###Code for Kendall et al. (2018): Pollinator size and its consequences: Robust estimates of body size in pollinating insects

#Data preparation

#libraries
library(ape)
library(bayesplot)
library(broom)
library(brms)
library(cvTools)
library(caret)
library(grid)
library(gridExtra)
library(lattice) 
library(lme4)
library(MCMCglmm)
library(ModelMetrics)
library(MuMIn)
library(rstan)
library(parallel)
library(phytools)
library(plyr)
library(dplyr)
library(stargazer)

#dataframes
set.seed(123)

poll_all <- read.csv(file="data/pollimetry_10172018.csv",header=T)

#split to bees and hoverflies
poll_all_split=split(poll_all,poll_all$Superfamily)
bee_all=poll_all_split[[1]]
hov_all=poll_all_split[[2]]

#JUST AUSTRALIA
bee_country=split(bee_all,bee_all$Country)
bee_australia=bee_country$Australia

bee_all$Family=relevel(bee_all$Family,ref="Apidae")
bee_all$Region=relevel(bee_all$Region,ref="Europe")
bee_all$Species=droplevels(bee_all$Species)
bee_all=droplevels(bee_all)
hov_all=droplevels(hov_all)


#remove species not in phylogeny
bee_all=bee_all[!bee_all$Species=="Flavipanurgus_venustus",] #Genus is not in phylogeny
bee_all=bee_all[!bee_all$Species=="Protomeliturga_turnerea",] #Genus not in phylogeny
bee_all=bee_all[!bee_all$Species=="Tetrapedia_diversipes",] #Genus not in phylogeny

#for complete nestedness - remove species from introduced range
bee_all=bee_all[!(bee_all$Species=="Andrena_wilkella" & bee_all$Region=="NorthAmerica"),] #Hurd (1979) presumes it is an #introduction in North America)
bee_all=bee_all[!(bee_all$Species=="Halictus_rubicundus" & bee_all$Region=="NorthAmerica"),]
bee_all=bee_all[!(bee_all$Species=="Lasioglossum_leucozonium" & bee_all$Region=="NorthAmerica"),]
bee_all=bee_all[!(bee_all$Species=="Anthidium_manicatum" & bee_all$Region=="NorthAmerica"),]
bee_all=bee_all[!(bee_all$Species=="Apis_mellifera" & bee_all$Region=="Australasia"),]

##PHYLO Dataframe for calculating phylogenetic signal

bee_phylo=aggregate(Latitude~Family+Subfamily+
                      Genus+Species,bee_all,median)

bee_phylo$Longitude=as.numeric(unlist(aggregate(Longitude~Family+Subfamily+Genus+Species,bee_all,median)[5]))
bee_phylo$Spec.wgt=as.numeric(unlist(aggregate(Spec.wgt~Family+Subfamily+
                                                 Genus+Species,bee_all,mean)[5]))
bee_phylo$Wgt.SD=as.numeric(unlist(aggregate(log(Spec.wgt)~Family+Subfamily+
                                               Genus+Species,bee_all,sd)[5]))
bee_phylo$IT=as.numeric(unlist(aggregate(IT~Family+Subfamily+
                                           Genus+Species,bee_all,mean)[5]))
bee_phylo$IT.SD=as.numeric(unlist(aggregate(log(IT)~Family+Subfamily+
                                              Genus+Species,bee_all,sd)[5]))

rownames(bee_phylo)=droplevels(bee_phylo$Species)


##LOAD TREE
bee.trees=read.tree(file="data/hedtke_genera_tree.txt")
##Use tree 1 (376 genera) #Genera-level phylogney
bee.mcmc=bee.trees[[1]]
range(bee.mcmc$edge.length) 

###root with apoid wasp outgroup
bee.mcmc=root(bee.mcmc,outgroup="Tachysphex")
range(bee.mcmc$edge.length) 
bee.mcmc=as.phylo(bee.mcmc)

##Make ultrametric
bee.mcmc=chronos(bee.mcmc)

bee.tree=drop.tip(bee.mcmc, setdiff(bee.mcmc$tip.label,unique(bee_all$Genus)))

is.ultrametric(bee.tree)

## Will's suggestion
bee.tree$tip.label<-paste(bee.tree$tip.label,"_dum",sep="")
for(i in 1:length(species$Genus_species)){
  bee.tree<-add.species.to.genus(bee.tree,species$Genus_species[i],
                                 where="root")
}
## prune out these same taxa
ii<-grep("dum",bee.tree$tip.label)
bee.tree<-drop.tip(bee.tree,bee.tree$tip.label[ii])

plot(bee.tree)

##ADD missing species
setdiff(species$Genus_species,bee.tree$tip.label)
bee.tree<-add.species.to.genus(bee.tree,"Lasioglossum_paradmirandum",
                               where="root")
bee.tree<-add.species.to.genus(bee.tree,"Lasioglossum_admirandum",
                               where="root")

#Remove node labels
bee.tree$node.label=NULL

##Intraspecific variance data frames
bee_species=split(bee_all,bee_all$Species)
hov_species=split(hov_all,hov_all$Species)

##Cane function
Cane=function(IT){exp(0.6453 + 2.4691*log(IT))}

##FOR intraspecific species analyses
bee_species=split(bee_all,bee_all$Species)


#BRMS Hamiltonian monte carlo  diagnostic checks - FROM MICHAEL BETANCOURT
# Check transitions that ended with a divergence
check_div <- function(fit) {
  sampler_params <- get_sampler_params(fit, inc_warmup=FALSE)
  divergent <- do.call(rbind, sampler_params)[,'divergent__']
  n = sum(divergent)
  N = length(divergent)
  
  print(sprintf('%s of %s iterations ended with a divergence (%s%%)',
                n, N, 100 * n / N))
  if (n > 0)
    print('  Try running with larger adapt_delta to remove the divergences')
}

# Check transitions that ended prematurely due to maximum tree depth limit
check_treedepth <- function(fit, max_depth = 10) {
  sampler_params <- get_sampler_params(fit, inc_warmup=FALSE)
  treedepths <- do.call(rbind, sampler_params)[,'treedepth__']
  n = length(treedepths[sapply(treedepths, function(x) x == max_depth)])
  N = length(treedepths)
  
  print(sprintf('%s of %s iterations saturated the maximum tree depth of %s (%s%%)',
                n, N, max_depth, 100 * n / N))
  if (n > 0)
    print('  Run again with max_depth set to a larger value to avoid saturation')
}

# Checks the energy Bayesian fraction of missing information (E-BFMI)
check_energy <- function(fit) {
  sampler_params <- get_sampler_params(fit, inc_warmup=FALSE)
  no_warning <- TRUE
  for (n in 1:length(sampler_params)) {
    energies = sampler_params[n][[1]][,'energy__']
    numer = sum(diff(energies)**2) / length(energies)
    denom = var(energies)
    if (numer / denom < 0.2) {
      print(sprintf('Chain %s: E-BFMI = %s', n, numer / denom))
      no_warning <- FALSE
    }
  }
  if (no_warning)
    print('E-BFMI indicated no pathological behavior')
  else
    print('  E-BFMI below 0.2 indicates you may need to reparameterize your model')
}

# Checks the effective sample size per iteration
check_n_eff <- function(fit) {
  fit_summary <- summary(fit, probs = c(0.5))$summary
  N <- dim(fit_summary)[[1]]
  
  iter <- dim(extract(fit)[[1]])[[1]]
  
  no_warning <- TRUE
  for (n in 1:N) {
    ratio <- fit_summary[,5][n] / iter
    if (ratio < 0.001) {
      print(sprintf('n_eff / iter for parameter %s is %s!',
                    rownames(fit_summary)[n], ratio))
      no_warning <- FALSE
    }
  }
  if (no_warning)
    print('n_eff / iter looks reasonable for all parameters')
  else
    print('  n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated')
}

# Checks the potential scale reduction factors
check_rhat <- function(fit) {
  fit_summary <- summary(fit, probs = c(0.5))$summary
  N <- dim(fit_summary)[[1]]
  
  no_warning <- TRUE
  for (n in 1:N) {
    rhat <- fit_summary[,6][n]
    if (rhat > 1.1 || is.infinite(rhat) || is.nan(rhat)) {
      print(sprintf('Rhat for parameter %s is %s!',
                    rownames(fit_summary)[n], rhat))
      no_warning <- FALSE
    }
  }
  if (no_warning)
    print('Rhat looks reasonable for all parameters')
  else
    print('  Rhat above 1.1 indicates that the chains very likely have not mixed')
}

check_all_diagnostics <- function(fit) {
  check_n_eff(fit)
  check_rhat(fit)
  check_div(fit)
  check_treedepth(fit)
  check_energy(fit)
}

# Returns parameter arrays separated into divergent and non-divergent transitions
partition_div <- function(fit) {
  nom_params <- extract(fit, permuted=FALSE)
  n_chains <- dim(nom_params)[2]
  params <- as.data.frame(do.call(rbind, lapply(1:n_chains, function(n) nom_params[,n,])))
  
  sampler_params <- get_sampler_params(fit, inc_warmup=FALSE)
  divergent <- do.call(rbind, sampler_params)[,'divergent__']
  params$divergent <- divergent
  
  div_params <- params[params$divergent == 1,]
  nondiv_params <- params[params$divergent == 0,]
  
  return(list(div_params, nondiv_params))
}

#Bee priors
#without random effects
bprior <- prior(normal(0,0.4), class = b) + 
  prior(normal(1,1),class=b,coef="logIT") +
  prior(normal(0,1), class = Intercept) +
  prior(normal(0,0.4), class = sigma) 

#with random effects
bprior1 <- prior(normal(0,0.4), class = b) + 
  prior(normal(1,1),class=b,coef="logIT") +
  prior(normal(0,1), class = Intercept) + 
  prior(normal(0,0.4), class = sd) +
  prior(normal(0,0.4), class = sigma) 

#Hoverfly priors
#without random effects
hprior <- prior(normal(0,0.4), class = b) + 
  prior(normal(1,1),class=b,coef="logIT") +
  prior(normal(0,1), class = Intercept) +
  prior(normal(0,0.4), class = sigma) 

#With random effects
hprior1 <- prior(normal(0,0.4), class = b) + 
  prior(normal(1,1),class=b,coef="logIT") +
  prior(normal(0,1), class = Intercept) + 
  prior(normal(0,0.4), class = sd) +
  prior(normal(0,0.4), class = sigma) 


##BRMS bee models and manual selection
#Test OLS models w. biogeography

#ITD ONLY MODEL
bee<- brm(log(Spec.wgt)~log(IT), data = bee_all, cores=4,
          family = gaussian(),prior=bprior,control=list(adapt_delta=0.99,max_treedepth=15))

#ITD + RE MODEL

bee1<- brm(log(Spec.wgt)~log(IT)+(1|Region/Species), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

##FULL MODEL
bee2<- brm(log(Spec.wgt) ~ Sex + Family + log(IT) + (1 | Region/Species) + 
             Family:log(IT) + Sex:log(IT), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

#Reduced models
bee3<- brm(log(Spec.wgt) ~ Sex + Family + log(IT) + (1 | Region/Species) + 
             Family:log(IT), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

bee4<- brm(log(Spec.wgt) ~ Sex + Family + log(IT) + (1 | Region/Species) + 
             Sex:log(IT), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

bee5<- brm(log(Spec.wgt) ~ Sex + Family + log(IT) + (1 | Region/Species), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

bee6<- brm(log(Spec.wgt) ~ Family + log(IT) + (1 | Region/Species) + Family:log(IT), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))
#good

bee7<- brm(log(Spec.wgt) ~ Family + log(IT) + (1 | Region/Species), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

bee8<- brm(log(Spec.wgt) ~ Sex * log(IT) + (1 | Region/Species), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))

bee9<- brm(log(Spec.wgt) ~ Sex + log(IT) + (1 | Region/Species), data = bee_all, cores=4,
           family = gaussian(),prior=bprior1,control=list(adapt_delta=0.99,max_treedepth=15))



#BEE PHYLO models


##Nested phylogenetic co-variance matrix

inv.phylo <- MCMCglmm::inverseA(bee.tree, nodes = "TIPS", scale = TRUE)
A <- solve(inv.phylo$Ainv)
rownames(A) <- rownames(inv.phylo$Ainv)
isSymmetric(A, check.attributes = FALSE)

B=A
bee_all$Rspecies=paste(bee_all$Region,bee_all$Species,sep="_")
region_species=unique(bee_all[order(match(bee_all$Species, bee.tree$tip.label)), ]$Rspecies)
rownames(B)=unique(region_species)
isSymmetric(B,check.attributes=FALSE)

##Phylogenetic bee models

bee_phy1<- brm(log(Spec.wgt) ~ Sex + log(IT) + (1 | Region/Species) + Sex:log(IT), data = bee_all, cores=4,
               family = gaussian(),cov_ranef = list("Region:Species" = B),
               prior=bprior1,control = list(adapt_delta = 0.99,max_treedepth=15))

#good

bee_phy2<- brm(log(Spec.wgt) ~ Sex + log(IT) + (1 | Region/Species), data = bee_all,prior=bprior1, cores=4,
               family = gaussian(),cov_ranef = list("Region:Species" = B),
               control = list(adapt_delta = 0.99,max_treedepth=15))
#good

bee_phy3<- brm(log(Spec.wgt) ~ log(IT) + (1 | Region/Species), data = bee_all,prior=bprior1, cores=4,
               family = gaussian(),cov_ranef = list("Region:Species" = B),
               control = list(adapt_delta = 0.99,max_treedepth=15))

##MODEL CHECKS
check_all_diagnostics(bee$fit)
plot(bee)
np_bee <- nuts_params(bee)
mcmc_nuts_energy(np_bee,binwidth=1)

bee1
check_all_diagnostics(bee1$fit)
plot(bee1)
np_bee1 <- nuts_params(bee1)
mcmc_nuts_energy(np_bee1,binwidth=10)

bee2
check_all_diagnostics(bee2$fit)
plot(bee2)
np_bee2 <- nuts_params(bee2)
mcmc_nuts_energy(np_bee2,binwidth=10)

bee3
check_all_diagnostics(bee3$fit)
plot(bee3)
np_bee3 <- nuts_params(bee3)
mcmc_nuts_energy(np_bee3,binwidth=10)

bee4
check_all_diagnostics(bee4$fit)
plot(bee4)
np_bee4 <- nuts_params(bee4)
mcmc_nuts_energy(np_bee4,binwidth=10)

bee5
check_all_diagnostics(bee5$fit)
plot(bee5)
np_bee5 <- nuts_params(bee5)
mcmc_nuts_energy(np_bee5,binwidth=10)

bee6
check_all_diagnostics(bee6$fit)
plot(bee6)
np_bee6 <- nuts_params(bee6)
mcmc_nuts_energy(np_bee6,binwidth=10)

bee7
check_all_diagnostics(bee7$fit)
plot(bee7)
np_bee7 <- nuts_params(bee7)
mcmc_nuts_energy(np_bee7,binwidth=10)

bee8
check_all_diagnostics(bee8$fit)
plot(bee8)
np_bee8 <- nuts_params(bee8)
mcmc_nuts_energy(np_bee8,binwidth=10)

bee9
check_all_diagnostics(bee9$fit)
plot(bee9)
np_bee9 <- nuts_params(bee9)
mcmc_nuts_energy(np_bee9,binwidth=10)

bee_phy1
check_all_diagnostics(bee_phy1$fit)
plot(bee_phy1)
np_bee_phy1<- nuts_params(bee_phy1)
mcmc_nuts_energy(np_bee_phy1,binwidth=10)

bee_phy2
check_all_diagnostics(bee_phy2$fit)
plot(bee_phy2)
np_bee_phy2<- nuts_params(bee_phy2)
mcmc_nuts_energy(np_bee_phy2,binwidth=10)

bee_phy3
check_all_diagnostics(bee_phy3$fit)
plot(bee_phy3)
np_bee_p3<- nuts_params(bee_phy3)
mcmc_nuts_energy(np_bee_phy3,binwidth=10)
```

```{r bee WAIC loo-ic}
options(loo.cores = 4)
bee_list=list(bee,bee1,bee2,bee3,bee4,bee5,bee6,bee7,bee8,bee9,bee_phy1,bee_phy2,bee_phy3)


#Bayesian R2
bee_R2=lapply(bee_list,function (x) bayes_R2(x))
bee_R2 <- do.call("rbind", bee_R2)

##WAIC
bee_waic=lapply(bee_list,function (x) waic(x))

#poor diagnostics

##LOO-IC
bee_loo=lapply(bee_list,function (x) loo(x))

#poor diagnostics

##K-FOLD
bee_kfold=lapply(bee_list,function (x) kfold(x,cores=4))

##RMSE
bee_RMSE=lapply(bee_list,function (x) rmse(exp(predict(x)[,1]),bee_all$Spec.wgt))

##Hoverfly model selection

#basic IT
hov<- brm(log(Spec.wgt)~log(IT), data = hov_all, cores=4,
          family = gaussian(),prior=hprior,
          control = list(adapt_delta = 0.99))


#IT + Sex + RE
hov1<- brm(log(Spec.wgt) ~ Sex + log(IT) + (1 | Region/Species), data = hov_all, cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.99))

#good
# Sex * IT
hov2<- brm(log(Spec.wgt) ~ Sex + log(IT) + (1 | Region/Species) + Sex:log(IT), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.99,max_treedepth=15))

#3 divergent - gone with increased treedepth

#IT + Sex + Subfamily
hov3<- brm(log(Spec.wgt) ~ Sex + Subfamily + log(IT) + (1 | Region/Species), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.999))
#good
#IT * Subf + Sex
hov4<- brm(log(Spec.wgt) ~ Sex + Subfamily + log(IT) + (1 | Region/Species) + 
             Subfamily:log(IT), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.99,max_treedepth=15))
#good
#IT * Sex + Subf
hov5<- brm(log(Spec.wgt) ~ Sex + Subfamily + log(IT) + (1 | Region/Species) + 
             Sex:log(IT), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.99,max_treedepth=15))

#4 divergent transitions - gone with increased treedepth
##FULL MODEL IT* SEX + IT * SUBF
hov6<- brm(log(Spec.wgt) ~ Sex + Subfamily + log(IT) + (1 | Region/Species) + 
             Sex:log(IT) + Subfamily:log(IT), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.99))
#good

hov7<- brm(log(Spec.wgt) ~ log(IT) + (1 | Region/Species), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.999,max_treedepth=20))
#5 divergent transitions, 1 with treedepth 15 and 20, 
#reduced stepsize (0.1) made it worse, gone with delta 0.999

#SUBF * IT
hov8<- brm(log(Spec.wgt) ~ Subfamily + log(IT) + (1 | Region/Species) + 
             Subfamily:log(IT), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.99,max_treedepth=15))
#1 divergent transition - gone with increased treedepth 15

#SUBF + IT
hov9<- brm(log(Spec.wgt) ~ Subfamily + log(IT) + (1 | Region/Species), data = hov_all,  cores=4,
           family = gaussian(),prior=hprior1,
           control = list(adapt_delta = 0.999,max_treedepth=20))

#4 divergent transitions, increaed delta 0.999, treedepth 20 - fixed

#hoverfly model checks
hov
check_all_diagnostics(hov$fit)
plot(hov)
np_hov <- nuts_params(hov)
mcmc_nuts_energy(np_hov,binwidth=1)

hov1
check_all_diagnostics(hov1$fit)
plot(hov1)
np_hov1 <- nuts_params(hov1)
mcmc_nuts_energy(np_hov1,binwidth=1)

hov2
check_all_diagnostics(hov2$fit)
plot(hov2)
np_hov2 <- nuts_params(hov2)
mcmc_nuts_energy(np_hov2,binwidth=1)

hov3
check_all_diagnostics(hov3$fit)
plot(hov3)
np_hov3 <- nuts_params(hov3)
mcmc_nuts_energy(np_hov3,binwidth=1)

hov4
check_all_diagnostics(hov4$fit)
plot(hov4)
np_hov4 <- nuts_params(hov4)
mcmc_nuts_energy(np_hov4,binwidth=1)

hov5
check_all_diagnostics(hov5$fit)
plot(hov5)
np_hov5 <- nuts_params(hov5)
mcmc_nuts_energy(np_hov5,binwidth=1)

hov6
check_all_diagnostics(hov6$fit)
plot(hov6)
np_hov6 <- nuts_params(hov6)
mcmc_nuts_energy(np_hov6,binwidth=1)

hov7
check_all_diagnostics(hov7$fit)
plot(hov7)
np_hov7 <- nuts_params(hov7)
mcmc_nuts_energy(np_hov7,binwidth=1)

hov8
check_all_diagnostics(hov8$fit)
plot(hov8)
np_hov8 <- nuts_params(hov8)
mcmc_nuts_energy(np_hov8,binwidth=1)

hov9
check_all_diagnostics(hov9$fit)
plot(hov9)
np_hov9 <- nuts_params(hov9)
mcmc_nuts_energy(np_hov9,binwidth=1)

hov
check_all_diagnostics(hov$fit)
plot(hov)
np_hov <- nuts_params(hov)
mcmc_nuts_energy(np_hov,binwidth=1)



##ADD ICs to hoverfly models
hov_list=list(hov,hov1,hov2,hov3,hov4,hov5,hov6,hov7,hov8,hov9)

#Bayesian R2
hov_R2=lapply(hov_list,function (x) bayes_R2(x))

#WAIC
hov_waic=lapply(hov_list,function(x) waic(x))

#LOO-IC
hov_loo=lapply(hov_list,function(x) loo(x))

#K-FOLD
hov_kfold=lapply(hov_list,function(x) kfold(x,cores=4))

#RMSE
hov_RMSE=lapply(hov_list,function (x) rmse(exp(predict(x)[,1]),hov_all$Spec.wgt))



##Bee phylogenetic signal

#Weight
WGT=as.data.frame(bee_phylo[,c("Spec.wgt")])
WGTSE=as.data.frame(bee_phylo[,c("Spec.wgt")])

WGT=log(WGT)
rownames(WGT)=rownames(bee_phylo)

WGT<-as.matrix((WGT))[,1]
phylosig(tree=bee.tree,x=WGT,method="lambda",test=TRUE)

##Intraspecific predictions and variation

##Body size predictions - just females
```{r}

bee_top10=rbind(bee_species$Homalictus_urbanus[bee_species$Homalictus_urbanus$Sex == "Female",],
                bee_species$Lasioglossum_pauxillum[bee_species$Lasioglossum_pauxillum$Sex == "Female",],
                bee_species$Bombus_terrestris[bee_species$Bombus_terrestris$Sex == "Female",],
                bee_species$Andrena_flavipes[bee_species$Andrena_flavipes$Sex == "Female",],
                bee_species$Lasioglossum_lanarium[bee_species$Lasioglossum_lanarium$Sex == "Female",],
                bee_species$Trigona_spinipes[bee_species$Trigona_spinipes$Sex == "Female",],
                bee_species$Lasioglossum_glabriusculum[bee_species$Lasioglossum_glabriusculum$Sex == "Female",],
                bee_species$Bombus_lapidarius[bee_species$Bombus_lapidarius$Sex == "Female",],
                bee_species$Andrena_nigroaenea[bee_species$Andrena_nigroaenea$Sex == "Female",],
                bee_species$Bombus_impatiens[bee_species$Bombus_impatiens$Sex == "Male",])

HU_lm=lm(log(Spec.wgt)~log(IT),data=bee_species$Homalictus_urbanus[bee_species$Homalictus_urbanus$Sex == "Female",])

LP_lm=lm(log(Spec.wgt)~log(IT),data=bee_species$Lasioglossum_pauxillum[bee_species$Lasioglossum_pauxillum$Sex == "Female",])

BT_lm=lm(log(Spec.wgt)~log(IT),bee_species$Bombus_terrestris[bee_species$Bombus_terrestris$Sex == "Female",])

AF_lm=lm(log(Spec.wgt)~log(IT),bee_species$Andrena_flavipes[bee_species$Andrena_flavipes$Sex == "Female",])

LL_lm=lm(log(Spec.wgt)~log(IT),bee_species$Lasioglossum_lanarium[bee_species$Lasioglossum_lanarium$Sex == "Female",])

TS_lm=lm(log(Spec.wgt)~log(IT),bee_species$Trigona_spinipes[bee_species$Trigona_spinipes$Sex == "Female",])

LG_lm=lm(log(Spec.wgt)~log(IT),bee_species$Lasioglossum_glabriusculum[bee_species$Lasioglossum_glabriusculum$Sex == "Female",])

BL_lm=lm(log(Spec.wgt)~log(IT),bee_species$Bombus_lapidarius[bee_species$Bombus_lapidarius$Sex == "Female",])

AN_lm=lm(log(Spec.wgt)~log(IT),bee_species$Andrena_nigroaenea[bee_species$Andrena_nigroaenea$Sex == "Female",])

BI_lm=lm(log(Spec.wgt)~log(IT),bee_species$Bombus_impatiens[bee_species$Bombus_impatiens$Sex == "Male",])

summary(HU_lm)
summary(LP_lm)
summary(BL_lm)
summary(AF_lm)
summary(LL_lm)

summary(TS_lm)
summary(LG_lm)
summary(BL_lm)
summary(AN_lm)
summary(BI_lm)

#HOVERFLIES
hov_top5=rbind(hov_species$Helophilus_parallelus[hov_species$Helophilus_parallelus$Sex == "Female",],
               hov_species$Sphaerophoria_macrogaster[hov_species$Sphaerophoria_macrogaster$Sex == "Female",],
               hov_species$Episyrphus_balteatus[hov_species$Episyrphus_balteatus$Sex == "Female",],
               hov_species$Melanostoma_scalare[hov_species$Melanostoma_scalare$Sex == "Female",],
               hov_species$Austrosyphus_aussp1[hov_species$Austrosyphus_aussp1$Sex == "Female",])

HP_lm=lm(log(Spec.wgt)~log(IT),data=hov_species$Helophilus_parallelus[hov_species$Helophilus_parallelus$Sex == "Female",])

SM_lm=lm(log(Spec.wgt)~log(IT),data=hov_species$Sphaerophoria_macrogaster[hov_species$Sphaerophoria_macrogaster$Sex == "Female",])

EB_lm=lm(log(Spec.wgt)~log(IT),hov_species$Episyrphus_balteatus[hov_species$Episyrphus_balteatus$Sex == "Female",])

MS_lm=lm(log(Spec.wgt)~log(IT),hov_species$Melanostoma_scalare[hov_species$Melanostoma_scalare$Sex == "Female",])

AA_lm=lm(log(Spec.wgt)~log(IT),hov_species$Austrosyphus_aussp1[hov_species$Austrosyphus_aussp1$Sex == "Female",])

summary(HP_lm)
summary(SM_lm)
summary(EB_lm)
summary(MS_lm)
summary(AA_lm)


##Bee intraspecific variation with sample size


set.seed(123)
##ONE##
#Homalictus urbanus
#IT
HU_IT = c()
for(i in 1:length(bee_species$Homalictus_urbanus[bee_species$Homalictus_urbanus$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Homalictus_urbanus[bee_species$Homalictus_urbanus$Sex == "Female",]$IT, i)
  HU_IT[i] = mean(subset1)
}


#Specimen weight
HU_WT = c()
for(i in 1:length(bee_species$Homalictus_urbanus[bee_species$Homalictus_urbanus$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Homalictus_urbanus[bee_species$Homalictus_urbanus$Sex == "Female",]$Spec.wgt, i)
  HU_WT[i] = mean(subset1)
}


##TWO##

#Lasioglossum_pauxillum
#IT
LP_IT = c()
for(i in 1:length(bee_species$Lasioglossum_pauxillum[bee_species$Lasioglossum_pauxillum$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Lasioglossum_pauxillum[bee_species$Lasioglossum_pauxillum$Sex == "Female",]$IT, i)
  LP_IT[i] = mean(subset1)
}


#Specimen weight
LP_WT = c()
for(i in 1:length(bee_species$Lasioglossum_pauxillum[bee_species$Lasioglossum_pauxillum$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Lasioglossum_pauxillum[bee_species$Lasioglossum_pauxillum$Sex == "Female",]$Spec.wgt, i)
  LP_WT[i] = mean(subset1)
}


##THREE
#Bombus_lucorum
BT_IT = c()
for(i in 1:length(bee_species$Bombus_terrestris[bee_species$Bombus_terrestris$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Bombus_terrestris[bee_species$Bombus_terrestris$Sex == "Female",]$IT, i)
  BT_IT[i] = mean(subset1)
}


#Specimen weight
BT_WT = c()
for(i in 1:length(bee_species$Bombus_terrestris[bee_species$Bombus_terrestris$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Bombus_terrestris[bee_species$Bombus_terrestris$Sex == "Female",]$Spec.wgt, i)
  BT_WT[i] = mean(subset1)
}

##FOUR##
#Andrena_flavipes
#IT
AF_IT = c()
for(i in 1:length(bee_species$Andrena_flavipes[bee_species$Andrena_flavipes$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Andrena_flavipes[bee_species$Andrena_flavipes$Sex == "Female",]$IT, i)
  AF_IT[i] = mean(subset1)
}


#Specimen weight
AF_WT = c()
for(i in 1:length(bee_species$Andrena_flavipes[bee_species$Andrena_flavipes$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Andrena_flavipes[bee_species$Andrena_flavipes$Sex == "Female",]$Spec.wgt, i)
  AF_WT[i] = mean(subset1)
}

##FIVE##
#Lasioglossum_lanarium
LL_IT = c()
for(i in 1:length(bee_species$Lasioglossum_lanarium[bee_species$Lasioglossum_lanarium$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Lasioglossum_lanarium[bee_species$Lasioglossum_lanarium$Sex == "Female",]$IT, i)
  LL_IT[i] = mean(subset1)
}

#Specimen weight
LL_WT = c()
for(i in 1:length(bee_species$Lasioglossum_lanarium[bee_species$Lasioglossum_lanarium$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Lasioglossum_lanarium[bee_species$Lasioglossum_lanarium$Sex == "Female",]$Spec.wgt, i)
  LL_WT[i] = mean(subset1)
}

##Six##
#Andrena_nigroaenea 
AN_IT = c()
for(i in 1:length(bee_species$Andrena_nigroaenea[bee_species$Andrena_nigroaenea$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Andrena_nigroaenea[bee_species$Andrena_nigroaenea$Sex == "Female",]$IT, i)
  AN_IT[i] = mean(subset1)
}

#Specimen weight
AN_WT = c()
for(i in 1:length(bee_species$Andrena_nigroaenea[bee_species$Andrena_nigroaenea$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Andrena_nigroaenea[bee_species$Andrena_nigroaenea$Sex == "Female",]$Spec.wgt, i)
  AN_WT[i] = mean(subset1)
}

##Seven##
#Bombus_impatiens 
BI_IT = c()
for(i in 1:length(bee_species$Bombus_impatiens[bee_species$Bombus_impatiens$Sex == "Male",]$IT)){
  subset1 = sample(bee_species$Bombus_impatiens[bee_species$Bombus_impatiens$Sex == "Male",]$IT, i)
  BI_IT[i] = mean(subset1)
}

#Specimen weight
BI_WT = c()
for(i in 1:length(bee_species$Bombus_impatiens[bee_species$Bombus_impatiens$Sex == "Male",]$Spec.wgt)){
  subset1 = sample(bee_species$Bombus_impatiens[bee_species$Bombus_impatiens$Sex == "Male",]$Spec.wgt, i)
  BI_WT[i] = mean(subset1)
}

##Eight##
#Bombus_lapidarius 
BL_IT = c()
for(i in 1:length(bee_species$Bombus_lapidarius[bee_species$Bombus_lapidarius$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Bombus_lapidarius[bee_species$Bombus_lapidarius$Sex == "Female",]$IT, i)
  BL_IT[i] = mean(subset1)
}

#Specimen weight
BL_WT = c()
for(i in 1:length(bee_species$Bombus_lapidarius[bee_species$Bombus_lapidarius$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Bombus_lapidarius[bee_species$Bombus_lapidarius$Sex == "Female",]$Spec.wgt, i)
  BL_WT[i] = mean(subset1)
}

##Nine##
#Lasioglossum_glabriusculum 
LG_IT = c()
for(i in 1:length(bee_species$Lasioglossum_glabriusculum[bee_species$Lasioglossum_glabriusculum$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Lasioglossum_glabriusculum[bee_species$Lasioglossum_glabriusculum$Sex == "Female",]$IT, i)
  LG_IT[i] = mean(subset1)
}

#Specimen weight
LG_WT = c()
for(i in 1:length(bee_species$Lasioglossum_glabriusculum[bee_species$Lasioglossum_glabriusculum$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Lasioglossum_glabriusculum[bee_species$Lasioglossum_glabriusculum$Sex == "Female",]$Spec.wgt, i)
  LG_WT[i] = mean(subset1)
}

##Ten##
#Trigona_spinipes 
TS_IT = c()
for(i in 1:length(bee_species$Trigona_spinipes[bee_species$Trigona_spinipes$Sex == "Female",]$IT)){
  subset1 = sample(bee_species$Trigona_spinipes[bee_species$Trigona_spinipes$Sex == "Female",]$IT, i)
  TS_IT[i] = mean(subset1)
}

#Specimen weight
TS_WT = c()
for(i in 1:length(bee_species$Trigona_spinipes[bee_species$Trigona_spinipes$Sex == "Female",]$Spec.wgt)){
  subset1 = sample(bee_species$Trigona_spinipes[bee_species$Trigona_spinipes$Sex == "Female",]$Spec.wgt, i)
  TS_WT[i] = mean(subset1)
}


## Body length comparison

```{r}
##Relationship between BL AND IT

#bees
bee_bl=bee_all[!is.na(bee_all$BL),]
bee_blength=aggregate(bee_bl$BL~bee_bl$Species,FUN="mean")
bee_blength$IT=as.numeric(unlist(aggregate(bee_bl$IT~bee_bl$Species,FUN="mean")[2]))
bee_blength$Spec.wgt=as.numeric(unlist(aggregate(bee_bl$Spec.wgt~bee_bl$Species,
                                                 FUN="mean")[2]))

colnames(bee_blength)= c("Species","BL","IT","Spec.wgt")

#hoverflies
hov_bl=hov_all[!is.na(hov_all$BL),]
hov_blength=aggregate(hov_bl$BL~hov_bl$Species,FUN="mean")
hov_blength$IT=as.numeric(unlist(aggregate(hov_bl$IT~hov_bl$Species,FUN="mean")[2]))
hov_blength$Spec.wgt=as.numeric(unlist(aggregate(hov_bl$Spec.wgt~hov_bl$Species,FUN="mean")[2]))

colnames(hov_blength)= c("Species","BL","IT","Spec.wgt")

###BEES
cor.test(~log(IT)+log(BL),data=bee_blength)

str(bee_blength)
summary(lm( log(Spec.wgt)~ log(BL),bee_blength))
summary(lm( log(Spec.wgt)~ log(IT),bee_blength))


###HOV
cor.test(~log(IT)+log(BL),hov_blength)

summary(lm(log(Spec.wgt)~log(BL),hov_blength))
summary(lm(log(Spec.wgt)~log(IT),hov_blength))

lengthsize=function(BL, Eq = "DIP"){
  
  if(!Eq %in% c("DIP","HYM","LEP", "S93DB","Sabo02DB", "Sabo02DA", "Sabo02DBB", "R77D",
                "S93DC", "BN06D", "G97D", "GR84D", "JS00DA",
                "S80DCF", "S80DCR", "S80DMF", "S93DA", "W13D", "JS00DN", 
                "S93DN", "Sabo02DN","DIP","Brachycera","Nematocera",
                "Asilidae","Bombyliidae")){
    stop("Equation should be one of 'DIP','HYM','LEP','R77D',
         'S93DB', 'Sabo02DB', 'Sabo02DA', 'Sabo02DBB', 
         'S93DC', 'BN06D', 'G97D', 'GR84D', 'JS00DA', 
         'S80DCF', 'S80DCR', 'S80DMF', 'S93DA', 'W13D', 'JS00DN', 
         'S93DN', 'Sabo02DN','All','Brachycera','Nematocera','Asilidae','Bombyliidae'")
  } else {
    S93DB <- exp(-3.374+2.158*log(BL))
    Sabo02DB <- 0.006*(BL)^3.05
    Sabo02DA <- 0.38*(BL)^1.5
    Sabo02DBB <- 0.007*(BL)^3.337
    S93DC <- exp(-3.619+2.632*log(BL))
    BN06D <- exp(-0.041+0.010*(BL))
    G97D <- exp(-3.4294+2.5943*log(BL))
    GR84D <- exp(-3.653+2.546*log(BL))
    JS00DA <- exp(-2.462+1.881*log(BL))
    R77D <- exp(-3.293+2.366*log(BL))
    S80DCF <- exp(log(0.074)+1.64*log(BL))
    S80DCR <- exp(log(0.068)+1.59*log(BL))
    S80DMF <- exp(log(0.022)+2.42*log(BL))
    S93DA <- exp(-3.184+2.23*log(BL))
    W13D <- exp(-3.29+2.65*log(BL))
    JS00DN <- exp(-2.462+1.881*log(BL))
    S93DN <- exp(-3.675+2.212*log(BL))
    Sabo02DN <- 0.1*(BL)^1.57
    
    
    Sabo02HA <- 0.006*(BL)^3.407
    S93HB <- exp(-3.854+2.441*log(BL))
    BN06HF <- exp(log(0.001)+2.33*log(BL))
    GR84F <- exp(-3.997+log(BL)*2.489)
    JS00HF <- exp(-3.730+2.103*log(BL))
    R77A <- exp(-4.029+2.572*log(BL))
    S80FCF <- exp(log(0.012)+2.72*log(BL))
    S80FCR <- exp(log(0.021)+2.31*log(BL))
    S80FMF <- exp(log(0.034)+2.19*log(BL))
    S93HF <- exp(-4.727+2.919*log(BL))
    S93HH <- exp(-2.891+2.302*log(BL))
    S93HI <- exp(-4.149+2.464*log(BL))
    BN06H1 <- exp(-6.783+2.544*log(BL))
    G97H <- exp(-3.5917+2.6429*log(BL))
    G97F <- exp(-3.1415+2.3447*log(BL))
    GR84H <- exp(-2.86+(BL)*0.478)
    JS00HA <- exp(-3.556+2.193*log(BL))
    R77H <- exp(-3.871+2.407*log(BL))
    S80HCF <- exp(log(0.043)+2.07*log(BL))
    S80HCR <- exp(log(0.022)+2.29*log(BL))
    S80HMF <- exp(log(0.016)+2.55*log(BL))
    S93HA <- exp(-4.284+2.696*log(BL))
    Sabo02H <- 0.56*(BL)^1.56
    W13H <- exp(-4.3+3*log(BL))
    S93HP <- exp(-2.341+2.006*log(BL))
    S93HV <- exp(-3.54+2.782*log(BL))
    Sabo02HV <- 0.001*(BL)^3.723
    S93LG <- exp(-4.172+2.628*log(BL))
    S93LM <- exp(-4.913+2.918*log(BL))
    BN06L <- exp(log(0.001)+2.313*log(BL))
    G97L <- exp(-4.7915+2.8585*log(BL))
    JS00L <- exp(-3.268+2.243*log(BL))
    R77L <- exp(-4.037+2.903*log(BL))
    S80LCF <- exp(log(0.026)+2.5*log(BL))
    S80LCR <- exp(log(0.078)+1.32*log(BL))
    S80LMF <- exp(log(0.014)+2.55*log(BL))
    S93LA <- exp(-5.036+3.122*log(BL))
    W13L <- exp(-3.83+2.77*log(BL))
    S93LC <- exp(-3.755+2.658*log(BL))
    S93LN <- exp(-3.337+2.499*log(BL))
    
    
    if (Eq ==  "S93DB") out <- S93DB
    if (Eq == "Sabo02DB") out <- Sabo02DB
    if (Eq == "Sabo02DA") out <- Sabo02DA
    if (Eq == "Sabo02DBB") out <- Sabo02DBB
    if (Eq == "S93DC") out <- S93DC
    if (Eq == "BN06D") out <- BN06D
    if (Eq == "G97D") out <- G97D
    if (Eq == "GR84D") out <- GR84D
    if (Eq == "JS00DA") out <- JS00DA
    if (Eq == "R77D") out <- R77D
    if (Eq == "S80DCF") out <- S80DCF
    if (Eq == "S80DCR") out <- S80DCR
    if (Eq == "S80DMF") out <- S80DMF
    if (Eq == "S93DA") out <- S93DA
    if (Eq == "W13D") out <- W13D
    if (Eq == "JS00DN") out <- JS00DN
    if (Eq == "S93DN") out <- S93DN
    if (Eq == "Sabo02DN") out <- Sabo02DN
    if (Eq == "Brachycera") out <- cbind(S93DB, Sabo02DB)
    if (Eq == "Nematocera") out <- cbind(JS00DN, S93DN, Sabo02DN)
    if (Eq == "Asilidae") out <- cbind(Sabo02DA, S93DB)
    if (Eq == "Bombyliidae") out <-cbind(Sabo02DBB,S93DB)
    if (Eq == "DIP") out <- cbind(BN06D, G97D, GR84D, JS00DA, R77D, S80DCF, S80DCR, S80DMF, S93DA, W13D)
    
    if (Eq ==  "Sabo02HA") out <- Sabo02HA
    if (Eq == "S93HB") out <- S93HB
    if (Eq == "BN06HF") out <- BN06HF
    if (Eq == "GR84F") out <- GR84F
    if (Eq == "JS00HF") out <- JS00HF
    if (Eq == "R77A") out <- R77A
    if (Eq == "S80FCF") out <- S80FCF
    if (Eq == "S80FCR") out <- S80FCR
    if (Eq == "S80FMF") out <- S80FMF
    if (Eq == "S93HF") out <- S93HF
    if (Eq == "S93HH") out <- S93HH
    if (Eq == "S93HI") out <- S93HI
    if (Eq == "BN06H1") out <- BN06H1
    if (Eq == "G97H") out <- G97H
    if (Eq == "G97F") out <- G97F
    if (Eq == "GR84H") out <- GR84H
    if (Eq == "JS00HA") out <- JS00HA
    if (Eq == "R77H") out <- R77H
    if (Eq == "S80HCF") out <- S80HCF
    if (Eq == "S80HCR") out <- S80HCR
    if (Eq == "S80HMF") out <- S80HMF
    if (Eq == "S93HA") out <- S93HA
    if (Eq == "Sabo02H") out <- Sabo02H
    if (Eq == "W13H") out <- W13H
    if (Eq == "S93HP") out <- S93HP
    if (Eq == "S93HV") out <- S93HV
    if (Eq == "Sabo02HV") out <- Sabo02HV
    if (Eq == "Vespidae") out <- cbind(S93HV,Sabo02HV)
    if (Eq == "Formicidae") out <- cbind(BN06HF,GR84F,JS00HF,R77A,S80FCF,S80FCR,S80FMF,S93HF,S93HH,S93HI,BN06H1,G97H,G97F)
    if (Eq == "HYM") out = cbind(BN06H1,G97H, G97F,GR84H,JS00HA,R77H,S80HCF,S80HCR,S80HMF,S93HA,Sabo02H,W13H)
    
    if (Eq ==  "S93LG") out <- S93LG
    if (Eq == "S93LM") out <- S93LM
    if (Eq == "BN06L") out <- BN06L
    if (Eq == "G97L") out <- G97L
    if (Eq == "JS00L") out <- JS00L
    if (Eq == "R77L") out <- R77L
    if (Eq == "S80LCF") out <- S80LCF
    if (Eq == "S80LCR") out <- S80LCR
    if (Eq == "S80LMF") out <- S80LMF
    if (Eq == "S93LA") out <- S93LA
    if (Eq == "W13L") out <- W13L
    if (Eq == "S93LC") out <- S93LC
    if (Eq == "S93LN") out <- S93LN
    if (Eq == "LEP") out <- cbind(BN06L,G97L,JS00L,R77L,S80LCF, S80LCR,S80LMF,S93LA,W13L)
    if (Eq == "Noctuidea") out <- cbind(S93LC, S93LN)
    out
  }
} 


#BL analyses


##Pre-existing equations
hov_bl_rmse=cbind(rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,1])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,2])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,3])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,4])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,5])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,6])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,7])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,8])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,9])),
                  rmse((hov_bl$Spec.wgt),(lengthsize(hov_bl$BL,"DIP")[,10])))

#mean
mean(hov_bl_rmse)

#standard error
mean(hov_bl_rmse)/sqrt(10)

bee_bl_rmse=cbind(rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,1])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,2])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,3])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,4])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,5])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,6])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,7])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,8])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,9])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,10])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,11])),
                  rmse((bee_bl$Spec.wgt), (lengthsize(bee_bl$BL,"HYM")[,12])))

#mean
mean(bee_bl_rmse)

#standard error
mean(bee_bl_rmse)/sqrt(12)

#Comparison with Cane 1989
rmse((bee_all$Spec.wgt),(Cane(IT=bee_all$IT)))