###This file defines the source functions used for each of the four trade-off models as implemented in the main model

## Define a function to simulate age at death in a Gompertz model where the b parameter varies
G_mort_b <- function(G_aa = G_aa, bbs = bbs){
  age_death <- round(rgompertz(length(bbs), shape = bbs, rate = G_aa))
  return(age_death)
}


####Define a function to calculate lifespans, fertilities, and reproductive successes for each trade-off model.

##The single-trade-off model
#This one ignores trade-off2 and uses only trade-off 1
live1 <- function(i = i, t_o1s = t_o1s, t_o2s = t_o2s, t_o1_wt = t_o1_wt, t_o2_wt = t_o2_wt, sig1 = sig1, 
 b0 = b0, maxfert = maxfert, n_inds = n_inds, aa = aa, cc = cc, yy = yy)
 {
 x <- t_o2s/t_o2_wt #Does nothing; Just to use the parameters for consistency
 t_os <- t_o1s #The full trade-off is trade-off 1 in this model 
 t_o_wt <- t_o1_wt #Trade-off weight fot T-) 1
 #The b is multiplied by the exponent of the trade-off adjusted by its weight
 bs <- b0 + aa*exp((t_os + yy)*cc/t_o_wt) 
 #Age at death is calculated based on a Gompertz model
 a_ds <- G_mort_b(G_aa = G_aa, bbs = bs)
 #Fertility is perturbed like b. Constant at all ages, bounded between zero and a maximum
 ferts <- maxfert/(1 + exp(-t_os*t_o_wt)) 
 #Reproductive success is the product of fertility and age at death, with a random perturbation
 rep_sucs <- pmax(0, ferts*a_ds + rnorm(n_inds, 0, ferts*a_ds*sig1))
 #This makes the reproductive success sum to 1 so we can use it as a weight for sampling the next generation
 probs <- rep_sucs/sum(rep_sucs)
 #Output results
 res <- cbind(t_o1s, t_o2s, bs, a_ds, ferts, rep_sucs, t_os, probs)
 return(res)
}

##The "Additive" model
#This model multiplies the exponential of the trade-offs
#The two trade-offs interact by both applying their effect to fertility and mortality
#They can thus be either antagonistic or synergistic depending on their directions (weights)
live2 <- function(i = i, t_o1s = t_o1s, t_o2s = t_o2s, t_o1_wt = t_o1_wt, t_o2_wt = t_o2_wt, sig1 = sig1, 
 b0 = b0, maxfert = maxfert, n_inds = n_inds, aa = aa, cc = cc, yy = yy)
 {
 t_os <- t_o1s  +  t_o2s #Does nothing; Just to use the parameters for consistency
 bs <- b0 + aa*exp(((t_o1s + yy/2)*cc)/t_o1_wt + ((t_o2s + yy/2)*cc)/t_o2_wt)
 a_ds <- G_mort_b(G_aa = G_aa, bbs = bs)
 ferts <- maxfert/(1 + exp(-t_o1s*t_o1_wt  +  -t_o2s*t_o2_wt)) 
 rep_sucs <- pmax(0, ferts*a_ds + rnorm(n_inds, 0, ferts*a_ds*sig1))
 probs <- rep_sucs/sum(rep_sucs)
 res <- cbind(t_o1s, t_o2s, bs, a_ds, ferts, rep_sucs, t_os, probs)
 return(res)
}


##The "Maximum" model
#This model chooses the larger of the two trade-offs in either direction
#Each individual can have a different trade-off from the others
live3 <- function(i = i, t_o1s = t_o1s, t_o2s = t_o2s, t_o1_wt = t_o1_wt, t_o2_wt = t_o2_wt, sig1 = sig1, 
 b0 = b0, maxfert = maxfert, n_inds = n_inds, aa = aa, cc = cc, yy = yy)
 {
 t_os <- ifelse(abs(t_o1s) > abs(t_o2s), t_o1s, t_o2s) #Choose which trade based on the one with the larger absolute effect in either direction
 t_o_wts <- ifelse(abs(t_o1s) > abs(t_o2s), t_o1_wt, t_o2_wt)
 bs <- b0 + aa*exp((t_os + yy)*cc/t_o_wts)
 a_ds <- G_mort_b(G_aa = G_aa, bbs = bs)
 ferts <- maxfert/(1 + exp(-t_os*t_o_wts)) 
 rep_sucs <- pmax(0, ferts*a_ds + rnorm(n_inds, 0, ferts*a_ds*sig1))
 probs <- rep_sucs/sum(rep_sucs)
 res <- cbind(t_o1s, t_o2s, bs, a_ds, ferts, rep_sucs, t_os, probs)
 return(res)
}


##The "Minimum" model
#This model chooses the smaller of the two trade-offs in either direction
#Each individual can have a different trade-off from the others
live4 <- function(i = i, t_o1s = t_o1s, t_o2s = t_o2s, t_o1_wt = t_o1_wt, t_o2_wt = t_o2_wt, sig1 = sig1, 
 b0 = b0, maxfert = maxfert, n_inds = n_inds, aa = aa, cc = cc, yy = yy)
 {
 t_os <- ifelse(abs(t_o1s) < abs(t_o2s), t_o1s, t_o2s) #Choose which trade based on the one with the larger absolute effect in either direction
 t_o_wts <- ifelse(abs(t_o1s) < abs(t_o2s), t_o1_wt, t_o2_wt)
 bs <- b0 + aa*exp((t_os + yy)*cc/t_o_wts)
 a_ds <- G_mort_b(G_aa = G_aa, bbs = bs)
 ferts <- maxfert/(1 + exp(-t_os*t_o_wts)) 
 rep_sucs <- pmax(0, ferts*a_ds + rnorm(n_inds, 0, ferts*a_ds*sig1))
 probs <- rep_sucs/sum(rep_sucs)
 res <- cbind(t_o1s, t_o2s, bs, a_ds, ferts, rep_sucs, t_os, probs)
 return(res)
}