### Appendix S1 R functions to fit the Stochastic Ricker Model

### Time Series

### Armigeres subalbatus abundance at t+1 (biweeks 2-12)
nt1<-c(4,  7,  5, 34,  1, 17,  5, 25,  9,  1,  4)
### Armigeres subalbatus abundance at t (biweeks 1-11)
nt<- c(2,  4,  7,  5, 34,  1, 17,  5, 25,  9,  1)
### Cumulative bi-weekly rainfall before t+1 
RR<- c(34.5,  29.0, 197.5, 376.5,  34.0, 301.0,  73.0, 188.0,  43.5,  68.5,  53.5)


### Calling a library with the Negative Binomial Generalized linear model fitting function
library(MASS)

### Fitting the environmental stochastic Ricker model as a Neg-Bin GLM (Autonomous)
rglmnba<-glm.nb(nt1~offset(log(nt))+nt)
### Calling the model summary (to see parameter estimates)

summary(rglmnba)
### Fitting the environmental stochastic Ricker model as a Neg-Bin GLM (Forced by Rainfall)

rglmnbF<-glm.nb(nt1~offset(log(nt))+nt+RR)

### Calling the model summary

summary(rglmnbF)


### Likelihood functions

### Calling a library with convenient functions to fit Maximum likelihood models
library(bbmle)

###Function to fit the environmental stochastic Ricker model (Autonomous)
renva <- function (lambda0, b, kappa){
	nt1<-nt1
	nt<-nt
	-sum(dnbinom(nt1, mu=(lambda0*nt*exp(-1*b*nt)),size=kappa,log=TRUE))
}
### Fitting the model
fitrenva=mle2(renva,start=list(lambda0=7.37, b=0.15, kappa=1.43))
### Calling the model summary
summary(fitrenva)

###Function to fit the environmental stochastic Ricker model (Forced by Rainfall)
renvF <- function (lambda0, b, kappa,g){
	nt1<-nt1
	nt<-nt
	RR<-RR
	-sum(dnbinom(nt1, mu=(lambda0*nt*exp(-1*b*nt+g*RR)),size=kappa,log=TRUE))
}
### Fitting the model
fitrenvF=mle2(renvF,start=list(lambda0=2.1714, b=0.115, kappa=2.678,g=0.0054))
### Calling the model summary
summary(fitrenvF)


###Function to fit the demographic stochastic Ricker model (Autonomous)
rdema <- function (lambda0, b, kappa){
	nt1<-nt1
	nt<-nt
	-sum(dnbinom(nt1, mu=(lambda0*nt*exp(-1*b*nt)),size=kappa*nt,log=TRUE))
}
### Fitting the model
fitrdema=mle2(rdema,start=list(lambda0=5.4005, b=0.1314215, kappa=0.2724))
### Calling the model summary
summary(fitrdema)

###Function to fit the demographic stochastic Ricker model (Forced by Rainfall)
rdemF <- function (lambda0, b, kappa,g){
	nt1<-nt1
	nt<-nt
	RR<-RR
	-sum(dnbinom(nt1, mu=(lambda0*nt*exp(-1*b*nt+g*RR)),size=kappa*nt,log=TRUE))
}
### Fitting the model
fitrdemF=mle2(rdemF,start=list(lambda0=1.5716, b=0.0979, kappa=0.5574,g=0.00536))
### Calling the model summary
summary(fitrdemF)