*Ecological Archives*
E090-027-A1

**José Miguel Ponciano, Mark L. Taper, Brian Dennis, and Subhash R. Lele. 2009. Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning. ***Ecology* 90:356–362.

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 (Thompson and Wijsman 1990 and Thompson 1994), as shown in steps 2 and 5 of the data cloned likelihood ratio (DCLR) algorithm and of the profile likelihood (DCPL) algorithm, respectively. Click here for a PDF file of the appendix.

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