Use of the correlation coefficient to study effects of demographic rates on population growth rate in an IPM

[Marc Kery]

Dear all,

in the attached memo, we describe our current understanding of the issue brought up by Tomas Telensky (later seconded by Matt Hollanders). In summary, we still believe that the method presented in the BPA book (pp. 378-379) is correct when understood as an instance of finite-sample inference. However, it would be wrong when one wants the more typical population-level inferences.

To be honest, when we wrote the BPA book, we were not aware of this difference. The text on page 378 (and reprinted in the attached memo) *seems* to imply an interest in finite-sample inference rather than in population-level inference. But this is not clear, and we admit that it might be easy to be confused by this and take the correlation coefficient and especially its Bayesian significance test as having a population-level meaning. We would like to apologize for any inconvenience that this may have caused.

We would also like to thank Tomas and Matt for bringing this up.

Best regards  --- Marc & Michael