################################################################################
##  Appendix 1: State-space formulation of a multi-state model of mark-       ##
##              recapture of Anaea aidea larvae                               ##
##              Code modified from Gimenez, O. et al. 2012. Estimating        ##
##              demographic parameters using hidden process dynamic models.   ##
##               Theor. Popul. Biol. 82: 307-316.                            ##
################################################################################
# model: p(stage)  phi(stage,density)  psi(stage,temperature)
# p = detection probability, phi = survival probability, psi = growth probabilities

rm(list=ls(all=T))  ##Clears R's short term memory
# Enter Data: Each row is a caterpillar with 9 survey dates
# 0 = not observed, 1 = Egg, 2 = 1st instar, 3 = 2nd, 4 = 3rd, 5 = 4th, 6 = 5th,
# 7 = Pupa, 8 = dead 1st, 9 = dead 2nd, 10 = dead 3rd, 11 = dead 4th, 12 = dead 5th,
# 13 = removed, a category that removes dead individuals from the study and includes 
# dead eggs and pupae that cannot be observed. 
mydata<-matrix(c(
0,0,0,0,0,0,0,2,3,
0,0,0,0,0,0,0,2,2,
0,0,0,0,0,0,0,2,3,
2,2,0,0,0,0,0,0,0,
5,5,5,6,6,6,0,0,0,
5,5,0,0,0,0,0,0,0,
3,3,3,3,0,0,0,0,0,
0,0,0,2,3,0,4,0,0,
0,0,0,2,3,0,9,0,0,
0,0,0,2,3,0,4,5,6,
2,2,3,0,0,0,0,0,0,
2,0,0,0,0,0,0,0,0,
0,0,0,2,3,4,5,0,0,
2,2,3,3,4,0,0,0,0,
3,3,3,4,5,11,0,0,0,
4,4,4,5,5,6,6,6,6,
4,4,4,5,6,6,6,6,0,
2,2,3,3,4,5,6,6,6,
0,2,2,8,0,0,0,0,0,
2,2,3,3,4,5,5,6,6,
3,3,4,4,4,4,0,0,0,
0,2,2,3,4,5,5,6,6,
0,2,2,3,4,4,5,5,6,
2,2,3,0,0,0,0,0,0,
2,2,3,4,0,5,6,0,0,
3,4,4,4,0,5,11,0,0,
4,4,5,5,6,6,6,6,6,
4,4,5,5,5,6,6,0,0,
4,4,5,5,6,6,6,0,0,
3,3,10,0,0,0,0,0,0,
2,2,2,3,9,0,0,0,0,
2,2,3,3,0,0,0,0,0,
2,2,0,0,0,0,0,0,0,
0,2,2,3,4,11,0,0,0,
0,0,0,0,2,2,3,4,4,
0,0,3,4,5,5,6,0,0,
2,2,3,4,5,5,11,0,0,
3,3,0,0,0,0,0,0,0,
3,3,4,5,5,5,6,6,0,
4,4,10,0,0,0,0,0,0,
0,0,0,0,2,3,0,0,0,
3,3,4,5,5,6,6,6,0,
0,0,0,0,0,2,3,4,4,
0,0,0,0,0,0,0,0,5,
0,2,0,0,0,0,0,0,0,
2,3,4,0,0,0,0,0,0,
2,2,3,4,4,5,6,6,0,
2,2,3,4,5,5,6,0,0,
2,2,3,3,0,0,0,0,0,
0,2,3,3,3,4,0,0,0,
0,2,3,4,4,5,5,6,6,
0,0,0,0,2,0,3,0,0,
0,0,2,2,3,4,5,5,6,
2,2,3,3,4,5,5,6,6,
0,0,2,8,0,0,0,0,0,
2,0,0,0,0,0,0,0,0,
0,0,2,3,4,5,5,6,6,
2,2,3,4,4,5,6,6,0,
0,0,0,0,0,2,0,0,0,
0,0,0,0,2,3,3,4,11,
0,0,2,2,0,0,0,0,0,
0,0,0,2,3,4,5,5,6,
0,0,0,0,2,0,0,0,0,
0,0,0,0,0,2,3,3,4,
0,0,2,3,0,0,0,0,0,
0,0,2,0,0,0,0,0,0,
0,0,2,2,3,4,5,5,6,
2,0,0,0,0,0,0,0,0,
2,2,3,4,5,6,6,6,0,
0,0,0,0,3,4,5,5,6,
0,0,0,0,2,3,0,0,0,
0,0,0,0,2,3,0,0,0,
0,0,0,0,0,2,0,0,0,
2,2,3,4,5,5,5,0,0,
2,2,3,4,4,5,5,6,6,
0,0,2,3,4,0,0,0,0,
0,0,1,0,0,0,0,0,0,
0,0,0,2,3,0,0,0,0,
2,3,4,4,4,4,5,5,6,
2,0,0,0,0,0,0,0,0,
2,2,0,0,0,0,0,0,0,
2,0,0,0,0,0,0,0,0,
2,2,3,4,4,5,5,5,6,
4,5,5,6,6,6,0,0,0,
0,2,2,0,0,0,0,0,0,
0,2,2,3,3,4,0,0,0,
0,0,2,2,3,4,5,5,11,
0,0,2,3,4,4,5,11,0,
0,0,2,2,3,0,0,0,0,
0,0,2,2,3,4,10,0,0,
0,0,2,3,4,4,11,0,0,
0,0,2,0,0,0,0,0,0,
0,0,0,0,2,3,3,4,5,
0,0,0,0,2,3,3,4,0,
2,2,8,0,0,0,0,0,0,
3,3,4,5,0,0,0,0,0,
3,3,4,5,6,6,6,6,0,
2,0,0,0,0,0,0,0,0,
0,0,0,2,2,3,0,0,0,
3,0,0,0,0,0,0,0,0,
2,2,3,4,5,5,6,6,12,
4,4,10,0,0,0,0,0,0,
4,4,5,5,6,6,0,0,0,
4,4,5,5,0,0,0,0,0,
2,2,3,4,4,5,6,0,0,
0,2,3,4,5,5,0,0,0,
0,0,2,2,3,4,5,5,6,
0,0,2,2,3,4,4,5,0,
0,0,2,2,3,4,4,5,0,
0,0,0,3,4,5,0,0,0,
0,0,0,2,3,4,5,5,12,
0,0,0,0,2,3,0,0,0,
0,0,0,0,0,0,0,0,4,
0,0,0,0,1,8,0,0,0,
0,0,2,0,0,0,0,0,0,
2,2,3,4,5,5,6,6,6,
0,0,0,2,3,4,4,5,5,
2,2,3,4,5,5,6,6,0,
0,2,3,0,0,0,0,0,0,
0,0,0,2,3,4,5,11,0,
0,0,0,0,2,3,4,5,5,
0,2,3,0,0,0,0,0,0,
0,0,2,3,4,5,5,12,0,
0,0,2,0,0,0,0,0,0,
0,0,2,2,3,4,5,5,12,
0,0,0,0,2,3,3,4,0,
0,0,0,0,2,3,0,0,0,
2,3,4,10,0,0,0,0,0,
0,0,0,2,3,4,0,0,0,
0,0,0,0,0,2,0,0,0,
0,0,0,0,0,2,0,0,0,
2,2,8,0,0,0,0,0,0,
2,2,2,3,4,4,0,0,0,
0,2,3,3,4,4,0,0,0,
0,0,0,0,2,3,9,0,0,
3,3,4,5,5,5,6,0,0,
3,4,4,0,0,0,0,0,0,
0,0,2,3,3,10,0,0,0,
0,0,2,2,0,0,0,0,0,
0,0,0,0,2,8,0,0,0,
0,0,0,0,0,0,0,0,3,
2,3,3,4,5,5,6,0,0,
0,0,2,3,4,4,5,5,5,
0,0,2,3,3,4,5,11,0,
4,4,0,0,0,0,0,0,0,
0,0,2,0,0,0,0,0,0,
0,0,2,3,4,4,5,5,6,
0,0,2,2,3,4,5,5,5,
0,0,0,2,2,0,0,0,0,
1,0,0,0,0,0,0,0,0,
2,2,3,3,4,5,5,5,0,
0,0,0,0,2,3,4,11,0,
0,0,2,3,4,5,5,6,6,
0,0,0,0,0,0,0,4,5,
0,1,2,0,0,0,5,6,6,
0,1,1,2,2,3,4,5,5,
4,5,5,6,6,6,6,0,0,
4,4,5,6,6,6,0,0,0,
0,0,2,3,3,4,4,0,0,
0,0,2,0,3,4,5,5,0,
0,0,0,0,2,3,9,0,0,
0,0,2,3,4,5,5,6,0,
0,0,2,2,3,4,5,6,12,
0,0,0,0,2,3,4,0,0,
4,4,10,0,0,0,0,0,0,
3,4,5,5,6,0,0,0,0,
3,4,5,5,6,0,0,0,0,
4,4,5,5,6,0,0,0,0,
4,4,5,6,6,0,0,0,0,
0,0,2,2,3,4,4,4,4,
0,0,0,0,0,6,6,0,0,
3,3,4,5,11,0,0,0,0,
0,0,2,3,4,4,5,5,0,
0,0,0,2,3,4,5,5,0,
4,4,5,5,6,6,0,0,0,
0,0,0,0,2,3,4,5,0,
3,3,4,5,5,6,6,0,0,
0,2,3,3,9,0,0,0,0,
0,0,3,3,4,5,6,0,0,
0,0,0,0,3,4,5,5,6,
4,4,0,0,0,0,0,0,0,
0,0,2,3,4,4,0,0,0,
0,0,2,3,4,10,0,0,0,
2,2,3,4,5,5,6,0,0,
0,0,0,2,3,4,0,0,0,
0,0,0,2,3,4,5,0,0,
4,4,5,5,6,6,0,0,0,
4,4,5,5,6,6,0,0,0,
4,4,5,6,6,6,6,0,0,
2,2,3,4,5,5,0,0,0,
0,0,0,2,2,3,4,0,0,
0,0,0,0,0,0,6,6,0,
2,3,4,4,4,5,5,0,0,
0,0,0,0,2,8,0,0,0,
3,3,4,4,5,0,0,0,0,
4,5,5,6,6,6,6,0,0,
3,3,4,4,5,5,5,11,0,
0,2,3,4,5,5,5,0,0,
0,0,2,3,9,0,0,0,0,
0,0,0,0,2,3,4,10,0,
0,3,4,4,5,5,5,11,0,
0,0,0,5,5,6,6,0,0,
0,0,0,0,0,0,6,0,0,
0,0,0,0,2,3,9,0,0,
2,2,8,0,0,0,0,0,0,
3,4,5,5,5,6,0,0,0,
3,4,5,6,6,6,0,0,0,
4,5,5,5,6,6,0,0,0,
0,0,0,0,2,0,0,0,0,
0,0,0,0,1,0,0,0,0,
0,0,0,0,1,0,0,0,0,
0,0,0,0,2,3,4,4,5,
0,0,0,3,4,4,5,5,5,
0,0,0,0,2,3,4,0,0,
0,3,4,4,10,0,0,0,0,
0,2,3,4,5,5,6,6,6,
0,0,0,0,2,0,0,0,0,
4,4,5,5,5,11,0,0,0,
4,11,0,0,0,0,0,0,0,
4,4,0,0,0,0,0,0,0,
3,3,9,0,0,0,0,0,0,
3,3,0,0,0,0,0,0,0,
0,5,5,6,6,6,6,0,0,
0,0,2,3,4,4,4,5,5,
0,0,0,0,2,3,3,4,4,
2,2,3,3,4,5,5,0,0,
0,0,5,6,6,6,6,12,0,
4,5,5,6,6,6,0,0,0,
3,4,5,5,6,6,6,0,0,
0,0,2,2,3,4,10,0,0,
0,0,2,3,4,4,10,0,0,
4,4,5,5,5,5,5,6,6,
2,2,3,4,5,0,0,0,0,
4,4,4,5,0,0,0,0,0,
4,0,5,5,5,0,0,0,0,
2,3,4,10,0,0,0,0,0,
2,0,0,0,0,0,0,0,0,
0,2,3,3,9,0,0,0,0,
0,0,2,3,4,4,5,0,0,
0,0,2,2,3,0,0,0,0,
0,0,2,3,4,5,5,0,0,
0,0,2,2,3,0,0,0,0,
0,0,0,0,2,2,0,0,0,
0,0,0,0,2,3,4,0,0,
0,0,0,0,3,0,0,0,0,
3,4,5,5,6,6,6,0,0,
3,3,9,0,0,0,0,0,0,
0,0,0,3,4,4,0,0,0,
0,0,0,2,3,3,3,4,5,
0,0,0,2,3,9,0,0,0,
0,0,0,0,2,3,0,0,0,
0,0,0,0,2,3,4,4,10,
2,3,4,10,0,0,0,0,0,
2,3,4,4,5,5,6,0,0,
4,4,5,6,6,6,0,0,0,
2,2,3,4,5,5,6,6,6,
0,0,2,3,4,5,5,5,0,
0,0,0,2,3,4,0,0,0,
0,0,0,0,2,3,0,0,0,
2,2,3,4,5,5,6,6,6,
0,0,3,4,10,0,0,0,0,
0,0,0,2,3,3,4,10,0,
0,0,0,4,0,0,0,0,0,
0,0,0,4,10,0,0,0,0,
0,0,0,0,0,0,6,6,0,
0,0,0,0,0,0,0,0,2,
2,2,3,4,5,5,6,6,6,
3,4,5,5,6,12,0,0,0,
2,2,3,4,5,5,5,5,0,
0,0,0,0,0,5,6,0,0,
0,2,2,2,0,0,0,0,0,
0,2,3,0,5,5,6,0,0,
0,2,3,0,0,0,0,0,0,
0,4,5,6,6,6,0,0,0,
3,4,5,5,6,6,0,0,0,
3,4,5,5,6,6,6,0,0,
3,4,5,5,6,6,6,0,0,
3,3,4,4,4,10,0,0,0,
0,0,2,3,4,5,0,0,0,
3,3,4,5,5,0,0,0,0,
0,0,0,2,3,4,10,0,0,
5,5,0,0,0,0,0,0,0,
0,0,2,3,4,10,0,0,0,
5,6,6,6,6,7,0,0,0,
4,5,5,6,0,0,0,0,0,
0,0,0,0,2,0,0,0,0,
0,0,0,0,0,0,2,2,8,
4,4,5,6,6,6,0,0,0,
0,0,0,0,2,0,0,0,0,
0,2,3,3,5,5,11,0,0,
0,0,0,2,0,0,0,0,0,
0,0,0,3,4,5,5,6,0,
0,0,0,2,3,4,4,4,5,
0,0,0,2,3,4,10,0,0,
0,0,0,0,0,0,0,0,2,
0,2,3,0,0,0,0,0,0,
0,2,0,0,0,0,0,0,0,
0,2,0,0,0,0,0,0,0,
4,4,5,6,6,6,0,0,0,
0,3,4,5,5,6,6,6,0,
3,3,4,5,5,5,0,0,0,
0,0,2,3,4,5,0,0,0,
0,0,0,2,3,3,3,0,0,
0,0,0,0,0,0,3,4,10,
5,5,5,0,0,0,0,0,0,
0,2,0,0,0,0,0,0,0,
0,0,0,0,3,4,10,0,0,
0,2,2,3,0,0,0,0,0,
0,0,2,2,0,0,0,0,0,
0,0,2,3,4,4,0,0,0,
0,0,0,2,0,0,0,0,0,
0,0,0,0,0,0,2,2,3,
0,0,2,2,3,4,5,11,0,
0,0,0,2,2,3,4,5,0,
0,0,0,0,2,2,3,9,0,
0,0,0,0,2,2,4,4,5,
0,0,0,0,0,0,2,2,2,
0,0,0,0,0,0,0,0,2,
0,2,2,0,0,0,0,0,0,
0,0,0,2,0,0,0,0,0,
2,2,3,4,5,5,6,6,0,
0,0,2,3,4,5,5,6,0,
0,0,0,0,2,8,0,0,0,
0,0,1,0,0,0,0,0,0,
0,0,0,0,3,4,10,0,0,
0,0,0,0,3,4,4,5,6,
0,0,0,0,3,4,4,10,0,
3,4,4,10,0,0,0,0,0,
4,5,5,6,6,0,0,0,0,
0,2,3,4,11,0,0,0,0,
0,0,0,0,2,3,4,4,0,
0,0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,
0,0,0,0,3,0,0,0,0,
0,0,2,3,4,4,5,5,6,
0,0,0,0,2,3,4,5,5,
2,8,0,0,0,0,0,0,0,
0,0,0,2,4,4,5,5,6,
4,5,6,6,6,0,0,0,0,
6,6,6,6,6,0,0,0,0,
3,4,5,11,0,0,0,0,0,
2,3,4,0,0,0,0,0,0,
0,2,2,3,4,5,5,6,6,
0,0,2,3,4,5,5,0,0,
0,0,0,0,0,0,0,3,4,
2,3,4,4,4,11,0,0,0,
2,2,3,4,5,5,6,0,0,
3,4,5,5,12,0,0,0,0,
2,3,4,5,5,6,6,6,6,
0,2,3,4,5,5,5,6,6,
0,0,0,0,0,0,3,0,0,
0,0,0,0,0,0,2,3,0,
2,2,3,4,0,0,0,0,0,
2,2,3,4,5,0,0,0,0,
2,3,4,5,6,6,6,6,6,
2,3,0,5,5,5,0,0,0,
2,2,3,9,0,0,0,0,0,
2,3,4,5,5,6,6,0,0,
2,3,4,4,4,5,5,6,0,
0,2,2,3,0,0,0,0,0,
0,0,2,3,4,4,5,5,6,
0,0,2,3,4,5,5,6,6,
0,0,0,2,3,0,0,0,0,
0,0,0,2,0,0,0,0,0,
2,3,4,5,6,6,6,6,0,
0,2,2,3,5,5,11,0,0,
0,0,4,5,5,6,0,0,0,
0,0,2,3,4,5,5,6,12,
0,0,0,0,0,0,5,11,0,
2,2,3,4,5,5,6,0,0,
4,5,0,0,0,0,0,0,0,
2,3,4,4,5,5,6,6,0,
2,2,3,0,0,0,0,0,0,
0,2,2,0,0,0,0,0,0,
0,0,2,2,0,0,0,0,0,
0,0,0,2,0,0,0,0,0,
0,0,0,2,3,0,0,0,0,
0,0,2,3,4,5,5,6,0,
2,2,3,4,5,6,6,0,0,
3,3,0,0,0,0,0,0,0,
2,2,3,3,0,0,0,0,0,
2,2,3,4,5,6,6,0,0,
0,2,2,3,4,5,11,0,0,
0,0,0,2,0,0,0,0,0,
0,0,0,2,0,0,0,0,0,
2,2,3,4,5,5,6,6,0,
0,0,0,0,0,0,4,5,6,
2,3,4,4,5,0,0,0,0,
0,0,0,0,2,3,4,5,6,
0,0,0,0,2,8,0,0,0,
0,0,0,0,0,0,5,0,0,
0,3,4,4,0,0,0,0,0,
2,3,3,4,0,5,5,11,0,
2,3,4,5,6,6,6,0,0,
0,0,0,0,0,0,0,3,4,
2,2,0,0,0,0,0,0,0,
0,4,5,5,6,6,0,0,0,
0,3,4,5,5,11,0,0,0,
1,2,2,3,4,10,0,0,0,
2,2,0,0,0,0,0,0,0,
2,2,0,0,0,0,0,0,0,
0,2,3,3,0,5,5,6,6,
0,0,3,4,5,6,0,6,0,
0,0,2,0,0,0,0,0,0,
0,0,0,0,0,4,0,10,0,
0,3,4,5,5,6,0,0,0,
0,0,0,0,2,3,4,0,0,
0,0,0,0,0,3,4,5,5,
2,2,3,9,0,0,0,0,0,
0,0,0,2,0,0,0,0,0,
0,0,0,2,3,4,0,0,0,
0,0,0,3,4,5,5,0,0,
0,0,0,0,2,3,3,10,0,
0,0,0,0,2,3,4,4,11,
4,0,0,0,0,0,0,0,0,
0,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,2,4,
2,3,4,4,10,0,0,0,0,
2,2,3,0,0,0,0,0,0,
0,2,3,4,0,0,0,0,0,
2,3,4,4,5,5,0,0,0,
0,2,3,4,5,6,6,0,0,
0,0,3,4,5,5,6,6,6,
0,0,0,0,3,4,0,0,0,
0,0,0,0,0,0,0,2,3,
3,3,4,5,6,0,0,0,0,
0,0,3,0,0,0,0,0,0,
0,0,0,2,3,3,4,5,6,
0,0,4,5,6,6,0,0,0,
0,2,3,3,4,5,5,6,6,
0,2,2,3,4,5,5,6,6,
0,0,2,3,4,10,0,0,0,
0,2,3,4,5,6,6,0,0,
0,0,2,3,4,0,0,0,0,
0,0,2,3,3,9,0,0,0,
0,0,0,0,0,0,0,0,3,
0,0,0,3,4,5,5,6,6,
2,2,3,4,5,0,0,0,0,
4,5,5,6,6,0,0,0,0,
0,2,3,4,4,0,0,0,0,
0,2,2,3,4,0,0,0,0,
0,0,2,3,4,0,0,0,0,
3,4,5,5,6,6,0,0,0,
2,2,3,4,5,5,11,0,0,
0,0,0,0,6,0,0,0,0,
0,0,2,3,4,5,5,5,6,
5,5,6,6,0,0,0,0,0,
0,0,3,4,5,6,6,0,0,
0,0,0,0,2,3,4,4,0,
2,3,3,0,0,0,0,0,0,
0,0,0,3,4,4,4,4,4,
0,0,0,0,0,2,2,8,0,
0,3,3,4,0,0,0,0,0,
0,0,0,0,0,2,0,0,0,
0,0,0,0,0,3,0,0,0,
2,0,0,0,0,0,0,0,0,
0,2,3,4,5,5,0,0,0,
0,2,3,9,0,0,0,0,0,
2,3,3,9,0,0,0,0,0,
2,0,0,0,0,0,0,0,0,
0,0,0,0,2,2,8,0,0,
0,0,2,3,4,5,5,6,6,
0,0,2,3,4,4,5,5,5,
0,0,2,3,4,4,5,5,11,
0,0,0,2,3,4,4,5,0,
0,0,0,0,0,0,0,3,4,
2,3,4,4,5,0,0,0,0,
4,4,5,5,0,0,0,0,0,
4,5,5,6,0,0,0,0,0,
0,0,2,3,0,0,0,0,0,
0,5,5,6,6,6,0,0,0,
3,4,4,5,6,6,6,6,7,
4,5,5,6,0,0,0,0,0,
5,5,6,0,0,0,0,0,0,
3,3,4,4,5,5,6,0,0,
3,3,4,5,0,0,0,0,0,
2,2,3,3,5,5,6,6,0,
2,3,4,5,5,5,6,0,0,
2,3,4,4,5,0,0,0,0,
0,0,3,3,4,0,0,0,0,
0,0,0,2,3,3,4,5,0,
0,0,0,2,0,0,0,0,0,
0,0,0,2,3,4,5,5,0,
0,0,0,0,3,4,5,0,0,
0,0,0,0,3,4,5,11,0,
0,0,0,0,0,0,2,0,0,
0,3,4,5,5,5,0,0,0,
0,0,0,0,2,2,3,4,5,
4,4,0,0,0,0,0,0,0,
3,4,5,11,0,0,0,0,0,
4,4,5,5,0,0,0,0,0,
4,5,11,0,0,0,0,0,0,
0,0,0,2,3,4,4,0,0,
0,0,0,0,2,3,0,0,0,
0,0,0,0,0,0,0,0,2,
4,5,5,6,0,0,0,0,0,
4,5,6,6,0,0,0,0,0,
4,4,4,5,5,5,6,0,0,
3,4,5,11,0,0,0,0,0,
0,2,0,0,0,0,0,0,0,
0,0,0,2,3,4,5,5,6,
0,0,0,0,0,0,0,0,2,
4,4,5,6,6,6,0,0,0,
4,4,5,6,6,0,0,0,0,
0,0,0,0,2,3,0,0,0,
3,4,10,0,0,0,0,0,0,
5,5,6,6,6,0,0,0,0,
0,0,5,0,0,6,12,0,0,
0,0,0,0,2,2,0,0,0,
3,3,4,5,0,0,0,0,0),byrow=T,nrow=510)

# number of individuals
n <- dim(mydata)[[1]]
# number of capture occasions
K <- dim(mydata)[[2]]
# compute date of first capture
e <- NULL
f <- mat.or.vec(n,1)
g <- mat.or.vec(n,1)
for (i in 1:n){
  temp <- 1:K
  e <- c(e,min(temp[mydata[i,]>=1]))
  f[i] <- min(temp[mydata[i,]>=8])
  g[i] <- max(temp[mydata[i,]>=1])
  if (g[i] <= 5) f[i] = g[i] + 4
}
f[f>9]<-K

# Environmental covariate data
# Start of survey: values = 1:3 indicating the day surveys started for each indiv
survst<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,3,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2)
# Temperature: mean air temp over the three day census interval, 1st entry
# represents the interval between the 1st and 2nd survey.
#              1        2        3        4        5        6        7        8
temp<-matrix(c(58.22222,73.98387,66.27778,76.36066,75.15493,74.47458,69.35000,81.18571,
               60.72222,76.96774,65.30556,78.67213,72.16901,72.82979,75.08451,80.57143,
               66.98611,69.85484,70.88889,79.54098,71.49296,68.63830,79.94366,80.31429),byrow=T,nrow=3)
# Caterpillar density: the summed length of caterpillars per host plant at each census.
catdens<-matrix(c(0,0,0,0,0,0,0,8.9,14.8,
                  0,0,0,0,0,0,0,8.9,14.8,
                  0,0,0,0,0,0,0,8.9,14.8,
                  4.1,4.5,0,0,0,0,0,0,0,
                  33.1,33.5,23.1,23.5,24.2,26,0,0,0,
                  33.1,33.5,23.1,23.5,24.2,26,0,0,0,
                  33.1,33.5,23.1,23.5,24.2,26,0,0,0,
                  0,0,0,14.1,20.9,0,22.5,16.9,16.2,
                  0,0,0,14.1,20.9,0,22.5,16.9,16.2,
                  0,0,0,14.1,20.9,0,22.5,16.9,16.2,
                  9.9,5,7.6,4.4,7.4,10.8,11.1,0,0,
                  9.9,5,7.6,4.4,7.4,10.8,11.1,0,0,
                  9.9,5,7.6,4.4,7.4,10.8,11.1,0,0,
                  29.9,31.3,41,47.6,66.8,54.2,80.4,77.3,45.1,
                  29.9,31.3,41,47.6,66.8,54.2,80.4,77.3,45.1,
                  29.9,31.3,41,47.6,66.8,54.2,80.4,77.3,45.1,
                  29.9,31.3,41,47.6,66.8,54.2,80.4,77.3,45.1,
                  29.9,31.3,41,47.6,66.8,54.2,80.4,77.3,45.1,
                  0,3.3,4.3,0,0,0,0,0,0,
                  10.8,14.2,19.3,22.8,28.6,30.6,27.6,28,34.9,
                  10.8,14.2,19.3,22.8,28.6,30.6,27.6,28,34.9,
                  10.8,14.2,19.3,22.8,28.6,30.6,27.6,28,34.9,
                  0,2.5,4.4,5.4,8,10.4,11.7,12.1,16.1,
                  17.4,18.8,26.9,18.9,0,33.3,20,0,0,
                  17.4,18.8,26.9,18.9,0,33.3,20,0,0,
                  17.4,18.8,26.9,18.9,0,33.3,20,0,0,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  49.1,52.5,48,57.1,49,61.8,70.9,25.9,25.2,
                  0,2.8,4.6,5.7,11.8,4.2,7,6.3,10,
                  0,2.8,4.6,5.7,11.8,4.2,7,6.3,10,
                  0,0,5.9,7.4,11.5,12.8,16.8,0,0,
                  27.9,20.4,18.4,20,30.6,35.5,16.1,22.2,0,
                  27.9,20.4,18.4,20,30.6,35.5,16.1,22.2,0,
                  27.9,20.4,18.4,20,30.6,35.5,16.1,22.2,0,
                  27.9,20.4,18.4,20,30.6,35.5,16.1,22.2,0,
                  27.9,20.4,18.4,20,30.6,35.5,16.1,22.2,0,
                  8.4,8.4,10.5,11.7,12.1,19.4,21.5,28.1,0,
                  0,0,0,0,0,4.4,5.6,6.6,9.6,
                  0,0,0,0,0,0,0,0,12.2,
                  0,2.5,0,0,0,0,0,0,0,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  17.6,29.2,42.2,37.3,41.8,55.1,68.8,44.6,25.5,
                  0,0,3.8,4.5,7.2,10,11.4,19.5,16,
                  2.5,4.2,4.4,7.1,10,11.6,13.6,16.5,20.6,
                  0,0,4.1,0,0,0,0,0,0,
                  2.8,0,4.7,5,7.3,8.8,13.6,14.5,19.4,
                  2.8,0,4.7,5,7.3,8.8,13.6,14.5,19.4,
                  3.6,4.4,6.5,5.7,8.8,14.2,15.2,16.1,0,
                  0,0,0,0,0,4.9,0,0,0,
                  0,0,0,0,3,4,8.5,9.8,0,
                  0,0,3.6,5,0,0,0,0,0,
                  0,0,0,5,6.8,11,14,14.9,16.9,
                  0,0,0,0,2.2,0,0,0,0,
                  0,0,0,0,0,4,4.2,5.8,8.5,
                  0,0,5.2,6.2,0,0,0,0,0,
                  0,0,9.1,5,7.3,11.7,13.4,16.1,21.1,
                  0,0,9.1,5,7.3,11.7,13.4,16.1,21.1,
                  7.5,5.2,7.2,9.8,31.1,42.2,33.6,35.9,24,
                  7.5,5.2,7.2,9.8,31.1,42.2,33.6,35.9,24,
                  7.5,5.2,7.2,9.8,31.1,42.2,33.6,35.9,24,
                  7.5,5.2,7.2,9.8,31.1,42.2,33.6,35.9,24,
                  7.5,5.2,7.2,9.8,31.1,42.2,33.6,35.9,24,
                  7.5,5.2,7.2,9.8,31.1,42.2,33.6,35.9,24,
                  8.2,10.6,19,21.7,31.3,25.2,29.8,12.8,16,
                  8.2,10.6,19,21.7,31.3,25.2,29.8,12.8,16,
                  8.2,10.6,19,21.7,31.3,25.2,29.8,12.8,16,
                  8.2,10.6,19,21.7,31.3,25.2,29.8,12.8,16,
                  0,0,0,4.1,7.1,0,0,0,0,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  33.1,32.9,53.9,57.9,85.6,102.5,58.7,58.1,46.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  65,69,81.9,104.5,119.5,162.2,117,101.1,35.3,
                  4.5,5.6,7.1,15,18.1,20.7,28,29.5,38.1,
                  4.5,5.6,7.1,15,18.1,20.7,28,29.5,38.1,
                  3.9,10.5,13.8,15.3,18.5,23.5,31.1,18.5,0,
                  3.9,10.5,13.8,15.3,18.5,23.5,31.1,18.5,0,
                  3.9,10.5,13.8,15.3,18.5,23.5,31.1,18.5,0,
                  0,0,0,0,5.4,8.1,11.2,12.1,15.8,
                  0,4.8,7.5,0,0,0,0,0,0,
                  0,0,13.2,10.8,22.1,32.8,36.7,22.4,0,
                  0,0,13.2,10.8,22.1,32.8,36.7,22.4,0,
                  0,0,13.2,10.8,22.1,32.8,36.7,22.4,0,
                  0,0,13.2,10.8,22.1,32.8,36.7,22.4,0,
                  0,0,13.2,10.8,22.1,32.8,36.7,22.4,0,
                  5.1,5.7,9.7,4.4,6.6,17,0,0,0,
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                  40.4,46.9,37.3,46,43.9,34.7,36.8,10,12.3,
                  40.4,46.9,37.3,46,43.9,34.7,36.8,10,12.3,
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                  0,0,3.5,7.8,15.7,19.2,24.2,7.3,0,
                  0,0,3.5,7.8,15.7,19.2,24.2,7.3,0,
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                  3.5,4.6,11.2,16.4,30.7,28.5,37.2,43.6,0,
                  3.5,4.6,11.2,16.4,30.7,28.5,37.2,43.6,0,
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                  16.7,20.5,31.2,26.1,31.4,5.9,6.5,10.8,0,
                  16.7,20.5,31.2,26.1,31.4,5.9,6.5,10.8,0,
                  16.7,20.5,31.2,26.1,31.4,5.9,6.5,10.8,0,
                  16.7,20.5,31.2,26.1,31.4,5.9,6.5,10.8,0,
                  16.7,20.5,31.2,26.1,31.4,5.9,6.5,10.8,0,
                  0,0,0,0,5.2,0,0,0,0,
                  0,0,5,5.5,6.7,8.2,10.6,14.8,16.1,
                  0,0,0,0,4.3,5,5.7,11.4,15.8,
                  4.1,0,0,0,0,0,0,0,0,
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                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  43,57.2,72.3,62,47.4,23.3,33.3,24.8,37.1,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  20.4,31.9,43,53.1,54.6,50.7,70.3,57.7,57.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  29.3,42.3,63.5,88.5,96.8,83.2,85.8,64.2,54.3,
                  4.5,8.7,27.4,36.9,51,69.7,57.1,37.2,0,
                  4.5,8.7,27.4,36.9,51,69.7,57.1,37.2,0,
                  4.5,8.7,27.4,36.9,51,69.7,57.1,37.2,0,
                  4.5,8.7,27.4,36.9,51,69.7,57.1,37.2,0,
                  4.5,8.7,27.4,36.9,51,69.7,57.1,37.2,0,
                  13.4,17.1,7.7,11.7,15.9,15.3,16.5,0,0,
                  13.4,17.1,7.7,11.7,15.9,15.3,16.5,0,0,
                  7.6,12.6,24.2,20.7,23.2,16.4,16.5,20,0,
                  7.6,12.6,24.2,20.7,23.2,16.4,16.5,20,0,
                  7.6,12.6,24.2,20.7,23.2,16.4,16.5,20,0,
                  7.6,12.6,24.2,20.7,23.2,16.4,16.5,20,0,
                  7.6,12.6,24.2,20.7,23.2,16.4,16.5,20,0,
                  7.6,12.6,24.2,20.7,23.2,16.4,16.5,20,0,
                  0,0,4.4,7.9,11.5,12.1,15.1,17.3,0,
                  4,4.5,6.9,9.8,15.4,16.7,18.3,0,0,
                  13,17.2,16.3,30.2,22.4,25.7,17.5,0,0,
                  13,17.2,16.3,30.2,22.4,25.7,17.5,0,0,
                  13,17.2,16.3,30.2,22.4,25.7,17.5,0,0,
                  13,17.2,16.3,30.2,22.4,25.7,17.5,0,0,
                  13,17.2,16.3,30.2,22.4,25.7,17.5,0,0,
                  13,17.2,16.3,30.2,22.4,25.7,17.5,0,0,
                  4.2,4.2,7.1,10.5,14.6,15.6,26,32.4,14.1,
                  4.2,4.2,7.1,10.5,14.6,15.6,26,32.4,14.1,
                  4.3,6,8.1,9.5,14.4,0,0,0,0,
                  0,0,0,0,9.8,5.9,16,12.1,15.9,
                  0,0,0,0,9.8,5.9,16,12.1,15.9,
                  0,0,0,0,9.8,5.9,16,12.1,15.9,
                  0,5.5,5.9,8.7,0,0,0,0,0,
                  4.5,4.3,7,8.3,0,13.9,15,0,0,
                  5.1,6.8,10.2,10.9,14.5,19,20.6,0,0,
                  0,0,0,0,0,0,0,4.8,7.5,
                  3.6,5,0,0,0,0,0,0,0,
                  0,19.8,25.3,35,50,22.7,0,0,0,
                  0,19.8,25.3,35,50,22.7,0,0,0,
                  0,19.8,25.3,35,50,22.7,0,0,0,
                  8.9,13.5,16.5,14.6,18.7,34,11.3,38.6,20.8,
                  8.9,13.5,16.5,14.6,18.7,34,11.3,38.6,20.8,
                  8.9,13.5,16.5,14.6,18.7,34,11.3,38.6,20.8,
                  8.9,13.5,16.5,14.6,18.7,34,11.3,38.6,20.8,
                  8.9,13.5,16.5,14.6,18.7,34,11.3,38.6,20.8,
                  8.9,13.5,16.5,14.6,18.7,34,11.3,38.6,20.8,
                  0,5.6,8.7,11.5,15,16.3,0,0,0,
                  0,0,0,0,4.5,5.4,7.1,0,0,
                  0,0,0,0,0,6.8,8.1,11.3,16.3,
                  4.6,5.3,6.8,0,0,0,0,0,0,
                  0,0,0,12.4,21.1,21.6,19.8,0,0,
                  0,0,0,12.4,21.1,21.6,19.8,0,0,
                  0,0,0,12.4,21.1,21.6,19.8,0,0,
                  0,0,0,12.4,21.1,21.6,19.8,0,0,
                  0,0,0,0,4.3,5.4,6.5,9.6,0,
                  10,2.5,0,0,0,0,0,4.3,5.5,
                  10,2.5,0,0,0,0,0,4.3,5.5,
                  10,2.5,0,0,0,0,0,4.3,5.5,
                  9.8,16,23.4,19.8,0,0,0,0,0,
                  9.8,16,23.4,19.8,0,0,0,0,0,
                  9.8,16,23.4,19.8,0,0,0,0,0,
                  5.3,5.8,8.2,9.3,9.5,6.7,0,0,0,
                  0,3.7,11.8,15.5,29.4,45.5,41.4,23.1,28.6,
                  0,3.7,11.8,15.5,29.4,45.5,41.4,23.1,28.6,
                  0,3.7,11.8,15.5,29.4,45.5,41.4,23.1,28.6,
                  0,3.7,11.8,15.5,29.4,45.5,41.4,23.1,28.6,
                  6.3,6.9,16.4,16.5,24.6,6.8,8.1,12.5,15.6,
                  6.3,6.9,16.4,16.5,24.6,6.8,8.1,12.5,15.6,
                  6.3,6.9,16.4,16.5,24.6,6.8,8.1,12.5,15.6,
                  0,0,10.1,16,23.1,17,0,0,0,
                  0,6.8,10,13.6,19.4,25.7,26.7,31.2,37.4,
                  0,6.8,10,13.6,19.4,25.7,26.7,31.2,37.4,
                  0,0,3.6,5.6,7.2,0,0,0,0,
                  0,4.8,14.8,20.2,29.8,16.8,25,0,6,
                  0,4.8,14.8,20.2,29.8,16.8,25,0,6,
                  0,4.8,14.8,20.2,29.8,16.8,25,0,6,
                  0,4.8,14.8,20.2,29.8,16.8,25,0,6,
                  0,0,0,6.7,9.9,14,12.2,16,20.9,
                  15.4,23.5,34.8,45.8,66.2,0,0,0,0,
                  15.4,23.5,34.8,45.8,66.2,0,0,0,0,
                  15.4,23.5,34.8,45.8,66.2,0,0,0,0,
                  15.4,23.5,34.8,45.8,66.2,0,0,0,0,
                  15.4,23.5,34.8,45.8,66.2,0,0,0,0,
                  12.2,15.7,16,26,51.7,35.6,0,0,0,
                  12.2,15.7,16,26,51.7,35.6,0,0,0,
                  12.2,15.7,16,26,51.7,35.6,0,0,0,
                  0,0,4.3,5.9,10,9.3,9.3,14.5,20.4,
                  12.3,15.9,24.9,34.7,19.5,23.1,26.6,9.8,0,
                  12.3,15.9,24.9,34.7,19.5,23.1,26.6,9.8,0,
                  12.3,15.9,24.9,34.7,19.5,23.1,26.6,9.8,0,
                  3.9,5,7,0,0,0,0,0,0,
                  0,0,0,4.6,6.6,10.4,10.5,7,7.1,
                  0,0,0,4.6,6.6,10.4,10.5,7,7.1,
                  0,4.2,6.1,10.3,0,8.6,0,0,0,
                  0,4.2,6.1,10.3,0,8.6,0,0,0,
                  0,4.2,6.1,10.3,0,8.6,0,0,0,
                  2.7,4.1,6.4,9,12.5,11.8,0,0,0,
                  2.7,4.1,6.4,9,12.5,11.8,0,0,0,
                  0,4.7,5.8,0,0,0,0,0,0,
                  4,4.2,6.1,0,0,0,0,0,0,
                  4,0,0,0,0,0,0,0,0,
                  0,0,0,0,3.4,4.9,0,0,0,
                  0,0,13,21.1,32.8,40.1,43.2,61.2,49.5,
                  0,0,13,21.1,32.8,40.1,43.2,61.2,49.5,
                  0,0,13,21.1,32.8,40.1,43.2,61.2,49.5,
                  0,0,13,21.1,32.8,40.1,43.2,61.2,49.5,
                  0,0,13,21.1,32.8,40.1,43.2,61.2,49.5,
                  20.9,24.6,40.8,51.3,14.7,0,0,0,0,
                  20.9,24.6,40.8,51.3,14.7,0,0,0,0,
                  20.9,24.6,40.8,51.3,14.7,0,0,0,0,
                  20.9,24.6,40.8,51.3,14.7,0,0,0,0,
                  0,9.4,9.8,12.9,15.6,22.3,0,0,0,
                  6.5,6.7,11.6,12.6,16,18.5,25.8,21.2,0,
                  24,21.6,30.1,16.9,0,0,0,0,0,
                  24,21.6,30.1,16.9,0,0,0,0,0,
                  4.6,6.5,9,10.5,9.9,16.7,15.7,0,0,
                  6.5,7.4,12,10.2,0,0,0,0,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  13.1,18.1,34.3,44.7,79.1,62.7,76.9,50,0,
                  0,6.5,11.2,10.2,15.1,18.4,7,9.4,12.9,
                  0,6.5,11.2,10.2,15.1,18.4,7,9.4,12.9,
                  19.2,20,15.6,0,0,0,0,0,0,
                  19.2,20,15.6,0,0,0,0,0,0,
                  9.4,10.8,11.8,17,0,0,0,0,0,
                  11,10.9,0,0,0,0,0,0,0,
                  0,0,0,3.8,6.1,6.7,6.9,0,0,
                  0,0,0,0,5.2,7.5,0,0,4.3,
                  0,0,0,0,5.2,7.5,0,0,4.3,
                  34.7,36.7,42,56.8,14.7,15.5,13,0,0,
                  34.7,36.7,42,56.8,14.7,15.5,13,0,0,
                  34.7,36.7,42,56.8,14.7,15.5,13,0,0,
                  8.2,11.1,12.4,3.5,6.6,9,9.9,16.3,23.2,
                  8.2,11.1,12.4,3.5,6.6,9,9.9,16.3,23.2,
                  8.2,11.1,12.4,3.5,6.6,9,9.9,16.3,23.2,
                  8.2,11.1,12.4,3.5,6.6,9,9.9,16.3,23.2,
                  21.3,22,34.2,30.2,58.6,31.5,0,0,0,
                  21.3,22,34.2,30.2,58.6,31.5,0,0,0,
                  21.3,22,34.2,30.2,58.6,31.5,0,0,0,
                  19.7,23.1,15.5,23.2,24.7,0,0,0,0,
                  19.7,23.1,15.5,23.2,24.7,0,0,0,0,
                  0,0,10.9,0,2.6,21,0,0,0,
                  0,0,10.9,0,2.6,21,0,0,0,
                  7.2,7.3,10.4,12.2,0,0,0,0,0),byrow=T,nrow=510)
## HYPOTHESIS: ###################################################
# 1) I am testing the hypothesis that temperature affects transition rates with
# the prediction that warmer temperatures yield quicker development and stage
# transitions.
# 2) I am also testing the hypothesis that density affects survival with the
# prediction that increasing density results in decreased survival.  This pattern
# if observed could be the result of predator attraction at high densities and/or
# decreasing food at high densities.
##################################################################
# 2 - BUGS MODEL
##################################################################

sink("HMM_bayes_model.bug")
cat("

model	{
	###########################
	# LIKELIHOOD             ##
	# probabilities for each initial state
		px0[1] <- 1/7 # prob. of being in initial state Egg
		px0[2] <- 1/7 # prob. of being in initial state 1st
		px0[3] <- 1/7 # prob. of being in initial state 2nd
		px0[4] <- 1/7 # prob. of being in initial state 3rd
		px0[5] <- 1/7 # prob. of being in initial state 4th
		px0[6] <- 1/7 # prob. of being in initial state 5th
		px0[7] <- 1/7 # prob. of being in initial state Pupa
    px0[8] <- 0 # prob. of being in initial state dead 1st is 0
		px0[9] <- 0 # prob. of being in initial state dead 2nd is 0
		px0[10] <- 0 # prob. of being in initial state dead 3rd is 0
		px0[11] <- 0 # prob. of being in initial state dead 4th is 0
		px0[12] <- 0 # prob. of being in initial state dead 5th is 0
    px0[13] <- 0 # prob. of being in initial state removed is 0
	# probabilities of observations at a given occasion given states at this occasion
	# note: row 1 = not observed, row 2 = obs. in state 1 (Egg), . . . 
	# po[given stage i, pr(obs in state j)]
		po[1,1] <- 1-p[1]    # Pr(obs Egg)
		po[1,2] <- p[1]
		po[1,3] <- 0
    po[1,4] <- 0
    po[1,5] <- 0
    po[1,6] <- 0
    po[1,7] <- 0
    po[1,8] <- 0
    po[1,9] <- 0
    po[1,10] <- 0
    po[1,11] <- 0
    po[1,12] <- 0
    po[1,13] <- 0

		po[2,1] <- 1-p[2]    # Pr(obs 1st)
		po[2,2] <- 0
		po[2,3] <- p[2]
    po[2,4] <- 0
    po[2,5] <- 0
    po[2,6] <- 0
    po[2,7] <- 0
    po[2,8] <- 0
    po[2,9] <- 0
    po[2,10] <- 0
    po[2,11] <- 0
    po[2,12] <- 0
    po[2,13] <- 0

		po[3,1] <- 1-p[3]    # Pr(obs 2nd)
		po[3,2] <- 0
		po[3,3] <- 0
		po[3,4] <- p[3]
		po[3,5] <- 0
		po[3,6] <- 0
		po[3,7] <- 0
		po[3,8] <- 0
		po[3,9] <- 0
		po[3,10] <- 0
    po[3,11] <- 0
    po[3,12] <- 0
    po[3,13] <- 0

		po[4,1] <- 1-p[4]    # Pr(obs 3rd)
		po[4,2] <- 0
		po[4,3] <- 0
		po[4,4] <- 0
		po[4,5] <- p[4]
		po[4,6] <- 0
		po[4,7] <- 0
		po[4,8] <- 0
		po[4,9] <- 0
		po[4,10] <- 0
    po[4,11] <- 0
    po[4,12] <- 0
    po[4,13] <- 0

		po[5,1] <- 1-p[5]    # Pr(obs 4th)
		po[5,2] <- 0
		po[5,3] <- 0
		po[5,4] <- 0
		po[5,5] <- 0
		po[5,6] <- p[5]
		po[5,7] <- 0
		po[5,8] <- 0
		po[5,9] <- 0
		po[5,10] <- 0
    po[5,11] <- 0
    po[5,12] <- 0
    po[5,13] <- 0

		po[6,1] <- 1-p[6]     # Pr(obs 5th)
		po[6,2] <- 0
		po[6,3] <- 0
		po[6,4] <- 0
		po[6,5] <- 0
		po[6,6] <- 0
		po[6,7] <- p[6]
		po[6,8] <- 0
		po[6,9] <- 0
		po[6,10] <- 0
    po[6,11] <- 0
    po[6,12] <- 0
    po[6,13] <- 0

		po[7,1] <- 1-p[7]     # Pr(obs Pupa)
		po[7,2] <- 0
		po[7,3] <- 0
		po[7,4] <- 0
		po[7,5] <- 0
		po[7,6] <- 0
		po[7,7] <- 0
		po[7,8] <- p[7]
		po[7,9] <- 0
		po[7,10] <- 0
    po[7,11] <- 0
    po[7,12] <- 0
    po[7,13] <- 0

		po[8,1] <- 1-p[8]      # Pr(obs dead 1st)
		po[8,2] <- 0
		po[8,3] <- 0
		po[8,4] <- 0
		po[8,5] <- 0
		po[8,6] <- 0
		po[8,7] <- 0
		po[8,8] <- 0
		po[8,9] <- p[8]
		po[8,10] <- 0
    po[8,11] <- 0
    po[8,12] <- 0
    po[8,13] <- 0

		po[9,1] <- 1-p[9]      # Pr(obs dead 2nd)
		po[9,2] <- 0
		po[9,3] <- 0
		po[9,4] <- 0
		po[9,5] <- 0
		po[9,6] <- 0
		po[9,7] <- 0
		po[9,8] <- 0
		po[9,9] <- 0
		po[9,10] <- p[9]
    po[9,11] <- 0
    po[9,12] <- 0
    po[9,13] <- 0

    po[10,1] <- 1-p[10]       # Pr(obs dead 3rd)
		po[10,2] <- 0
		po[10,3] <- 0
		po[10,4] <- 0
		po[10,5] <- 0
		po[10,6] <- 0
		po[10,7] <- 0
		po[10,8] <- 0
		po[10,9] <- 0
		po[10,10] <- 0
    po[10,11] <- p[10]
    po[10,12] <- 0
    po[10,13] <- 0

    po[11,1] <- 1-p[11]       # Pr(obs dead 4th)
		po[11,2] <- 0
		po[11,3] <- 0
		po[11,4] <- 0
		po[11,5] <- 0
		po[11,6] <- 0
		po[11,7] <- 0
		po[11,8] <- 0
		po[11,9] <- 0
		po[11,10] <- 0
    po[11,11] <- 0
    po[11,12] <- p[11]
    po[11,13] <- 0

    po[12,1] <- 1-p[12]      # Pr(obs dead 5th)
		po[12,2] <- 0
		po[12,3] <- 0
		po[12,4] <- 0
		po[12,5] <- 0
		po[12,6] <- 0
		po[12,7] <- 0
		po[12,8] <- 0
		po[12,9] <- 0
		po[12,10] <- 0
    po[12,11] <- 0
    po[12,12] <- 0
    po[12,13] <- p[12]

    po[13,1] <- 1       # Pr(obs dead pupa or egg or gone) = 0
		po[13,2] <- 0
		po[13,3] <- 0
		po[13,4] <- 0
		po[13,5] <- 0
		po[13,6] <- 0
		po[13,7] <- 0
		po[13,8] <- 0
		po[13,9] <- 0
		po[13,10] <- 0
    po[13,11] <- 0
    po[13,12] <- 0
    po[13,13] <- 0
  # Survival and transition matrix
	for (i in 1:N) 	{		 # for each individual
		alive[i,First[i]] ~ dcat(px0[1:13])	# est. prob(initial state) = prop in each state at first cap
		for (j in (First[i]+1):Last[i])	{	  # loop over time
      # Egg(t)->?
  		px[1,i,j-1,1] <- phi1 * 1/(1+exp(alpha1[1])+exp(alpha1[2]))
			px[1,i,j-1,2] <- phi1 * exp(alpha1[1])/(1+exp(alpha1[1])+exp(alpha1[2]))
      px[1,i,j-1,3] <- phi1 * exp(alpha1[2])/(1+exp(alpha1[1])+exp(alpha1[2]))
      px[1,i,j-1,4] <- 0
      px[1,i,j-1,5] <- 0
      px[1,i,j-1,6] <- 0
      px[1,i,j-1,7] <- 0
      px[1,i,j-1,8] <- 1-phi1 * exp(alpha1[1])/(1+exp(alpha1[1])+exp(alpha1[2]))
      px[1,i,j-1,9] <- 1-phi1 * exp(alpha1[2])/(1+exp(alpha1[1])+exp(alpha1[2]))
      px[1,i,j-1,10] <- 0
      px[1,i,j-1,11] <- 0
      px[1,i,j-1,12] <- 0
      px[1,i,j-1,13] <- 1-phi1 * 1/(1+exp(alpha1[1])+exp(alpha1[2]))
      # 1st(t)->?
      px[2,i,j-1,1] <- 0
      px[2,i,j-1,2] <- phi[1,i,j-1] * 1/(1+exp(alpha[1,1,Survst[i],j-1])+exp(alpha[1,2,Survst[i],j-1]))
      px[2,i,j-1,3] <- phi[1,i,j-1] * exp(alpha[1,1,Survst[i],j-1])/(1+exp(alpha[1,1,Survst[i],j-1])+exp(alpha[1,2,Survst[i],j-1]))
      px[2,i,j-1,4] <- phi[1,i,j-1] * exp(alpha[1,2,Survst[i],j-1])/(1+exp(alpha[1,1,Survst[i],j-1])+exp(alpha[1,2,Survst[i],j-1]))
      px[2,i,j-1,5] <- 0
      px[2,i,j-1,6] <- 0
      px[2,i,j-1,7] <- 0
      px[2,i,j-1,8] <- 1-phi[1,i,j-1] * 1/(1+exp(alpha[1,1,Survst[i],j-1])+exp(alpha[1,2,Survst[i],j-1]))
      px[2,i,j-1,9] <- 1-phi[1,i,j-1] * exp(alpha[1,1,Survst[i],j-1])/(1+exp(alpha[1,1,Survst[i],j-1])+exp(alpha[1,2,Survst[i],j-1]))
      px[2,i,j-1,10] <- 1-phi[1,i,j-1] * exp(alpha[1,2,Survst[i],j-1])/(1+exp(alpha[1,1,Survst[i],j-1])+exp(alpha[1,2,Survst[i],j-1]))
      px[2,i,j-1,11] <- 0
      px[2,i,j-1,12] <- 0
      px[2,i,j-1,13] <- 0
      # 2nd(t)->?
      px[3,i,j-1,1] <- 0
      px[3,i,j-1,2] <- 0
      px[3,i,j-1,3] <- phi[2,i,j-1] * 1/(1+exp(alpha[2,1,Survst[i],j-1])+exp(alpha[2,2,Survst[i],j-1]))
      px[3,i,j-1,4] <- phi[2,i,j-1] * exp(alpha[2,1,Survst[i],j-1])/(1+exp(alpha[2,1,Survst[i],j-1])+exp(alpha[2,2,Survst[i],j-1]))
      px[3,i,j-1,5] <- phi[2,i,j-1] * exp(alpha[2,2,Survst[i],j-1])/(1+exp(alpha[2,1,Survst[i],j-1])+exp(alpha[2,2,Survst[i],j-1]))
      px[3,i,j-1,6] <- 0
      px[3,i,j-1,7] <- 0
      px[3,i,j-1,8] <- 0
      px[3,i,j-1,9] <- 1-phi[2,i,j-1] * 1/(1+exp(alpha[2,1,Survst[i],j-1])+exp(alpha[2,2,Survst[i],j-1]))
      px[3,i,j-1,10] <- 1-phi[2,i,j-1] * exp(alpha[2,1,Survst[i],j-1])/(1+exp(alpha[2,1,Survst[i],j-1])+exp(alpha[2,2,Survst[i],j-1]))
      px[3,i,j-1,11] <- 1-phi[2,i,j-1] * exp(alpha[2,2,Survst[i],j-1])/(1+exp(alpha[2,1,Survst[i],j-1])+exp(alpha[2,2,Survst[i],j-1]))
      px[3,i,j-1,12] <- 0
      px[3,i,j-1,13] <- 0
      # 3rd(t)->?
      px[4,i,j-1,1] <- 0
      px[4,i,j-1,2] <- 0
      px[4,i,j-1,3] <- 0
      px[4,i,j-1,4] <- phi[3,i,j-1] * 1/(1+exp(alpha[3,1,Survst[i],j-1])+exp(alpha[3,2,Survst[i],j-1]))
      px[4,i,j-1,5] <- phi[3,i,j-1] * exp(alpha[3,1,Survst[i],j-1])/(1+exp(alpha[3,1,Survst[i],j-1])+exp(alpha[3,2,Survst[i],j-1]))
      px[4,i,j-1,6] <- phi[3,i,j-1] * exp(alpha[3,2,Survst[i],j-1])/(1+exp(alpha[3,1,Survst[i],j-1])+exp(alpha[3,2,Survst[i],j-1]))
      px[4,i,j-1,7] <- 0
      px[4,i,j-1,8] <- 0
      px[4,i,j-1,9] <- 0
      px[4,i,j-1,10] <- 1-phi[3,i,j-1] * 1/(1+exp(alpha[3,1,Survst[i],j-1])+exp(alpha[3,2,Survst[i],j-1]))
      px[4,i,j-1,11] <- 1-phi[3,i,j-1] * exp(alpha[3,1,Survst[i],j-1])/(1+exp(alpha[3,1,Survst[i],j-1])+exp(alpha[3,2,Survst[i],j-1]))
      px[4,i,j-1,12] <- 1-phi[3,i,j-1] * exp(alpha[3,2,Survst[i],j-1])/(1+exp(alpha[3,1,Survst[i],j-1])+exp(alpha[3,2,Survst[i],j-1]))
      px[4,i,j-1,13] <- 0
      # 4th(t)->?
      px[5,i,j-1,1] <- 0
      px[5,i,j-1,2] <- 0
      px[5,i,j-1,3] <- 0
      px[5,i,j-1,4] <- 0
      px[5,i,j-1,5] <- phi[4,i,j-1] * 1/(1+exp(beta[Survst[i],j-1]))
      px[5,i,j-1,6] <- phi[4,i,j-1] * exp(beta[Survst[i],j-1])/(1+exp(beta[Survst[i],j-1]))
      px[5,i,j-1,7] <- 0
      px[5,i,j-1,8] <- 0
      px[5,i,j-1,9] <- 0
      px[5,i,j-1,10] <- 0
      px[5,i,j-1,11] <- 1-phi[4,i,j-1] * 1/(1+exp(beta[Survst[i],j-1]))
      px[5,i,j-1,12] <- 1-phi[4,i,j-1] * exp(beta[Survst[i],j-1])/(1+exp(beta[Survst[i],j-1]))
      px[5,i,j-1,13] <- 0
      # 5th(t)->?
      px[6,i,j-1,1] <- 0
      px[6,i,j-1,2] <- 0
      px[6,i,j-1,3] <- 0
      px[6,i,j-1,4] <- 0
      px[6,i,j-1,5] <- 0
      px[6,i,j-1,6] <- phi[5,i,j-1] * 1/(1+exp(beta2))
      px[6,i,j-1,7] <- phi[5,i,j-1] * exp(beta2)/(1+exp(beta2))
      px[6,i,j-1,8] <- 0
      px[6,i,j-1,9] <- 0
      px[6,i,j-1,10] <- 0
      px[6,i,j-1,11] <- 0
      px[6,i,j-1,12] <- 1-phi[5,i,j-1]
      px[6,i,j-1,13] <- 0
      # Pupa(t)->?
      px[7,i,j-1,1] <- 0
      px[7,i,j-1,2] <- 0
      px[7,i,j-1,3] <- 0
      px[7,i,j-1,4] <- 0
      px[7,i,j-1,5] <- 0
      px[7,i,j-1,6] <- 0
      px[7,i,j-1,7] <- phi7
      px[7,i,j-1,8] <- 0
      px[7,i,j-1,9] <- 0
      px[7,i,j-1,10] <- 0
      px[7,i,j-1,11] <- 0
      px[7,i,j-1,12] <- 0
      px[7,i,j-1,13] <- 1-phi7
      # dead 1st(t)->gone
      px[8,i,j-1,1] <- 0
      px[8,i,j-1,2] <- 0
      px[8,i,j-1,3] <- 0
      px[8,i,j-1,4] <- 0
      px[8,i,j-1,5] <- 0
      px[8,i,j-1,6] <- 0
      px[8,i,j-1,7] <- 0
      px[8,i,j-1,8] <- 0
      px[8,i,j-1,9] <- 0
      px[8,i,j-1,10] <- 0
      px[8,i,j-1,11] <- 0
      px[8,i,j-1,12] <- 0
      px[8,i,j-1,13] <- 1
      # dead 2nd(t)->gone
      px[9,i,j-1,1] <- 0
      px[9,i,j-1,2] <- 0
      px[9,i,j-1,3] <- 0
      px[9,i,j-1,4] <- 0
      px[9,i,j-1,5] <- 0
      px[9,i,j-1,6] <- 0
      px[9,i,j-1,7] <- 0
      px[9,i,j-1,8] <- 0
      px[9,i,j-1,9] <- 0
      px[9,i,j-1,10] <- 0
      px[9,i,j-1,11] <- 0
      px[9,i,j-1,12] <- 0
      px[9,i,j-1,13] <- 1
      # dead 3rd(t)->gone
      px[10,i,j-1,1] <- 0
      px[10,i,j-1,2] <- 0
      px[10,i,j-1,3] <- 0
      px[10,i,j-1,4] <- 0
      px[10,i,j-1,5] <- 0
      px[10,i,j-1,6] <- 0
      px[10,i,j-1,7] <- 0
      px[10,i,j-1,8] <- 0
      px[10,i,j-1,9] <- 0
      px[10,i,j-1,10] <- 0
      px[10,i,j-1,11] <- 0
      px[10,i,j-1,12] <- 0
      px[10,i,j-1,13] <- 1
      # dead 4th(t)->gone
      px[11,i,j-1,1] <- 0
      px[11,i,j-1,2] <- 0
      px[11,i,j-1,3] <- 0
      px[11,i,j-1,4] <- 0
      px[11,i,j-1,5] <- 0
      px[11,i,j-1,6] <- 0
      px[11,i,j-1,7] <- 0
      px[11,i,j-1,8] <- 0
      px[11,i,j-1,9] <- 0
      px[11,i,j-1,10] <- 0
      px[11,i,j-1,11] <- 0
      px[11,i,j-1,12] <- 0
      px[11,i,j-1,13] <- 1
      # dead 5th(t)->gone
      px[12,i,j-1,1] <- 0
      px[12,i,j-1,2] <- 0
      px[12,i,j-1,3] <- 0
      px[12,i,j-1,4] <- 0
      px[12,i,j-1,5] <- 0
      px[12,i,j-1,6] <- 0
      px[12,i,j-1,7] <- 0
      px[12,i,j-1,8] <- 0
      px[12,i,j-1,9] <- 0
      px[12,i,j-1,10] <- 0
      px[12,i,j-1,11] <- 0
      px[12,i,j-1,12] <- 0
      px[12,i,j-1,13] <- 1
      # gone(t)->gone forever
      px[13,i,j-1,1] <- 0
      px[13,i,j-1,2] <- 0
      px[13,i,j-1,3] <- 0
      px[13,i,j-1,4] <- 0
      px[13,i,j-1,5] <- 0
      px[13,i,j-1,6] <- 0
      px[13,i,j-1,7] <- 0
      px[13,i,j-1,8] <- 0
      px[13,i,j-1,9] <- 0
      px[13,i,j-1,10] <- 0
      px[13,i,j-1,11] <- 0
      px[13,i,j-1,12] <- 0
      px[13,i,j-1,13] <- 1
			## STATE EQUATIONS ##
			# draw states at j given states at j-1
			alive[i,j] ~ dcat(px[alive[i,j-1],i,j-1,1:13])
			mydata[i,j] ~ dcat(po[alive[i,j],1:13])
			}
	}
	######################
  # PRIORS            ##
  # transition
  for (i in 1:3)   {		 # for each survey start date
    for (j in 1:8)  { # loop over all surveys (time steps)
      for (k in 1:3)  {  # loop over stages 2-4 (1st - 3rd instar)
        alpha[k,1,i,j]<-b0.t[k,1]+b1.t[k]*Temp[i,j]  # transition  ~ f(temperature)
        alpha[k,2,i,j]<-b0.t[k,2]+b1.t[k]*Temp[i,j]  # 1to2 and 1to3 have same temp response
      }
      beta[i,j]<-b0.tb+b1.t[4]*Temp[i,j]  # 4th instar transition  ~ f(Temperature)
    }
  }
  # transition
  for (k in 1:3)  {  # loop over stages 2-4 (1st - 3rd instar)
    b0.t[k,1] ~ dnorm(0,1.0E-2)
    b0.t[k,2] ~ dnorm(0,1.0E-2)
    b1.t[k] ~ dnorm(0,1.0E-2)
  }  

  for (k in 1:5)  { # loop over all stages (1st - 5th instar)
    for (i in 1:N)  { # loop over all individuals (each with their own density)
      for (j in 1:8)  { # loop over all surveys (time steps)
      # survival
        logit(phi[k,i,j])<-b0.s[k]+b1.s[k]*Catdens[i,j]  # survival  ~ f(density)
      }
    }
    b0.s[k] ~ dnorm(0,1.0E-2)
    b1.s[k] ~ dnorm(0,1.0E-2)
  }
  # for 4th instar only
  b0.tb ~ dnorm(0,1.0E-2)
  b1.t[4] ~ dnorm(0,1.0E-2)
  
  phi1 ~ dunif(0,1)	# egg survival (sample size too small for complex function)
	phi7 ~ dunif(0,1)	# pupa survival (sample size too small for complex function)
  alpha1[1] ~ dnorm(1.0,1)  # parm for psi12
  alpha1[2] ~ dnorm(-1.9,1)  # parm for psi13
  p[1] ~ dunif(0.02,0.4)	# pr(obs egg)
	p[2] ~ dunif(0,1)	# pr(obs 1st)
	p[3] ~ dunif(0,1)	# pr(obs 2nd)
	p[4] ~ dunif(0,1)	# pr(obs 3rd)
	p[5] ~ dunif(0,1)	# pr(obs 4th)
	p[6] ~ dunif(0,1)	# pr(obs 5th)
	p[7] ~ dunif(0.02,0.4)	# pr(obs pupa)
	p[8] ~ dunif(0,1)	# pr(obs dead 1st)
	p[9] ~ dunif(0,1)	# pr(obs dead 2nd)
	p[10] ~ dunif(0,1)	# pr(obs dead 3rd)
	p[11] ~ dunif(0,1)	# pr(obs dead 4th)
	p[12] ~ dunif(0,1)	# pr(obs dead 5th)
  beta2 ~ dnorm(-0.93,1)  # parm for psi67
} # END MODEL  ###

",fill=TRUE)
sink()

##################################################################
# 3 - BAYESIAN COMPUTATION WITH JAGS
##################################################################

# data
mydatax <- list(N=n,First=e,Last=f,mydata=as.matrix(mydata+1),
                Temp=temp,Survst=survst,Catdens=catdens)

# first list of inits
alive = mydata
for (i in 1:n) {
	for (j in 2:K) {
    if (j > e[i] & mydata[i,j]==0) {alive[i,j] = alive[i,j-1]}
		if (mydata[i,j-1]==8|mydata[i,j-1]==9|mydata[i,j-1]==10|mydata[i,j-1]==11|mydata[i,j-1]==12)
      {alive[i,j:K] = 13 }
    if (mydata[i,j-1]==0 & alive[i,j]<8 & (alive[i,j]-alive[i,j-1])>2) {alive[i,j-1]=alive[i,j-1]+1}
	}
	for (j in 1:K) {
		if (j < e[i]) {alive[i,j] = NA}
		if (j > f[i]) {alive[i,j] = NA}
	}
 }
alive <- as.matrix(alive)
init1 <- list(p=c(0.1,0.8,0.8,0.8,0.8,0.8,0.1,0.8,0.8,0.8,0.8,0.8),alive=alive)
# second list of inits
init2 <- list(p=c(0.2,0.5,0.5,0.5,0.5,0.5,0.2,0.5,0.5,0.5,0.5,0.5),alive=alive)

# concatenate list of initial values
inits <- list(init1,init2)

# specify the parameters to be monitored
parameters1 <- c("phi1","phi7","p",'alpha1','beta2') 
parameters2 <- c("alpha") 
parameters3 <- c("b0.s","b1.s","b0.t","b1.t","b0.tb",'beta')

# load R package to call JAGS from R
library(rjags)

# run JAGS
start<-as.POSIXlt(Sys.time())
jmodel <- jags.model("HMM_bayes_model.bug", 
                     mydatax, inits, n.chains = 2,n.adapt = 120000)
print('Finish burn in. Start Coda samples')
save(jmodel,file='HMM_model.Rdata')
print('Model Saved')
jsample1 <- coda.samples(jmodel, parameters1, n.iter=10000, thin = 1)
print('Finish Coda samples 1,')
save(jsample1,file='HMM_output1.Rdata')
print('Simulation 1 Saved')
rm(jsample1)
jsample2 <- coda.samples(jmodel, parameters2, n.iter=10000, thin = 1)
print('Finish Coda samples 2.')
save(jsample2,file='HMM_output2.Rdata')
print('Simulation 2 Saved')
rm(jsample2)
jsample3 <- coda.samples(jmodel, parameters3, n.iter=10000, thin = 1)
print('Finish Coda samples 3. Start Deviance samples')
save(jsample3,file='HMM_output3.Rdata')
print('Simulation 3 Saved')
rm(jsample3)
jdic<- dic.samples(jmodel,n.iter=10000,thin=1)
print('Finish Deviance samples')
end <-as.POSIXlt(Sys.time())
duration = end-start
save(jmodel,jdic,duration,file='HMM_model.Rdata')
print('Deviance Saved')
rm(jdic)
print('Job Complete!')

##################################################################
## HHM Output Analysis
##################################################################
load('HMM_output1.Rdata')
load('HMM_output2.Rdata')
load('HMM_output3.Rdata')

## check convergence
gelman.diag(jsample1)
gelman.diag(jsample2)
gelman.diag(jsample3)

x11();
plot(jsample3, trace = TRUE, density = FALSE,ask = dev.interactive())

# numerical summaries and posterior distributions
plot(jsample3, trace = FALSE, density = TRUE,ask = dev.interactive())
par.sum1<-summary(jsample1); # par.sum
par.sum2<-summary(jsample2); # par.sum
par.sum3<-summary(jsample3); # par.sum
# Median may be better for skewed parameter distributions
par.quan1<-par.sum1$quantiles[,c(1,3,5)]; par.quan1
par.quan2<-par.sum2$quantiles[,c(1,3,5)]; par.quan2
par.quan3<-par.sum3$quantiles[,c(1,3,5)]; par.quan3
# Medians are perhaps better.  Better for skewed distributions, and not different for centered distributions.
alpha1<-par.quan1[1:2,2];alpha1
beta2<-par.quan1[3,2];beta2
phi17<-par.quan1[16:17,2];phi17
alpha<-par.quan2[,2];alpha
beta1<-par.quan3[22:45,2];beta1
b0.s<-par.quan3[1:5,2];b0.s
b0.t<-par.quan3[6:11,2];b0.t
b0.tb<-par.quan3[12,2];b0.tb
b1.s<-par.quan3[13:17,2];b1.s
b1.t<-par.quan3[18:21,2];b1.t
#-- display transition probabilities (back-transformation using inverse multinomial logit)
a.array<-array(alpha, dim = c(3,2,3,8));a.array
a<-array(0, dim = c(3,3,3,8))
b.array<-array(beta1, dim = c(3,8));b.array
b<-array(0, dim = c(3,8))
psi<-array(0, dim = c(6,3,3,8))
psi.m<-array(0, dim = c(6,3,8))

for (i in 1:3) {
  for (j in 1:3) { # Loop over 3 survey dates each survey period
    for (k in 1:8) {
      a[i,,j,k]<-c(0,a.array[i,,j,k])
      psi[i+1,,j,k] <- exp(a[i,,j,k])/sum(exp(a[i,,j,k]))
      psi[1,,j,k] <- exp(c(0,alpha1))/sum(exp(c(0,alpha1)))
      psi[5,1:2,j,k] <- exp(c(0,b.array[j,k]))/sum(exp(c(0,b.array[j,k])))
      psi[6,1:2,j,k] <- exp(c(0,beta2))/sum(exp(c(0,beta2)))
    }
  }
}
big.psi<-psi
dimnames(big.psi)<-list(c('psi1','psi2','psi3','psi4','psi5','psi6'),
                        c('i_i','i_i+1','i_i+2'), c('1','2','3'),
                        c('S1','S2','S3','S4','S5','S6','S7','S8'))

for (i in 1:6) { # for each stage
  for (s in 1:3) { # for each stage transition ii, ii+1 ii+2
    for (k in 1:8) { # for each survey period
      psi.m[i,s,k]<-mean(psi[i,s,,k]) # average over 3 survey dates each survey period
    }
  }
}

dimnames(psi.m)<-list(c('psi1','psi2','psi3','psi4','psi5','psi6'),
                        c('i_i','i_i+1','i_i+2'), 
                        c('S1','S2','S3','S4','S5','S6','S7','S8'))

# group parameter estimates
m_output<-list('par.quan1'=par.quan1,'par.quan2'=par.quan2,'par.quan3'=par.quan3,
                   'psi'=psi.m,'b0.s'=b0.s,'b1.s'=b1.s,
                   'b0.t'=b0.t,'b0.tb'=b0.tb,'b1.t'=b1.t)

################################################################################
###############                    End Script                 ##################
################################################################################
