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Mészáros, Z. (ed.) 1984. Results of faunistical and floristical studies in Hungarian apple orchards. Acta Phytopathol. Acad. Sci. Hung. 19:91–176. Niemelä, J., E. Halme and Y. Haila. 1990. Balancing sampling effort

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In Europe, epiphytic lichens are incorporated in forest diversity monitoring projects in which sampling at the tree level is carried out on 4 grids on the 4 cardinal points (N, S, E, W) of the trunk. Our results, based on the analysis of a dataset referring to six forest sites in NE-Italy and including 264 trees, indicate that a lichen assessment based on sampling at the tree level less than four cardinal points might be effective in estimating species richness across different forest types, showing very high rates of species capture. Similar results were achieved if the reduction of sampling effort is applied to the number of trees sampled within each area. This effect can be explained taking into account the redundant information collected on the same tree. In the framework of forest monitoring programs, the main perspective of our results is related to the possibility of investing saved resources for improving lichen inventories by including in the surveys currently neglected microhabitats. Further studies would be welcome to identify an optimal balance between sampling effort and information gathered, as economic resources are often a constraint to activate and maintain large-scale and long-term monitoring projects.

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Rarefaction has long represented a powerful tool for detecting species richness and its variation across spatial scales. Some authors recently reintroduced the mathematical expression for calculating sample-based rarefaction curves. While some of them did not claim any advances, others presented this formula as a new analytical solution. We provide evidence about formulations of the sample-based rarefaction formula older than those recently proposed in ecological literature.

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Walther, B.A. and J.-L. Martin. 2001. Species richness estimation of bird communities: how to control for sampling effort? Ibis 143:413-419. Species richness estimation of bird communities: how to control for sampling effort

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Moreno, C.E. and G. Halffter. 2001. On the measure of sampling effort used in species accumulation curves. J. App. Ecol. 38: 487–490. Halffter G. On the measure of sampling effort

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Similarity indices are often used for measuring b-diversity and as the starting point of multivariate analysis. In this study, I used simulation to examine the direction and amount of bias in estimates of two similarity indices, Jaccard Coefficient (J) and incidence-based J (J^). I design a novel simulation to generate three sets of assemblages that vary in species richness, species-occurrence distributions, and b-diversity. I characterized assemblage differences with the ratio of [proportion of rare species in all shared species / proportion of rare species in all unshared species] (i.e., PR ss/PR us) and the Pearson’s correlation in the probabilities of shared species between two assemblages (i.e., share-species correlation). I found that J was subject to strong positive or negative bias, depending on PR ss/PR us. J^ was mainly subject to negative bias, which varied with share-species correlation. In both indices, bias varied substantially from one pair of assemblages to another and among datasets. The high variation in the bias across different comparisons of assemblages may compromise b-diversity estimation established at low sampling efforts based on the two indices or their variants.

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Rarefaction is a widely applied technique for comparing the species richness of samples that differ in area, volume or sampling effort. Despite widespread adoption of sample-based rarefaction curves, serious concerns persist. In this paper, we address the issue of the spatial arrangement of sampling units when computing sample-based rarefaction curves. If the spatial arrangement is neglected when building rarefaction curves, a direct comparison of species richness estimates obtained for areas that differ in their spatial extent is not possible, even if they were sampled with a similar intensity. We demonstrate a major effect of the spatial extent of the samples on species richness estimates through the use of data from a temperate forest. We show that the use of Spatially Constrained Rarefaction (SCR) results in species richness estimates that are directly comparable for areas that differ in spatial extent. As expected, standard rarefaction curves tend to overestimate species richness because they ignore the spatial autocorrelation of species composition among sampling units. This spatial autocorrelation is captured by the SCR, thus providing a useful technique for characterizing the spatial structure of biodiversity patterns. Further work is necessary to determine how species richness estimates and the shape of the SCR are affected by the method of spatial constraint and sampling unit density and distribution.

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Modern agriculture is one of the main anthropogenic threats to biodiversity. To explore the effects of agricultural intensification we investigated carabids and spiders in two studies; in 2003 in grasslands and two years later in cereal fields in the same region. Both aimed to study the effect of management on arthropod diversity and composition at local and landscape scales. In 2003, we used a paired design for grasslands (extensively vs. intensively grazed). In 2005, a gradient design was applied with a total of seven land-use intensity categories. In both studies, sampling was carried out using funnel traps with the same sampling effort. Linear mixed models showed that high grazing intensity in grasslands had a positive effect on carabid species richness and abundance, but no effect on spiders. Landscape diversity had a positive effect only on carabid abundance. In the case of cereal fields, the management intensity (nitrogen fertiliser kg/ha) had a negative effect on spider richness and no effect on carabids. After variance partitioning, both local and landscape characteristics seem to be important for both cereal and grassland arthropod communities. Based on our results, we think that current and future agri-environmental schemes should be concentrated on cropland extensification. Low intensity croplands could act as a buffer zone around the semi-natural grasslands, at least in this biogeographic region.

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Over the past several decades, fractal geometry has found widespread application in the theoretical and experimental sciences to describe the patterns and processes of nature. The defining features of a fractal object (or process) are self-similarity and scale-invariance; that is, the same pattern of complexity is present regardless of scale. These features imply that fractal objects have an infinite level of detail, and therefore require an infinite sample size for their proper characterization. In practice, operational algorithms for measuring the fractal dimension D of natural objects necessarily utilize a finite sample size of points (or equivalently, finite resolution of a path, boundary trace or other image). This gives rise to a paradox in empirical dimension estimation: the object whose fractal dimension is to be estimated must first be approximated as a finite sample in Euclidean embedding space (e.g., points on a plane). This finite sample is then used to obtain an approximation of the true (but unknown) fractal dimension. While many researchers have recognized the problem of estimating fractal dimension from a finite sample, none have addressed the theoretical relationship between sample size and the reliability of dimension estimates based on box counting. In this paper, a theoretical probability-based model is developed to examine this relationship. Using the model, it is demonstrated that very large sample sizes — typically, one to many orders of magnitude greater than those used in most empirical studies — are required for reliable dimension estimation. The required sample size increases exponentially with D, and a 10D increase in sampling effort is required for each decadal (order of magnitude) increase in the scaling range over which dimension is reliably estimated. It is also shown that dimension estimates are unreliable for box counts exceeding one-tenth the sample size.

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Niemelä, J., Halme, E. and Haila, Y. (1990): Balancing sampling effort in pitfall trapping of carabid beetles. Entomol. Fennica 1, 233-238. Balancing sampling effort in pitfall trapping

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