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#Nicholson's Blow Flies (Gurney et al 1983)
#Reproducing the first example in 'The systematic formulation of tractable single-species population models incorporating age structure'
#by WSC Gurney, RM Nisbet and J Lawton, Journal of Animal Ecology, 52, p479-495, 1983
#library(stagePop)
#All the vectors are specified in the order of the life cycle
#e.g. start with eggs and finish with reproducing adults
#solver.options=list(DDEsolver='deSolve',atol=1e-3,rtol=1e-3,hbsize=1e4)
solver.options=list(DDEsolver='PBS',tol=1e-4,hbsize=1e4,dt=0.01)
#--------------------------DEFINE RATE FUNCTIONS---------------------------------------
blowFliesFunctions <- list(
reproFunc=function(x,time,species,strain){
A0=600; q=8.5
reprod=q*x$blowflies['adults',1]*exp(-x$blowflies['adults',1]/A0)
return(reprod)
},
deathFunc=function(stage,x,time,species,strain){
#per capita death rate (/d)
a=c(0.07,0.004,0.003,0.0025,0.27)
return(a[stage])
},
durationFunc=function(stage,x,time,species,strain){
#duration of each stage in days
a=c(0.6,5.0,5.9,4.1)
return(a[stage])
},
immigrationFunc=function(stage,x,time,species,strain){
v=0
if (stage==5){if (time>=0 & time<=1){v=100}}
return(v)
},
emigrationFunc=function(stage,x,time,species,strain){return(0)}
)
#-------------------------------RUN MODEL---------------------------------------
modelOutput = popModel(
numSpecies=1,
numStages=5,
ICs=list(matrix(0,nrow=5,ncol=1)),
timeVec=seq(0,200,0.5),
timeDependLoss=TRUE,
timeDependDuration=FALSE,
rateFunctions=blowFliesFunctions,
solverOptions=solver.options,
stageNames=list(c('eggs','larvae','pupae','juveniles','adults')),
speciesNames=c('blowflies'),
saveFig=FALSE
)
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