Increasing the trust in hunting bag statistics: why random selection of hunters is so important

Hunting bag statistics are often the only available data for performing ecological studies about harvested species, and total harvest is sometimes used as a proxy of abundance of the game species under study in a given geo-graphical area and period of time. This practice raises at least two questions, (i) are the total hunting bag estimates good indices of population abundance, and if so, for what uses?, (ii) what is the reliability of given hunting bag statistics and is it possible to evaluate and take into account their uncertainty without relying on uncheckable assumptions? This methodological paper is aimed at answering the second question, from the point of view of the hunters' sampling. Through Monte Carlo simulations, we illustrate the potential selection bias induced by relying on volunteer samples of hunters. We expose the statistical causes and remedies to this issue. We put the emphasis on the paramount importance of random sampling, both for avoiding selection bias and to perform statistical inferences on a sound basis, in a framework free of statistical assumptions. We explain under what circumstances not taking into account unequal inclusion probabilities at the estimation stage could result in biased estimation. The acknowledgement that for a selection bias to occur, it is necessary that both the unequal inclusion probabilities are not accounted for in the estimators and these probabilities are correlated to the individual hunting bags is a statistical result that is neither widely known nor appreciated by most wildlife ecologists - and perhaps also, some wildlife statisticians.