## Appendix A: A proof showing that the ratio of two likelihoods initially written as the ratio of two integrals can be written as the integral of a ratio, as shown in steps 2 and 5 of the data cloned likelihood ratio algorithm and of the profile likelihood algorithm, respectively.

Ecological ArchivesE090-027-A1.## Appendix B: Simulation study.

Ecological ArchivesE090-027-A2.

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

Ecological ArchivesE090-027-S1.

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