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Marcon, E., Herault, B., Baraloto, C., & Lang, G. (2012). The decomposition of Shannon's entropy and a confidence interval for beta diversity. Oikos, 121(4), 516–522.
Abstract: Beta diversity is among the most employed theoretical concepts in ecology and biodiversity conservation. Up to date, a self-contained definition of it, with no reference to alpha and gamma diversity, has never been proposed. Using Kullback-Leibler divergence, we present the explicit formula of Shannon's β entropy, a bias correction for its estimator and a confidence interval. We also provide the mathematical framework to decompose Shannon diversity into several hierarchical nested levels. From botanical inventories of tropical forest plots in French Guiana, we estimate Shannon diversity at the plot, forest and regional level. We believe this is a complete and usefulness toolbox for ecologists interested in partitioning biodiversity. © 2011 The Authors. Oikos © 2012 Nordic Society Oikos.
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Marcon, E., & Puech, F. (2010). Measures of the geographic concentration of industries: improving distance-based methods. J. Econ. Geogr., 10(5), 745–762.
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.
Keywords: Geographic concentration; distance-based methods; K-density function; Ripley's K function; M function; C40; C60; R12; L60
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Marcon, E., & Puech, F. (2003). Evaluating the geographic concentration of industries using distance-based methods. J. Econ. Geogr., 3(4), 409–428.
Abstract: We propose new methods for evaluating the spatial distribution of firms. To assess whether firms are concentrated or dispersed, economists have traditionally used indices that analyse the heterogeneity of a spatial structure at a single geographic level. We introduce distance-based methods, Besag's L function (derived from Ripley's K function) and Diggle and Chetwynd's D function to describe simultaneously spatial distribution at different geographical scales. Our empirical applications consider the distribution of French manufacturing firms in the Paris area and in France generally. For some geographic levels, results show significant concentration or dispersion of firms according to their sector of activity.
Keywords: agglomeration; clustering; geographic concentration; location of firms
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Marcon, E., & Puech, F. (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics, 62, 56–67.
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.
Keywords: Agglomeration; Aggregation; Economic geography; Point patterns; Spatial concentration
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Marcon, E., Puech, F., & Traissac, S. (2012). Characterizing the relative spatial structure of point patterns. Int. J. Ecol., 2012(Article ID 619281), 11.
Abstract: We generalize Ripley's K function to get a new function, M, to characterize the spatial structure of a point pattern relatively to another one. We show that this new approach is pertinent in ecology when space is not homogenous and the size of objects matters. We present how to use the function and test the data against the null hypothesis of independence between points. In a tropical tree data set we detect intraspecific aggregation and interspecific competition. © 2012 Eric Marcon et al.
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Marcon, E., Scotti, I., Herault, B., Rossi, V., & Lang, G. (2014). Generalization of the partitioning of Shannon diversity. PLoS ONE, 9(3), e90289.
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.
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Marcon, E., Traissac, S., & Lang, G. (2013). A Statistical Test for Ripley’s Function Rejection of Poisson Null Hypothesis. ISRN Ecology, 2013(Article ID 753475), 9.
Abstract: Ripley’s K function is the classical tool to characterize the spatial structure of point patterns. It is widely used in vegetation studies. Testing its values against a null hypothesis usually relies on Monte-Carlo simulations since little is known about its distribution.
We introduce a statistical test against complete spatial randomness (CSR). The test returns the p-value to reject the null hypothesis of independence between point locations. It is more rigorous and faster than classical Monte-Carlo simulations. We show how to apply it to a tropical forest plot. The necessary R code is provided.
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Marcon, E., Traissac, S., Puech, F., & Lang, G. (2015). Tools to characterize point patterns: dbmss for R. Journal of Statistical Software, 67(Codesnippet3), 1–15.
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.
Keywords: Point patterns; R; Spatial structure
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Mariano, C. S. F., Silva Santos, I. D. A., Groc, S., Leroy, C., Malé, P. - J., Ruiz-González, M. X., et al. (2011). The karyotypes of Gigantiops destructor (Fabricius) and other ants from French Guiana (Formicidae). Ann. Soc. Entomol. Fr., 47(1-2), 140–146.
Abstract: The aim of this study, which was conducted in French Guiana, was to characterize the karyotypes of nine ant species belonging to the genera Anochetus, Apterostigma, Cyphomyrmex, Camponotus, Gigantiops, Myrmicocrypta, Odontomachus and Pseudomyrmex, and to compare them with published data. We present the first descriptions of the karyotypes of Gigantiops destructor (Fabricius), an endemic Formicinae of the Amazonian region, which is the only living species in the tribe Gigantiopini, and of a species from the poorly-known cryptic genus Myrmicocrypta, which belongs to the Myrmicinae tribe Attini.
Keywords: Chromosome number; Diversity; Minimum interaction theory
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Marino, N. A. C., Céréghino, R., Gilbert, B., Petermann, J. S., Srivastava, D. S., de Omena, P. M., et al. (2020). Species niches, not traits, determine abundance and occupancy patterns: A multi-site synthesis. Global Ecol. Biogeogr., 29(2), 295–308.
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
Keywords: abundance; environmental niche; functional distinctiveness; functional traits; metacommunity; niche breadth; niche position; occupancy; abundance; biodiversity; functional group; geographical distribution; invertebrate; Neotropical Region; niche breadth; Invertebrata
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