Éditeur(s) : HAL CCSD University of California, Los Angeles
Résumé : International audience
entropart is a package for R designed to estimate diversity based on HCDT entropy or similarity-based entropy. It allows calculating species-neutral, phylogenetic and functional entropy and diversity, partitioning them and correcting them for estimation bias. © 2015, American Statistical Association.
ISSN: 1548-7660

hal-01502646
https://hal-agroparistech.archives-ouvertes.fr/hal-01502646
DOI : 10.18637/jss.v067.i08

Éditeur(s) : HAL CCSD
Résumé : We unify the definitions of phylogenetic and functional entropy and diversity as a generalization of HCDT entropy when an ultrametric tree is considered. We derive the decomposition of phylodiversity and its estimation bias correction to allow its estimation from real, often undersampled data. Phyloentropy can be transformed into phylodiversity to provide a measure of true diversity, i.e. an effective number of species or communities.
https://hal-agroparistech.archives-ouvertes.fr/hal-00946177

hal-00946177
https://hal-agroparistech.archives-ouvertes.fr/hal-00946177
https://hal-agroparistech.archives-ouvertes.fr/hal-00946177/document
https://hal-agroparistech.archives-ouvertes.fr/hal-00946177/file/HAL_Decomposing_Phylodiversity.pdf

Éditeur(s) : HAL CCSD Public Library of Science
Résumé : 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.
ISSN: 1932-6203

hal-01189953
https://hal.archives-ouvertes.fr/hal-01189953
DOI : 10.1371/journal.pone.0090289
PRODINRA : 259795
PUBMED : 24603966

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
Measuring functional or phylogenetic diversity is the object of an active literature. The main issues to address are relating measures to a clear conceptual framework, allowing unavoidable estimation-bias correction and decomposing diversity along spatial scales. We provide a general mathematical framework to decompose measures of species-neutral, phylogenetic or functional diversity into α and β components. We first unify the definitions of phylogenetic and functional entropy and diversity as a generalization of HCDT entropy and Hill numbers when an ultrametric tree is considered. We then derive the decomposition of diversity. We propose a bias correction of the estimates allowing meaningful computation from real, often undersampled communities. Entropy can be transformed into true diversity, that is an effective number of species or communities. Estimators of α- and β-entropy, phylogenetic and functional entropy are provided. Proper definition and estimation of diversity is the first step towards better understanding its underlying ecological and evolutionary mechanisms.
ISSN: 2041-210X

hal-01502645
https://hal-agroparistech.archives-ouvertes.fr/hal-01502645
DOI : 10.1111/2041-210X.12323

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : A preliminary version appeared in the 18th ACM-SIAM Symposium on Discrete Algorithms, pp. 746- 755, 2007
International audience
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define various variants of Voronoi diagrams depending on the class of objects, the distance function and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow one to define information-theoretic Voronoi diagrams in sta- tistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connection with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation.
ISSN: 0179-5376

hal-00488441
https://hal.archives-ouvertes.fr/hal-00488441
https://hal.archives-ouvertes.fr/hal-00488441/document
https://hal.archives-ouvertes.fr/hal-00488441/file/BVD-DCG.pdf

Éditeur(s) : HAL CCSD Ecological Society of America
Résumé : Although niche-based and stochastic processes, including dispersal limitation and demographic stochasticity, can each contribute to community assembly, it is difficult to quantify the relative importance of each process in natural vegetation. Here, we extend Shipley's maxent model (Community Assembly by Trait Selection, CATS) for the prediction of relative abundances to incorporate both trait-based filtering and dispersal limitation from the larger landscape and develop a statistical decomposition of the proportions of the total information content of relative abundances in local communities that are attributable to trait-based filtering, dispersal limitation, and demographic stochasticity. We apply the method to tree communities in a mature, species-rich, tropical forest in French Guiana at 1-, 0.25- and 0.04-ha scales. Trait data consisted of species' means of 17 functional traits measured over both the entire meta-community and separately in each of nine 1-ha plots. Trait means calculated separately for each site always gave better predictions. There was clear evidence of trait-based filtering at all spatial scales. Trait-based filtering was the most important process at the 1-ha scale (34%), whereas demographic stochasticity was the most important at smaller scales (37-53%). Dispersal limitation from the meta-community was less important and approximately constant across scales (similar to 9%), and there was also an unresolved association between site-specific traits and meta-community relative abundances. Our method allows one to quantify the relative importance of local niche-based and meta-community processes and demographic stochasticity during community assembly across spatial and temporal scales.
ISSN: 0012-9658

hal-01032424
https://hal.archives-ouvertes.fr/hal-01032424

Éditeur(s) : HAL CCSD
Résumé : The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.
https://hal.inria.fr/inria-00137865

Report N° : RR-6154
inria-00137865
https://hal.inria.fr/inria-00137865
https://hal.inria.fr/inria-00137865v2/document
https://hal.inria.fr/inria-00137865/file/bregman.pdf

Éditeur(s) : HAL CCSD Springer Verlag/EDP Sciences
Résumé : International audience
The elucidation of relationships between biodiversity and ecosystem processes has been limited by the definition of metrics of biodiversity and their integration into experimental design. Functional trait screening can strengthen the performance of these designs.* We suggest the use of Rao's quadratic entropy to measure both functional diversity and phylogenetic diversity of species mixtures proposed for an experimental design, and demonstrate how they can provide complementary information.* We also present an index assessing the statistical performance of these independent variables in different experimental designs. Measurement of independent variables as continuous vs. discrete variables reduces statistical performance, but improves the model by quantifying species differences masked by group assignments.* To illustrate these advances, we present an example from a tropical forest tree community in which we screened 38 species for nine functional traits. The proposed TropiDEP design is based on the relative orthogonality of two multivariate trait axes defined using principal component analysis.* We propose that independent variables describing functional diversity might be grouped to calculate independent variables describing suites of different traits with potentially different effects on particular ecosystem processes. In other systems these axes may differ from those reported here, yet the methods of analysis integrating functional and phylogenetic diversity into experimental design could be universal.
La compréhension des relations pouvant exister entre biodiversité et fonctionnement des écosystèmes a été longtemps limitée par la définition de méthodes de quantification de la diversité biologique et la mise en œuvre de dispositifs expérimentaux permettant sa mesure. L'identification de syndromes de traits fonctionnels clefs influençant des fonctions écosystémiques particulières peut renforcer la performance de ces dispositifs.* Nous suggérons l'utilisation de l'entropie quadratique de Rao pour mesurer la diversité fonctionnelle et phylogénétique dans des assemblages synthétiques d'espèces, et montrons comment ces mesures de diversité sont complémentaires.* Nous présentons également un indice permettant de tester la performance statistique de ces variables indépendantes dans différents modèles expérimentaux. L'utilisation de variables indépendantes continues plutôt que discrètes réduit la performance statistique mais améliore le modèle en quantifiant les différences fonctionnelles entre espèces; différences généralement masquées lors de leur assignation en groupes fonctionnels.* Pour illustrer ces avancées, nous présentons un exemple d'assemblages synthétiques à partir de 38 espèces d'arbres de forêt tropicale sélectionnées pour 9 traits fonctionnels (TropiDEP). Le plan d'expérience de TropiDEP est basé sur l'orthogonalité relative de deux axes multivariés de traits fonctionnels définis par analyse en composantes principales.* Nous proposons que les variables décrivant la diversité fonctionnelle soient groupées pour calculer des variables indépendantes, divisées en plusieurs axes décrivant des combinaisons de différents traits pouvant influencer des processus différents de l'écosystème (e.g. processus du N et du C). Dans d'autres systèmes, ces axes peuvent différer de ceux présentés ici, mais les méthodes d'analyse peuvent être universelles.
ISSN: 1286-4560

Droits : info:eu-repo/semantics/OpenAccess
hal-00883621
https://hal.archives-ouvertes.fr/hal-00883621
https://hal.archives-ouvertes.fr/hal-00883621/document
https://hal.archives-ouvertes.fr/hal-00883621/file/hal-00883621.pdf
DOI : 10.1051/forest/2009110

Éditeur(s) : HAL CCSD BioMed Central
Résumé : International audience
BACKGROUND: Although widely used, area-based deprivation indices remain sensitive to urban-rural differences as such indices are usually standardised around typical urban values. There is, therefore, a need to determine to what extent available deprivation indices can be used legitimately over both urban and rural areas. METHODS: This study was carried out in Brittany, France, a relatively affluent region that contains deep rural areas. Among the 1,736 residential census block groups (IRIS) composing the Brittany region, 1,005 (57.9%) are rural. Four deprivation indices were calculated: two scores (Carstairs and Townsend) developed in the UK and two more recent French measures (Havard and Rey). Two standardisation levels were considered: all of the IRIS and only the urban IRIS of the region. Internal validity (Kappa coefficients and entropy values) and external validity (relationship with colorectal cancer screening [CCS] attendance) were investigated. RESULTS: Regardless of the deprivation measure used, wealthy areas are mostly clustered in the West and at the outskirts of major towns. Carstairs and Rey scores stand out by all evaluation criteria, capturing both urban and rural deprivation. High levels of agreements were found across standardisation levels (κ = 0.96). The distributions of deprivation scores were balanced across urban and rural areas, and high Shannon entropy values were observed in the capital city (≥0.93). Similar and significant negative trends were observed between CCS attendance and both deprivation indices, independent of the degree of urbanisation. CONCLUSIONS: These results provide support, despite potential sociological objections, for the use of a compromise index that would facilitate comparisons and interpretations across urban and rural locations in public health research.
ISSN: 1476-072X

hal-01063904
https://hal.archives-ouvertes.fr/hal-01063904
https://hal.archives-ouvertes.fr/hal-01063904/document
https://hal.archives-ouvertes.fr/hal-01063904/file/1476-072X-13-22.pdf
PUBMED : 24929662

Éditeur(s) : HAL CCSD
Résumé : Similarity-based diversity (Leinster and Cobbold 2012) encompasses classical measures of diversity, including the number of species, Shannon and Simpson diversity, and also phylogenetic and functional diversity. We derive two estimators to allow applying it to real, often under-sampled data, and its decomposition into alpha, beta and gamma diversity when an assemblage of communities is considered.
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454

hal-00989454
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454v3/document
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454/file/DqZ%20%28HAL%29.pdf

Éditeur(s) : HAL CCSD
Résumé : International audience
The corrosion rates in the presence of some indole derivates, namely, 9H-pyrido[3,4-b]indole (norharmane) and 1-methyl-9H-pyrido[3,4-b]indole (harmane), as inhibitors of C38 steel corrosion inhibitor in 1 M HCl solution, were measured by potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) techniques, in the range of temperatures from 25 to 55∘C. Results obtained revealed that the organic compounds investigated have inhibiting properties for all temperatures. The inhibition was assumed to occur via adsorption of the indole molecules on the metal surface. Adsorption of indole derivates was found to follow the Langmuir isotherm. The apparent activation energies, enthalpies, and entropies of the dissolution process and the free energies and enthalpies for the adsorption process were determined by potentiodynamic polarization and electrochemical impedance. The fundamental thermodynamic functions were used to collect important information about indole inhibitory behaviour.
international Journal of Corrosion

hal-01683120
https://hal.univ-antilles.fr/hal-01683120
DOI : 10.1155/2013/139798

Éditeur(s) : HAL CCSD
Résumé : Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, come with an effective number of species to simplify their interpretation, and estimators to apply them to real data. Generalized Simpson's entropy has all of these features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimator, which allows for robust estimation of the diversity of poorly sampled, rich communities.
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738

hal-01276738
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738/document
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738/file/GSimpson.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The characteristic frequencies at which two different melt-related attenuation mechanisms occur in partially molten gabbronorite are computed as a function of aspect ratios of the melt-filled cracks, and the melt viscosity. The computations were done for basaltic and andesitic melts. The melt viscosity is constrained by (i) laboratory measurements performed in the range 10(8)-10(14) Pa s with a creep apparatus and in the range 10(-1) to 10(5) Pas with a rotational Couette viscorneter, and (ii) modeling of viscosity at high temperatures. The results of the characteristic frequency calculations suggest that melt squirt flow is a viable attenuation mechanism at seismic frequencies for aspect ratio of melt inclusions in the range 10(-1) to 10(-2) for the andesite, and 10(-4) to 10(-3) for the two basalts.
ISSN: 0031-9201

hal-00412014
https://hal.archives-ouvertes.fr/hal-00412014
DOI : 10.1016/j.pepi.2008.04.010

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
ISSN: 2041-210X

hal-01504648
https://hal-agroparistech.archives-ouvertes.fr/hal-01504648
DOI : 10.1111/2041-210X.12591

Éditeur(s) : HAL CCSD
Résumé : Similarity-based diversity (Leinster and Cobbold 2012) encompasses classical measures of diversity, including the number of species, Shannon and Simpson diversity, and also phylogenetic and functional diversity. We derive two estimators to allow applying it to real, often under-sampled data, and its decomposition into alpha, beta and gamma diversity when an assemblage of communities is considered.
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454

hal-00989454
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454
https://hal-agroparistech.archives-ouvertes.fr/hal-00989454v2/document

Éditeur(s) : HAL CCSD
Résumé : For ecology scientists, spatial statistics are a set of tools allowing characterization of the structure of a point set, for instance a map of trees in a forest plot. This structure is defined implicitly as a departure from complete spatial randomness (CSR), the result of a Poisson point process. Inhomogeneity of the process and non-independence of points are its causes. As they cannot be disentangled by analyzing the data, so-called "spatial concentration" or "aggregation" (evenness due to repulsion also exists but is actually rare) usually concerns non-independence while intensity is assumed as known. The literature of point processes and measures of spatial structures is reviewed to clarify concepts and choices. The purpose of this thesis was to produce methodological enhancements. Its main results are: * A test for the most used statistic, Ripley's K function, against the null hypothesis of CSR. It can replace Monte-Carlo simulations used until now in the literature. * An extension of K to inhomogeneous processes, within a typology of available statistics (absolute, relative and topographic measures). When data is available as number of objects per zones (say a number of tree in each forest plot) rather than their exact position, information theory is used to define a general framework allowing to characterize spatial structure (of species) and diversity (of plots) as two aspects of a single measure of inequality. This framework is applied to Shannon's index of biodiversity to derive a self-sufficient definition of beta diversity, its calculation independently from the difference between gamma and alpha diversity, and a statistical test of significance against the null hypothesis that plots are samples of the same community. The way is paved for other applications to measures of diversity and spatial structures. As a conclusion, it appears clear that pattern characterization tools are a first step to deal with ecological questionings. Their development is still a matter of research. Yet, they are far from sufficient to address ecological processes as point processes ignore the temporal aspect of object locations.
Les statistiques spatiales sont pour les écologues un ensemble d'outils permettant de caractériser la structure d'un semis de points, par exemple une carte représentant des emplacements des arbres dans une parcelle de forêt. Cette structure est définie implicitement comme un écart à semis complètement aléatoire, résultat d'un processus de Poisson. L'hétérogénéité du processus ponctuel dont le semis de points est une réalisation et la non-indépendance des points en sont les causes indiscernables, ce qui amène généralement à supposer l'intensité du processus connu et nommer " concentration spatiale " ou " agrégation " (la régularité spatiale est possible, mais rare en pratique) la non-indépendance. Une revue de la littérature des processus ponctuels et des mesures de structures spatiales est fournie pour clarifier les concepts et les choix. L'objectif de ce travail de thèse était de produire des améliorations méthodologiques. Ses résultats principaux sont : * L'établissement d'un test pour la principale statistique utilisée, la fonction K de Ripley, permettant de s'affranchir de la méthode de Monte-Carlo utilisée dans la littérature pour rejeter l'hypothèse nulle d'un processus complètement aléatoire. * L'extension de K aux processus hétérogènes, dans le cadre d'une typologie claire des statistiques (absolues, relatives, topographiques). Lorsque la position exacte des objets n'est pas connue, mais que des effectifs par zone sont disponibles (par exemple des nombres d'arbres par parcelle), la théorie de l'information est utilisée pour définir un cadre général permettant de caractériser la structure spatiale (des espèces dans les parcelles) et la diversité (des parcelles, en termes d'espèces) comme deux aspects d'une même mesure d'inégalité. Ce cadre est appliqué à l'indice de biodiversité de Shannon pour définir clairement la mesure de diversité bêta, son calcul direct indépendamment de la différence entre diversités gamma et alpha, et fournir un test statistique de non nullité. La voie est ouverte pour l'application à d'autres mesures de diversité et de structure spatiale. En conclusion, il semble clair que ces outils de caractérisation sont un premier pas pour traiter les questions écologiques, leur développement étant toujours du domaine de la recherche. Ils sont cependant très insuffisants pour répondre à des questions liées aux processus écologiques, assez éloignés des processus ponctuels qui ignorent l'aspect temporel de l'installation des objets.
https://pastel.archives-ouvertes.fr/pastel-00540327

NNT : 2010AGPT0075
pastel-00540327
https://pastel.archives-ouvertes.fr/pastel-00540327
https://pastel.archives-ouvertes.fr/pastel-00540327/document
https://pastel.archives-ouvertes.fr/pastel-00540327/file/13_Marcon2010.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : Analyses of tree diversity and community composition in tropical rain forests are usually based either on general herbarium data or on a restricted number of botanical plots. Despite their high taxonomic accuracy, both types of data are difficult to extrapolate to landscape scales. Meanwhile, forestry surveys provide quantitative occurrence data on large areas, and are thus increasingly used for landscape-scale analyses of tree diversity. However, the reliability of these approaches has been challenged because of the ambiguity of the common (vernacular) names used by foresters and the complexity of tree taxonomy in those hyper-diverse communities.We developed and tested a novel approach to evaluate taxonomic reliability of forestry surveys and to propagate the resulting uncertainty in the estimates of several diversity indicators (alpha and beta entropy, Fisher-alpha and Sørensen similarity). Our approach is based on Monte-Carlo processes that simulate communities by taking into account the expected accuracy and reliability of common names. We tested this method in French Guiana, on 9 one-hectare plots (4279 trees – DBH ⩾ 10 cm) for which both common names and standardized taxonomic determinations were available. We then applied our method of community simulation on large forestry inventories (560 ha) at the landscape scale and compared the diversity indices obtained for 10 sites with those computed from precise botanical determination situated at the same localities.We found that taxonomic reliability of forestry inventories varied from 22% (species level) to 83% (family level) in this Amazonian region. Indices computed directly with raw forestry data resulted in incorrect values, except for Gini–Simpson beta-diversity. On the contrary, our correction method provides more accurate diversity estimates, highly correlated with botanical measurements, for almost all diversity indices at both regional and local scales. We obtained a robust ranking of sites consistent with those shown by botanical inventories.These results show that (i) forestry inventories represent a significant part of taxonomic information, (ii) the relative diversity of regional sites can be successfully ranked using forestry inventory data using our method and (iii) forestry inventories can valuably contribute to the detection of large-scale diversity patterns when biases are well-controlled and corrected.The tools we developed as R-functions are available in supplementary material and can be adapted with local parameters to be used for forest management and conservation issues in other regional contexts
ISSN: 0378-1127

hal-01204219
https://hal.archives-ouvertes.fr/hal-01204219
DOI : 10.1016/j.foreco.2014.05.045
PRODINRA : 286554

Éditeur(s) : HAL CCSD Nordic Ecological Society
Résumé : 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 beta 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.
ISSN: 0030-1299

hal-01032426
https://hal.archives-ouvertes.fr/hal-01032426
DOI : 10.1111/j.1600-0706.2011.19267.x

Éditeur(s) : HAL CCSD Public Library of Science
Résumé : International audience
Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, can be expressed as an effective number of species to simplify their interpretation, and come with estimators that allow one to apply them to real-world data. We introduce the generalized Simpson’s entropy as a measure of diversity and investigate its properties. We show that it has many useful features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimators, which allow for sound estimation of the diversity of poorly sampled, rich communities.
ISSN: 1932-6203

hal-01276738
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738v2/document
https://hal-agroparistech.archives-ouvertes.fr/hal-01276738/file/Grabchak%20et%20al.%20-%202017%20-%20The%20Generalized%20Simpson%27s%20Entropy%20is%20a%20Measure%20of%20Biodiversity.pdf
DOI : 10.1371/journal.pone.0173305

Éditeur(s) : HAL CCSD
Résumé : Measuring biodiversity requires empirical techniques to effectively estimate it from real data. The well-known underestimation of the number of species applies to low orders of diversity in general. I test nine estimators including three new ones on geometric and lognormal distributions that represent realistic, hyper-diverse communities. The best two estimators allow a good estimation of diversity of orders over 0.5, even when the sampling effort is low. I provide criteria to choose the estimator and the necessary code in the R package entropart.
https://hal-agroparistech.archives-ouvertes.fr/hal-01212435

hal-01212435
https://hal-agroparistech.archives-ouvertes.fr/hal-01212435
https://hal-agroparistech.archives-ouvertes.fr/hal-01212435v2/document
https://hal-agroparistech.archives-ouvertes.fr/hal-01212435/file/Estimation.pdf