1.Inventorying requires comprehensive sampling, while monitoring should build on it and focus on as few components as possible to detect changes in time or space. To sample or acquire information for both purposes can therefore be viewed as different processes, herewith called α-sampling and β-sampling. Biodiversity covers species, their genetic diversity and the way they interact in communities and ecosystems. Quantifying these aspects leads to the need to study taxon (TD), phylogenetic (PD) and functional diversity (FD). Here we propose and test a method for the optimization of sampling protocols to inventorying and monitoring TD, PD and FD for a wide range of taxa.2. We used spiders as a case-study, although the same optimization procedure could be applied to any taxon requiring a combination of sampling methods. Spiders were sampled in multiple sites in the Iberian Peninsula. PD and FD were measured as the sum of the length of branches on a phylogenetic or functional tree. To reach the optimal combination of methods for inventory, we followed an iterative procedure optimizing the accumulation curve of diversity values. Optimal monitoring in space or time required minimizing the difference between sampled and true β-diversity. We used a framework that disentangles species replacement and richness differences contributions to overall β-diversity.3. For α-diversity, the optimal combination of 24 samples for TD, PD and FD allowed sampling more than 50% of real diversity. For β-diversity, the optimal combination of six samples for all measures allowed reaching a bias (difference between sampled and true diversity) below 0.08. 4. The widespread use of similar sampling protocols worldwide and regular repetition in time can have a major impact on the scope and usefulness of global monitoring projects. In addition, the comparable sampling of biodiversity in space and/or time allows reusing of data collected for specific purposes, potentiating a synergistic effect among different projects. This makes data useful much beyond their initial plan. We strongly advocate the optimization, standardization and widespread adoption of sampling protocols for all taxa at a global level, for both inventory and monitoring of all levels of biodiversity: taxon, phylogenetic and functional. 2

Understanding the variation in community composition and species abundances, i.e., β-diversity, is at the heart of community ecology. A common approach to examine β-diversity is to evaluate directional turnover in community composition by measuring the decay in the similarity among pairs of communities along spatial or environmental distances. We provide the first global synthesis of taxonomic and functional distance decay along spatial and environmental distance by analysing 149 datasets comprising different types of organisms and environments. We modelled an exponential distance decay for each dataset using generalized linear models and extracted r2 and slope to analyse the strength and the rate of the decay. We studied whether taxonomic or functional similarity has stronger decay across the spatial and environmental distances. We also unveiled the factors driving the rate of decay across the datasets, including latitude, spatial extent, realm, and organismal features. Taxonomic distance decay was stronger along spatial and environmental distances compared with functional distance decay. The rate of taxonomic spatial distance decay was the fastest in the datasets from mid-latitudes while the rate of functional decay increased with latitude. Overall, datasets covering larger spatial extents showed a lower rate of decay along spatial distances but a higher rate of decay along environmental distances. Marine ecosystems had the slowest rate of decay. This synthesis is an important step towards a more holistic understanding of patterns and drivers of taxonomic and functional β-diversity.