### What do we mean by diversity? The path towards quantification

#### Abstract

The concept of biological diversity has evolved from a simple count of species to more sophisticated measures that are sensitive to relative abundances and even to evolutionary divergence times between species. In the course of this evolution, diversity measures have often been borrowed from other disciplines. Biological reasoning about diversity often implicitly assumed that measures of diversity had certain mathematical properties, but most of biology’s traditional diversity measures did not actually possess these properties, a situation which often led to mathematically and biologically invalid inferences. Biologists now usually transform the traditional measures to the «effective number of species», whose mathematics does support most of the rules of inference that biologists apply to them. The effective number of species, then, seems to capture most (though not all) of what biologists mean by diversity.

#### Keywords

#### Full Text:

PDF#### References

Chao, A. (1984). Nonparametric estimation of the number of classes in a population. Scandinavian Journal of Statistics, 11(4), 265–270.

Chao, A., Chiu, C. H., & Jost, L. (2010). Phylogenetic diversity measures based on Hill numbers. Philosophical Transactions of the Royal Society B Biological Sciences, 365(1558), 3599–3609. doi: 10.1098/rstb.2010.0272

Chao, A., Chiu, C. H., & Jost, L. (2014). Unifying species diversity, phylogenetic diversity, functional diversity, and related similarity and differentiation measures through Hill numbers. Annual Review of Ecology, Evolution, and Systematics, 45(1), 297–324. doi: 10.1146/annurev-ecolsys-120213-091540

Chao, A., Jost, L., Hsieh, T. C., Ma, K. H., Sherwin, W., & Rollins, L. A. (2015). Expected Shannon entropy and Shannon differentiation between subpopulations for neutral genes under the finite island model. PLOS ONE, 10(6), e0125471. doi: 10.1371/journal.pone.0125471

DeVries, P. J., & Walla, T. R. (2001). Species diversity and community structure in neotropical fruit-feeding butterflies. Biological Journal of the Linnean Society, 74(1), 1–15. doi: 10.1006/bijl.2001.0571

Hannah, L., & Kay, J. A. (1977). Concentration in modern industry. Theory, measurement and the UK experience. London: Macmillan.

Hill, M. (1973). Diversity and evenness: A unifying notation and its consequences. Ecology, 54, 427–432. doi: 10.2307/1934352

Hubbell, S. P. (2001). A unified theory of biodiversity and biogeography. Princeton, NJ: Princeton University Press.

Jost, L. (2006). Entropy and diversity. Oikos, 113(2), 363–375. doi: 10.1111/j.2006.0030-1299.14714.x

Jost, L. (2007). Partitioning diversity into independent alpha and beta components. Ecology, 88(10), 2427–2439. doi: 10.1890/06-1736.1

Jost, L. (2010). The relation between evenness and diversity. Diversity, 2(2), 207–232. doi: 10.3390/d2020207

Jost, L., DeVries, P. J., Walla, T., Greeney, H., Chao, A., & Ricotta, C. (2010). Partitioning diversity for conservation analyses. Diversity and Distributions, 16(1), 65–76. doi: 10.1111/j.1472-4642.2009.00626.x

Lande, R. (1996). Statistics and partitioning of species diversity and similarity among multiple communities. Oikos, 76(1), 5–13. doi: 10.2307/3545743

Moreno, C. E., Barragán, F., Pineda, E., & Pavón, N. P. (2011). Reanálisis de la diversidad alfa: Alternativas para interpretar y comparar información sobre comunidades ecológicas. Revista Mexicana de Biodiversidad, 82(4), 1249–1261. doi: 10.22201/ib.20078706e.2011.4.745

Rényi, A. (1961). On measures of information and entropy. In J. Neyman (Ed.), Proceedings of the fourth Berkeley Symposium on Mathematics, Statistics and Probability 1960 (pp. 547–561). Berkeley, CA: University of California Press.

Shannon, C. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423. doi: 10.1002/j.1538-7305.1948.tb01338.x

Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 479–487.

Texts in the journal are –unless otherwise indicated– published under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

____________________________________________________________________________________________________________________