Monitoring population size of mammals using a spotlight-count-based abundance index: How to relate the number of counts to the precision?

Abundance indices are widely used to study changes in population size in wildlife management. However, a truly appropriate measure of precision is often lacking in such studies. Statistically, the two crucial issues regarding the use of an abundance index are sampling and observability, which lead one to consider two kinds of errors, namely sampling and observation errors. The purpose of this methodological paper is to relate the number of counts to the precision of an abundance index by introducing the Hansen–Hurwitz–Bershad model which takes into account both sampling and observation errors. We illustrate this statistical approach in the case of a European rabbit (Oryctolagus cuniculus) abundance index based on spotlight counts, for two fixed spatial sampling units located in different ecological contexts. We show (i) that the usual sampling variance estimator is a downward-biased estimator of the total variance of the abundance index, (ii) that the bias of the usual variance estimator does not decrease when increasing the sampling size, (iii) that correlated observation errors may have a dramatic impact on the total variance, especially when the sampling size increases. The acknowledgement that the (pure) sampling variance underestimates the total variance because of observation errors is a statistical result that is neither widely known nor appreciated by most wildlife ecologists. The magnitude of this underestimation may be important and, therefore, observation errors cannot be always considered as a priori negligible in assessing the precision of a count-based abundance index.