sens and elast stoch2.R

In rosehartman/frog-trap: Draft manuscript and code on ecological traps

# Calculate stochastic sensitivities

source('R/StochSens.R')

# create an array of projection matricies for each time step
As <- replicate(tf, Getmat(p=.5, state, fx, n0, npatch, nstg, P, pred=.5))
# calculate the stochastic sensitivity matrix for that time period
StochSens(As)



# Make a function to calculate average sensitivites for a bunch to time runs
# over a bunch of attractiveness values
elsplot = function(pred) {
i=1:21
# Apparently this gets too big for R to handle if you run it for 100,000 time steps, but that doesn't make sense...
run = laply(i, function(x){
  ru = replicate(100,bigrun(tf=1000, p1=p[x], pred1=pred))
  aaply(ru, 1:2, function(thingy) {sum(thingy)/100})
},
            .parallel=T)

 # Data frame with the elasticity of each non-zero matrix entry
elsdf = data.frame(p=p, f1=run[, 1,2], j11=run[, 2,1], j21=run[, 2,3], a1=run[, 2,2], 
f2=run[, 3,4],  j12=run[, 4,1], j22=run[, 4,3], a2=run[, 4,4])
library(reshape2)
elsedf2 = melt(elsdf, id.vars="p", variable.name="stage",value.name="elas")
elsedf2$patch = rep(NA, 168)
elsedf2$stage = rep(NA, 168)
elsedf2$patch[1:84] = "1"
elsedf2$patch[85:168] = "2"
elsedf2$stage[1:21]="f"
elsedf2$stage[22:42]="j1"
elsedf2$stage[43:63]="j2"
elsedf2$stage[64:84]="a"
elsedf2$stage[85:105]="f"
elsedf2$stage[106:126]="j1"
elsedf2$stage[127:147]="j2"
elsedf2$stage[148:168]="a"

# plot the change in elasticities with different ammounts of migration
el = qplot(data=elsedf2, x=p, y=elas, geom="line", color=stage, linetype = patch,
           xlab="proportion of juveniles moving to \nhigh predation patch (patch1)", ylab="elasticity of log lambdas \n to changes in life stage",
           main=paste("predation = ", pred))
el
}

# Plot the elasticities for each matrix entry over many 
# attractivenesses and predation rates
pred.5 = elsplot(pred=.5)
pred.5
#pred.1 = elsplot(pred=c(.1,1))
pred.2 = elsplot(pred=.2)
#pred.3 = elsplot(pred=c(.3,1))
pred.4 = elsplot(pred=.4)
pred.6 = elsplot(pred=.6)
#pred.7 = elsplot(pred=c(.7,1))
pred.8 = elsplot(pred=.8)
#pred.9 = elsplot(pred=c(.9,1))
pred1 = elsplot(pred=1)
pred1

svg(filename="figure2.svg", width=8, height=5)
pred.5
dev.off()

# try keeping attractiveness equal and varying predation
elsplot2 = function(p) {
  i=seq(0,1, by=.1)
  run = aaply(i, 1, function(x){
    ru = replicate(100, bigrun(1000, p1=p, pred=x))
    aaply(ru, 1:2, function(thingy) {sum(thingy)/100})
  },
              .parallel=T)
  
  # Data frame with the elasticity of each non-zero matrix entry
  elsdf = data.frame(pred=i,  f1=run[, 1,3], l1=run[, 2,1], j21=run[, 3,5], j11=run[, 3,2], a1=run[, 3,3], 
                     f2=run[, 4,6], l2=run[, 5,4], j12=run[, 6,2], j22=run[, 6,5], a2=run[, 6,6])
  library(reshape2)
  elsedf2 = melt(elsdf, id.vars=c("pred"), variable.name="stage",value.name="elas")
  elsedf2$patch = rep(NA, 110)
  elsedf2$stage = rep(NA, 110)
  elsedf2$patch[1:55] = "1"
  elsedf2$patch[56:110] = "2"
  elsedf2$stage[1:11]="f"
  elsedf2$stage[12:22]="l"
  elsedf2$stage[23:33]="j2"
  elsedf2$stage[34:44]="j1"
  elsedf2$stage[45:55]="a"
  elsedf2$stage[56:66]="f"
  elsedf2$stage[67:77]="l"
  elsedf2$stage[78:88]="j1"
  elsedf2$stage[89:99]="j2"
  elsedf2$stage[100:110]="a"
  # plot the change in elasticities with different ammounts of migration
  el = qplot(data=elsedf2, x=(1-pred)*100, y=elas, geom="line", color=stage, linetype = patch,
             xlab="predation rate", ylab="elasticity of Ms to changes in life stage",
             main=paste("appearence = ", App))
  el
}

app.equal = elsplot2(c(100, 100))
app.equal
app.10 =elsplot2(c(10, 100))

svg(file = "elasticitypred5.svg", width=5, height=3)
pred.5
dev.off()

# elasticity of lambda to changes in matrix elements for the deterministic
# model when all years are average and migration and predation are at 50%
det = matrix(c(0, 150, 0, 0, 
               .009*.5*.5,.6,.009*.5,0, 
               0, 0, 0,150,  
               .009*.5*.5,0, .009*.5,.6), nrow=4, ncol=4, byrow=TRUE)
elasticity(det)