Encyclopedia of Distances

Deza, Michel; Deza, Elena

doi:10.1007/978-3-642-30958-8

Cited by 118 publications

(58 citation statements)

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“…In this note, we presented inequalities between seven well known similarities for two numerical vectors (Deza and Deza 2013). The inequalities are valid if the vectors contain non-negative real numbers.…”

Section: Resultsmentioning

confidence: 99%

“…The Motyka similarity (Deza and Deza 2013) is half S 3 . The Motyka similarity is not considered here because its upper bound is 1 2 instead of 1 if x = y.…”

Section: Similaritiesmentioning

confidence: 99%

“…Furthermore, similarities S 3 , S 4 and S 7 coincide if x and y are restricted to the values 0 and 1. In this case the three similarities are equal to the Dice or Sørensen similarity 2A/(2A + B + C) (Deza and Deza 2013). Moreover, both S 5 and S 6 reduce to the Jaccard similarity A/(A + B + C) if x and y are binary vectors (Warrens 2008a(Warrens , 2009).…”

Section: Similaritiesmentioning

confidence: 99%

“…A similarity can be used to quantify the strength of the relationship between two vectors with numerical data. Popular choices are the Bray-Curtis similarity, the Ellenberg similarity and the Gleason similarity (Deza and Deza 2013). A similarity measure or a distance has to be considered in the context of the descriptive statistical study of which it is a part.…”

Section: Introductionmentioning

confidence: 99%

“…A type of study that may enhance the understanding of similarities and how they are related is an analytic comparison (Warrens 2008b). Deza and Deza (2013) present a list of similarity measures that are used in practice. In this note we present inequalities between these similarities that hold for non-negative real data.…”

Section: Introductionmentioning

confidence: 99%

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Inequalities Between Similarities for Numerical Data

Warrens

2016

J Classif

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Section: Resultsmentioning

confidence: 99%

“…The Motyka similarity (Deza and Deza 2013) is half S 3 . The Motyka similarity is not considered here because its upper bound is 1 2 instead of 1 if x = y.…”

Section: Similaritiesmentioning

confidence: 99%

Section: Similaritiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inequalities Between Similarities for Numerical Data

Warrens

2016

J Classif

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(Dis)similarity measures

Cichosz

2015

Data Mining Algorithms

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Unclusterable, underdispersed arrangement of insect‐pollinated plants in pollinator niche space

Herrera

2021

Ecology

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Pollinators can mediate facilitative or competitive relationships between plant species, but the relative importance of these two conflicting phenomena in shaping community‐wide pollinator resource use remains unexplored. This article examines the idea that the arrangement of large samples of plant species in Hutchinsonian pollinator niche space (n‐dimensional hypervolume whose axes represent pollinator types) can help to evaluate the comparative importance of facilitation and competition as drivers of pollinator resource use at the community level. Pollinator composition data were gathered for insect‐pollinated plants from the Sierra de Cazorla mountains (southeastern Spain), comprising ~95% of widely distributed insect‐pollinated species. The following questions were addressed at regional (45 sites, 221 plant species) and local (1 site, 73 plant species) spatial scales: (1) Do plant species clusters occur in pollinator niche space? Four pollinator niche spaces differing in dimensionality were considered, the axes of which were defined by insect orders, families, genera, and species. (2) If all plant species form a single, indivisible cluster, are they overdispersed or underdispersed within the cluster relative to a random arrangement? “Clusterability” tests failed to reject the null hypothesis that there was only one pollinator‐defined plant species cluster in pollinator niche space, irrespective of spatial scale, pollinator niche space, or pollinator importance measurement (proportions of pollinator individuals or flowers visited by each pollinator type). Observed means of interspecific dissimilarity in pollinator composition were smaller than randomly simulated values in the order‐, family‐, and genus‐defined pollinator niche spaces. This finding revealed an underdispersed arrangement of plant species in each of these pollinator niche spaces. In the undisturbed montane habitats studied, arrangement of insect‐pollinated plant species in the various niche spaces defined by pollinator composition did not support a major role for interspecific competition as a force shaping community‐wide pollinator resource use by plants, but rather suggested a situation closer to the facilitation‐dominated extreme in a hypothetical competition‐facilitation gradient. Results also highlight the importance of investigations on complete or nearly complete insect‐pollinated plant communities for suggesting and testing novel hypotheses on the ecology and evolution of plant–pollinator systems.

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Encyclopedia of Distances

Cited by 118 publications

References 0 publications

Inequalities Between Similarities for Numerical Data

Inequalities Between Similarities for Numerical Data

(Dis)similarity measures

Unclusterable, underdispersed arrangement of insect‐pollinated plants in pollinator niche space

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