  There lies a latent danger in utilizing some known mathematical results in
ecology. Some results do not apply to the problem at hand. We identify one such
trend. Based on a couple of theorems in mathematical statistics, Link (2013)
cautions ecologists about the inappropriateness of using the discrete uniform
prior in their analysis under certain conditions and instead recommends the
routine use of the scale prior during analysis. This recommendation is been
absorbed immediately and widely among ecologists. In this study, we consider
the two fundamental capture-recapture models used widely in ecology, $M_0$ and
$M_h$, and derive conditions for posterior propriety by examining the behavior
of the right tail of the posterior distributions of animal population size $N$
in a Bayesian analysis. We demonstrate that both these likelihoods are far more
efficient than the ones considered in Link (2013). We argue that no
particularly prescriptive approach should be adopted by ecologists in regard to
choosing priors of the fear of posterior impropriety. Instead, we recommend the
efficient construction of likelihoods for the problem and data on hand,
choosing priors based existing knowledge of a parameter of interest and
encourage examining posterior propriety by asymptotic arguments as demonstrated
in this study.
