Multi-stage cluster sampling for estimating average species richness at different spatial grains

A multi-stage cluster sampling is proposed for quantifying and monitoring plant species richness at multiple spatial grains over large spatial extents. An unbiased estimator of average species richness at different grains and a conservative estimator of its sampling variance are obtained in a complete design-based framework, i.e., avoiding any assumption about the ecological community under study. An application to the Nature Reserve “Lago di Montepulciano” demonstrates that the proposed strategy may accomplish practical advantages and quite satisfactory levels of accuracy. Abbreviations: MP – Macroplot, PL – Plot, SP – Subplot. species richness at multiple spatial grains over large spatial extents. It is worth noting that the paper moves in the framework of the design-based inference, which is solely determined by the characteristics of the sampling scheme and, in contrast with model-based inference, avoids any assumption about the population under study. A revision of the two approaches and their implications in environmental surveys is considered in Gregoire (1998). As pointed out by Sarndal et al. (1992, p. 21), the main attractiveness of the design-based approach is that “Designbased inference is objective, nobody can challenge that the sample was really selected according to the given sampling design. The probability distribution associated with the design is “real”, not modelled or assumed”. Accordingly, without the help of assumptions regarding the ecological community under study (e.g., the spatial autocorrelation structure which is necessary to perform kriging), an unbiased estimator of the average species richness at different spatial scales is obtained by means of the well-known Horvitz-Thompson estimation criterion, while a conservative estimator of the sampling variance is obtained by means of the Hansen-Hurvitz criterion (for a complete treatment of these widely applied procedures see, among others, Hedayat and Shina, 1991, Chapter 3 and Thompson, 1992, Chapter 6). Finally, it should also be noticed that, as often in ecological sampling, multistage cluster schemes are adopted because of their convenience and practicability rather than for their statistical efficiency. Indeed, the great appeal of cluster schemes is that it is often easier and less expensive to locate and observe a sample of spatial units in the same cluster than to locate and observe the same number of units randomly spread over the study area (Thompson 1992, pp. 123132). Statistical background Consider a delineated study area, previously partitioned into L spatial zero-level blocks of equal size. If each block l (l = 1,...,L) is partitioned into N primary spatial units of equal size, and if y denotes the value of the interest variable within the primary unit h (h = 1,..., N ) in the zero-level block l, then the population total over the study area may be written as