Abstract: We discuss a property of distance-based measures that has not been addressed with regard to evaluating the geographic concentration of economic activities. The article focuses on the choice between a probability density function of point-pair distances or a cumulative function. We begin by introducing a new cumulative function, M, for evaluating the relative geographic concentration and the co-location of industries in a non-homogeneous spatial framework. Secondly, some rigorous comparisons are made with the leading probability density function of Duranton and Overman (2005), Kd. The merits of the simultaneous use of Kd and M is proved, underlining the complementary nature of the results they provide.

Abstract: Over the last decade, distance-based methods have been introduced and then improved in the field of spatial economics to gauge the geographic concentration of activities. There is a growing literature on this theme including new tools, discussions on their specific properties and various applications. However, there is currently no typology of distance-based methods. This paper fills that gap. The proposed classification helps understand all the properties of distance-based methods and proves that they are variations on the same framework. © 2016 Elsevier B.V.

Abstract: Traditional measures of diversity, namely the number of species as well as Simpson's and Shannon's indices, are particular cases of Tsallis entropy. Entropy decomposition, i.e. decomposing gamma entropy into alpha and beta components, has been previously derived in the literature. We propose a generalization of the additive decomposition of Shannon entropy applied to Tsallis entropy. We obtain a self-contained definition of beta entropy as the information gain brought by the knowledge of each community composition. We propose a correction of the estimation bias allowing to estimate alpha, beta and gamma entropy from the data and eventually convert them into true diversity. We advocate additive decomposition in complement of multiplicative partitioning to allow robust estimation of biodiversity. © 2014 Marcon et al.

Abstract: The dbmss package for R provides an easy-to-use toolbox to characterize the spatial structure of point patterns. Our contribution presents the state of the art of distance-based methods employed in economic geography and which are also used in ecology. Topographic functions such as Ripley’s K, absolute functions such as Duranton and Overman’s Kd and relative functions such as Marcon and Puech’s M are implemented. Their confidence envelopes (including global ones) and tests against counterfactuals are included in the package. © 2015, American Statistical Association. All rights reserved.

Abstract: Aim: Locally abundant species are usually widespread, and this pattern has been related to properties of the niches and traits of species. However, such explanations fail to account for the potential of traits to determine species niches and often overlook statistical artefacts. Here, we examine how trait distinctiveness determines the abilities of species to exploit either common habitats (niche position) or a range of habitats (niche breadth) and how niche position and breadth, in turn, affect abundance and occupancy. We also examine how statistical artefacts moderate these relationships. Location: Sixteen sites in the Neotropics. Time period: 1993–2014. Major taxa studied: Aquatic invertebrates from tank bromeliads. Methods: We measured the environmental niche position and breadth of each species and calculated its trait distinctiveness as the average trait difference from all other species at each site. Then, we used a combination of structural equation models and a meta-analytical approach to test trait–niche relationships and a null model to control for statistical artefacts. Results: The trait distinctiveness of each species was unrelated to its niche properties, abundance and occupancy. In contrast, niche position was the main predictor of abundance and occupancy; species that used the most common environmental conditions found across bromeliads were locally abundant and widespread. Contributions of niche breadth to such patterns were attributable to statistical artefacts, indicating that effects of niche breadth might have been overestimated in previous studies. Main conclusions: Our study reveals the generality of niche position in explaining one of the most common ecological patterns. The robustness of this result is underscored by the geographical extent of our study and our control of statistical artefacts. We call for a similar examination across other systems, which is an essential task to understand the drivers of commonness across the tree of life. © 2019 John Wiley & Sons Ltd