On comparing design-based estimation versus model-based prediction to assess the abundance of biological populations

Abstract

Assessing the abundance of biological populations is a central technical challenge in ecology, whether fundamental or applied. Although the question faced is simple, it is actually a complicated topic that has produced a vast array of methods. The first step is always sampling the geographical space, ideally by means of a randomized selection process. In that case, with a frequentist interpretation of probability, abundance can be estimated by taking into account randomization, or predicted conditionally on the sample at hand, by specifying a statistical model. This leads to a choice between so-called design-based estimation and model-based prediction. The goal of this methodological article is to contribute to the understanding of fundamental notions regarding these two statistical frameworks by the targeted audience, mainly quantitative ecologists. For this purpose, we illustrate the comparison between design-based estimation in the case of simple random sampling without replacement (SRSWOR) and model-based prediction. As an example, we model count data with a delta-lognormal distribution and rely on uniformly minimum-variance unbiased estimators (UMVUEs) for the prediction of abundance. We investigate the robustness of the predictor by contaminating the delta-lognormal distribution using actual count data. Data from a survey concerning wintering populations in France of two wader species, namely, northern lapwing (Vanellus vanellus) and European golden plover (Pluvialis apricaria) serve as illustrative examples. By means of Monte Carlo simulations, we highlight the lack of robustness of the predictor based on the delta-lognormal distributional model, in terms of both actual bias and precision. We organize the discussion around the illustrative examples in the context of the sampling design, the model and the data.