Zeta Diversity

Measuring and modelling compositional change in biodiversity with zeta diversity

Changes in the composition of ecological communities across sites are traditionally measured by computing how many species are shared across pairs of sites, using one of multiple possible beta diversity metrics.

Zeta (ζ) diversity (see the original paper here) is a concept that was recently proposed to overcome the limitations of pairwise metrics. Zeta diversity is not a single measure, but is decomposed into a set of measures, whose combination provides additional insights when considering multiple sites simultaneously. ζ1 is the average number of species per site (i.e. alpha diversity). ζ2 is the average number of species shared by any two sites (i.e. beta diversity). ζ3 is the average number of species shared by any three sites, and so on until the maximum number of sites is reached (the number of sites as subscript is referred to as the “order” of zeta). The advantage of zeta diversity therefore lies in the fact that low orders of zeta capture the contribution of all species in the community to turnover, whereas high orders of zeta only capture the more widespread (common) species (by definition, rare species cannot be shared by many sites).

The concepts underpinning zeta diversity and its calculation are introduced across 3 publications (2 peer-reviewed and 1 pre-print) and example applications are growing in the literature.


R-package – Zetadiv

The zetadiv R package (current version 1.0.1, https://CRAN.R-project.org/package=zetadiv) enables multiple analyses using zeta diversity to investigate changes in species composition across multiple sites. These analyses can be classified into 4 categories:

  • the decline of zeta diversity analyses how the number of species shared by multiple assemblages decreases with increasing number of assemblages within combinations, and what information is contained in the form of this decline;
  • the distance decay of zeta diversity analyses how zeta diversity for different orders varies with distance between sites;
  • Multi-Site Generalised Dissimilarity Modelling (MS-GDM; an adaptation of Generalised Dissimilarity Modelling; Ferrier, et al. 2007), computes the contribution of different environmental variables and distance to zeta diversity for different orders;
  • hierarchical scaling of zeta diversity analyses how zeta diversity varies with grain. The functions of the zetadiv package encompass analyses, such as the zeta decline, that use multiple species assemblages from different sites, and are specific to zeta diversity.

Other functions, related to distance decay, MS-GDM and the hierarchical scaling of zeta diversity, are classical analyses that have been applied to beta diversity in the literature, and have been adapted for higher orders of zeta diversity to illustrate the differences between common and rare species in their contribution to compositional turnover.


3 Papers outlining the concept of zeta diversity, its use and calculation

The original work

Hui & McGeoch (2014) introduced the concept of zeta diversity, and showed how it can link together to various incidence-based measures, including species accumulation curves, occupancy-frequency distributions, and the endemic-effort relationship.

Hui, C., & McGeoch, M. A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist184(5), 684-694. doi:10.1086/678125

Associated CIB blog post: http://academic.sun.ac.za/cib/highpaper/2014/06_zeta_beats_beta.htm


The broad relevance of zeta diversity

McGeoch et al. (2017) uses zeta diversity to analyse and compare a set of very diverse datasets, and show how zeta can be used to analyse and characterise different types of not only ecological communities, but any kind of data that can be describe by a row-by-column incidence matrix.

Melodie A. McGeoch, Guillaume Latombe, Nigel R. Andrew, Shinichi Nakagawa, David A. Nipperess, Mariona Roige, Ezequiel M Marzinelli, Alexandra H. Campbell, Adriana Verges, Torsten Thomas, Peter D. Steinberg, Katherine E. Selwood, Cang Hui (2017). The application of zeta diversity as a continuous measure of compositional change in ecology. bioRxiv, 216580; doi:10.1101/216580.


Multi-site generalised dissimilarity modelling

Latombe et al. (2017) showed how combining zeta diversity and generalised dissimilarity modelling, enables distinguishing between the drivers of species turnover for common and rare species.

Latombe, G., Hui, C., & McGeoch, M. A. (2017). Multi‐site generalised dissimilarity modelling: using zeta diversity to differentiate drivers of turnover in rare and widespread species. Methods in Ecology and Evolution8(4), 431-442. doi:10.1111/2041-210X.12756

Associated MEE blog post: https://methodsblog.wordpress.com/2017/04/13/multi-site-generalised-dissimilarity-modelling/#more-5740

The MS-GDM  article is part of the MEE special issue “Technological Advances at the Interface of Ecology and Statistics” (associated MEE blog post): https://methodsblog.wordpress.com/2017/04/11/issue-7-6-ecostats/#more-5734)


Some papers that use zeta diversity.

Validate and measure uncertainty in the output of Self-Organising Maps

Roigé, M., McGeoch, M. A., Hui, C., & Worner, S. P. (2017). Cluster validity and uncertainty assessment for self‐organizing map pest profile analysis. Methods in Ecology and Evolution8(3), 349-357. doi:10.1111/2041-210X.12669

Associated MEE blog post: https://methodsblog.wordpress.com/2017/05/25/zeta-diversity/#more-5860


Compute the number of research areas shared by papers on invasion science, to quantify multidisciplinarity.

Vaz, A. S., Kueffer, C., Kull, C. A., Richardson, D. M., Schindler, S., Muñoz-Pajares, A. J., Vicente, J. R., Martins, J., Hui, C., Khün, I & Honrado, J. P. (2017). The progress of interdisciplinarity in invasion science. Ambio, 1-15. doi:10.1007/s13280-017-0897-7


Compare patterns of diversity for native and exotic ants in islands

Roura‐Pascual, N., Sanders, N. J., & Hui, C. (2016). The distribution and diversity of insular ants: do exotic species play by different rules? Global Ecology and Biogeography25, 642-654. doi:10.1111/geb.12442


Assess the effect of human disturbance on cichlids in the Lake Tanganika

Britton, A. W., Day, J. J., Doble, C. J., Ngatunga, B. P., Kemp, K. M., Carbone, C., & Murrell, D. J. (2017). Terrestrial-focused protected areas are effective for conservation of freshwater fish diversity in Lake Tanganyika. Biological Conservation212, 120-129. doi:10.1016/j.biocon.2017.06.001


Analysing herbaceous plants diversity on 5 southern islands of Miadao Archipelago in North China

Chi, Y., Shi, H., Wang, X., Qin, X., Zheng, W., & Peng, S. (2016). Impact factors identification of spatial heterogeneity of herbaceous plant diversity on five southern islands of Miaodao Archipelago in North China. Chinese Journal of Oceanology and Limnology34(5), 937-951. doi:10.1007/s00343-016-5111-4