Cold")):name + 
           us(trait:at.level(TSIcat,"Benign")):name + 
           us(trait:at.level(TSIcat,"Hot")):name + idh(trait):year,
         rcov = ~us(trait:at.level(TSIcat,"Cold")):units +
           us(trait:at.level(TSIcat,"Benign")):units + 
           us(trait:at.level(TSIcat,"Hot")):units,
         data   = prior.cross.sperm.cs,
         family = c("poisson","multinomial2"),
         prior  = prior.cross.sperm.cs,
         nitt=3000000, thin=30000, burnin=3000, 
         verbose = T,
         pr = F)


#------------- 4d. Number of sperm vs Sperm viability using random regression model ----------------#


prior.cross.sperm.RR <- list(
  R=list(V = diag(2), nu=1.002, fix = FALSE),
  G=list(G1=list(V        = diag(4),
                 nu        = 3.002),
         G2=list(V        = diag(4),
                 nu        = 3.002),
         G3=list(V        = diag(4),
                 nu        = 3.002),
         G4=list(V        = diag(4),
                 nu        = 3.002),
         G5=list(V        = diag(2),
                 nu        = 1.002)))

twotrait.sperm.RR <- MCMCglmm(cbind(sperm_num5,cbind(sperm_live,sperm_notlive)) ~ trait-1 + trait:TSI:Stress + trait*poly(age,2),
         random = ~ us(trait-1+trait:TSI:at.level(Stress, "Heat")):name + us(trait-1+trait:TSI:at.level(Stress, "Cold")):year_name +us(trait-1+trait:TSI:at.level(Stress, "Heat")):year_name + us(trait-1+trait:TSI:at.level(Stress, "Cold")):name + idh(trait):year,
         rcov = ~us(trait):units,
         data   = prior.cross.sperm.RR,
         family = c("poisson","multinomial2"),
         prior  = prior.cross.sperm.RR,
         nitt=3000000, thin=30000, burnin=3000, 
         verbose = T,
         pr = F)