#This script will not work alone. Global parameters for temperature and copepodid attachment rate are in S2, S3 and S4 (only run one at a time). Calculations are for daily rates
#Install the packages
require(triangle)
require(popbio)
require(matrixStats)


#Parameters and sample sizes are here

#Parameters

SampleSize = 1 #Sample Size for each stage- set at 1 in the paper, larger sample sizes will increase the 'within-population' variation and reduce confidence intervals on outputs

#Developmental Parameters

EggB1 = 41.98
EggB1SE = 2.85
EggB2 = 0.338
EggB2SE = 0.01200
EggV = 2

NaupliiB1 = 24.79
NaupliiB1SE = 1.43
NaupliiB2 = 0.525
NaupliiB2SE = 0.017
NaupliiV = 0

ChB1 = 74.7
ChB1SE = 33.64
FChB2 = 0.246
FChB2SE = 0.007
FChV = 0.793


PreadB1 = 67.47
PreadB1SE = 20.36
FPreadB2 = 0.177
FPreadB2SE = 0.006
FPreadV = 0.30333


#Survival Parameters, (create a distribution of survival estimates using the triangle function)

EggPercentNonviable = rtriangle(SampleSize, .04, .25, .10)  
EggSurv = (0.96797)

NaupliiSurv = (0.83000)



FChalimusSurvMode =(0.992)
FChalimusSurvUpper = (0.997)
FChalimusSurvLower = (0.98)
FChalimusSurvVect = rtriangle(SampleSize, FChalimusSurvLower, FChalimusSurvUpper, FChalimusSurvMode)


FPreadSurvMode = (0.965)
FPreadSurvUpper = (0.98)
FPreadSurvLower = (0.953)
FPreadSurvVect = rtriangle (SampleSize, FPreadSurvLower, FPreadSurvUpper, FPreadSurvMode)


FAdultSurvMode = (0.965)
FAdultSurvUpper= (0.997)
FAdultSurvLower= (0.904)
FAdultSurvVect = rtriangle(SampleSize, FAdultSurvLower, FAdultSurvUpper, FAdultSurvMode)



#Fecundity
PropEggsFemale=0.5
TimeHatching = 1
FirstEggstringSize =152
FirstEggstringSizeSD = 31
RandFirstEggstringSize=rnorm(SampleSize, mean=FirstEggstringSize, sd=FirstEggstringSizeSD) #sample Eggstring sizes from a normal distribution

TimeToSubsequentEggstring = max(-1.2*Temp + 19.64, 1) #Equation 7
SubsequentEggstringSize = 296
SubsequentEggstringSizeSD = 100 
RandSubsequentEggstringSize=rnorm(SampleSize, mean=SubsequentEggstringSize, sd=SubsequentEggstringSizeSD) #sample Eggstring sizes from a normal distribution


#Copepodids
#CopAttach =0.1
CopDevel =4.6
CopSurv=(CopAttach)^(1/(CopDevel)) #Equation Six



#Calculate Developmental Times. For each life stage the time until development is calculated using a belahradek equation (equation 4) and adding it to the minimum development time (equation 5)


RandEggB1= rnorm(SampleSize, mean=EggB1, sd=EggB1SE)
RandEggB2= rnorm(SampleSize, mean=EggB2, sd=EggB2SE)


EggTimes=vector(mode="numeric",length=0)

for(i in 1:length(RandEggB1)){
  EggTime=((RandEggB1[[i]]/(Temp-10+(RandEggB1[[i]]*RandEggB2[[i]])))^2)+EggV;
  EggTimes=cbind(EggTimes, EggTime)}



#Nauplii

RandNaupliiB1= rnorm(SampleSize, mean=NaupliiB1, sd=NaupliiB1SE)
RandNaupliiB2= rnorm(SampleSize, mean=NaupliiB2, sd=NaupliiB2SE)

NaupliiTimes=vector(mode="numeric",length=0)

for(i in 1:length(RandNaupliiB1)){
  NaupliiTime=((RandNaupliiB1[[i]]/(Temp-10+(RandNaupliiB1[[i]]*RandNaupliiB2[[i]])))^2)+NaupliiV;
  NaupliiTimes=cbind(NaupliiTimes, NaupliiTime)}


#Female Chalimus

RandFChB1= rnorm(SampleSize, mean=ChB1, sd=ChB1SE)
RandFChB2= rnorm(SampleSize, mean=FChB2, sd=FChB2SE)

FChTimes=vector(mode="numeric",length=0)

for(i in 1:length(RandFChB1)){
  FChTime=((RandFChB1[[i]]/(Temp-10+(RandFChB1[[i]]*RandFChB2[[i]])))^2)+FChV;
  FChTimes=cbind(FChTimes, FChTime)}


#Female Preadults

RandFPreadB1= rnorm(SampleSize, mean=PreadB1, sd=PreadB1SE)
RandFPreadB2= rnorm(SampleSize, mean=FPreadB2, sd=FPreadB2SE)

FPreadTimes=vector(mode="numeric",length=0)

for(i in 1:length(RandFPreadB1)){
  FPreadTime=((RandFPreadB1[[i]]/(Temp-10+(RandFPreadB1[[i]]*RandFPreadB2[[i]])))^2)+FPreadV;
  FPreadTimes=cbind(FPreadTimes, FPreadTime)}


#Matrices from Vectors of Values

#Transition

#G
G1 =(1/median(EggTimes))*EggSurv #Equation 2

G2 = (1/(CopDevel+median(NaupliiTimes)))*CopSurv*NaupliiSurv #Equation 2

G3 =(1/(median(FChTimes)))*mean(FChalimusSurvVect) #Equation 2

G4 =(1/(median(FPreadTimes)))*mean(FPreadSurvVect) #Equation 2

G5 = 1/TimeHatching*mean(FAdultSurvVect) #Equation 8

G6 =(1/(median(TimeToSubsequentEggstring)+median(EggTimes)-TimeHatching))*mean(FAdultSurvVect) #Equation 9

G7 = 1/TimeHatching*mean(FAdultSurvVect) #Equation 8



#P

P1 = EggSurv*(1-G1) #equation 1

P2 = CopSurv*NaupliiSurv*(1-G2) #equation 1

P3 = mean(FChalimusSurvVect)*(1-G3) #equation 1

P4 = mean(FPreadSurvVect)*(1-G4) #equation 1

P5 = mean(FAdultSurvVect)*(1-G5) #equation 1

P6 = mean(FAdultSurvVect)*(1-G6) #equation 1

P7 = mean(FAdultSurvVect)*(1-G7) #equation 1


# Fecundity

FirstClutchSizes=vector(mode="numeric",length=0)
SubsequentClutchSizes=vector(mode="numeric",length=0)

for(i in 1:length(RandFirstEggstringSize)){
  FirstClutchSize=((1-EggPercentNonviable[[i]])*RandFirstEggstringSize[[i]])*2/(TimeHatching) #multiply by 2 for 2 eggstrings
  FirstClutchSizes=cbind(FirstClutchSizes, FirstClutchSize)}

F1 = mean(FirstClutchSizes)/2 #equation 3, divided by 2 for females only

for(i in 1:length(RandSubsequentEggstringSize)){
  SubsequentClutchSize=((1-EggPercentNonviable[[i]])*RandSubsequentEggstringSize[[i]])*2/(TimeHatching) #multiply by 2 for 2 eggstrings
  SubsequentClutchSizes=cbind(SubsequentClutchSizes, SubsequentClutchSize)}

F2 = mean(SubsequentClutchSizes)/2 #equation 3, divided by 2 for females only