Scaling the chord and Hellinger distances in the range [0,1]: An option to consider

다국어 초록 (Multilingual Abstract)

The chord and Hellinger distances are commonly used as measures of resemblance in ecological studies. Both distances are bound within the range [0,√2]. We propose to scale them within the range [0,1]. The scaling is mainly justified to report beta diversity values in the range [0,1] properly. Moreover, results for both unscaled distances in multivariate techniques such as cluster analysis or ordinations are not directly comparable with similar graphical displays obtained with indices bound in the range [0,1]. Although comparability and/or interpretability of values are compromised, the used of the unscaled Hellinger and chord distances do not void their validity in ecological studies. Nonetheless, we have found one exception when comparing clustering models using the Gower distance criterion.

참고문헌 (Reference)

1 Murtagh F, "Ward's hierarchical agglomerative clustering method: which algorithms implement ward's criterion?" 31 : 274-295, 2014

2 Oksanen J, "Vegan: Community ecology package. R package version 2.3-0"

3 Pielou EC, "The interpretation of ecological data: a primer on classification and ordination" Wiley 1984

4 Singh W, "Robustness of fish assemblages derived from three hierarchical agglomerative clustering algorithms performed on Icelandic groundfish survey data" 68 : 189-200, 2011

5 R Core Team, "R: a Language and environment for statistical computing" R Foundation for Statistical Computing

6 Chiu CH, "Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers" 84 : 21-44, 2014

7 Kindt R, "Package for community ecology and suitability analysis"

8 Anderson MJ, "PERMANOVA+ for PRIMER: guide to software and statistical methods" PRIMER-E 2008

9 Pavoine S, "On the challenge of treating various types of variables: application for improving the measurement of functional diversity" 118 : 391-402, 2009

10 Sneath PHA, "Numerical taxonomy - The principles and practice of numerical classification" Freeman 1973

11 Borcard D, "Numerical ecology with R" Springer 2011

12 Legendre P, "Numerical ecology" Elsevier 1998

13 Anderson MJ, "Multivariate dispersion as a measure of beta diversity" 9 : 683-693, 2006

14 Orloci L, "Multivariate Analysis in Vegetation Research" Junk 1978

15 Warren DL, "Environmental niche equivalency versus conservatism: quantitative approaches to niche evolution" 62 : 2868-2883, 2008

16 Legendre P, "Ecologically meaningful transformations for ordination of species data" 129 : 271-280, 2001

17 Krebs CJ, "Ecological methodology" Benjamin Cummings 1999

18 Faith DP, "Compositional dissimilarity as a robust measure of ecological distance" 69 : 57-68, 1987

19 Clarke KR, "Change in marine communities: an approach to statistical analysis and interpretation" Plymouth Marine Laboratory 1994

20 Szava-Kovats RC, "Biodiversity patterns along ecological gradients: unifying ${\beta}$-diversity indices" 9 (9): e110485-, 2014

21 Legendre P, "Beta diversity as the variance of community data: dissimilarity coefficients and partitioning" 16 : 951-963, 2013

22 Mason NWH, "An index of functional diversity" 14 : 571-578, 2003