Supplement 1. :R program illustrating the calculations needed to construct a profile likelihood for one ofthe Stochastic Beverton-Holt state space model parameters.

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SBHPLR is a program written in R to calculate the profile likelihood for the parameter lambda of the Stochastic Beverton Holt state-space model as described in the main text. In this program, the necessary MCMC calculations are carried by calling and running the software WinBugs from R using the package BRUGS freely available at . Previous installation of WinBugs and BRUGS is required to run this code. Detailed instructions on how to use this program are listed as comments in the file header. The Data Cloning Profile Likelihood (DCPL) algorithm presented in this program is described in the original paper and the proof of why it works can be read in Appendix A.