Alpha Diversity Metrics - Richness, Shannon-Weiner, Simpsons, Reynis Entropy, and Effective Number of Species

Alpha Diversity Metrics - Richness, Shannon-Weiner, Simpsons, Reynis Entropy, and Effective Number of Species

Alpha diversity describes the amount of diversity local to a specific area. Diversity is then contextualized using:

species richness, which is simply the number of species
species evenness, which is how equal are the abundances of each species 
species composition, which is the identity of species in a site (e.g. % of species that are producers vs prey, habitat specialists, nitrogen fixers etc.)

Several indices are used to synthesize these richness and evenness into "diversity". Composition is then used to give context to the index. 

The Shannon-Weiner Index takes into account the mean abundance for species. The higher the value, the higher the diversity. However, the index is non-linear and becomes less informative at very high values. Rényi entropy is derived from the Shannon index and allows for variation in how the mean is weighted

The Simpsons Index also takes into account the mean abundance of species. Bounded between 0 and 1, with 0 representing no diversity (1 species) and 1 representing infinite diversity. 

The Shannon index gives more weight to rare species, while the Simpsons index gives more weight to abundant species. As such, the Shannon index reflects evenness in terms of species richness, and may not be as well suited for determining ecological diversity by itself (Strong 2016). When the index is equal, we can be assured they are equal in terms diversity, however, when values differ it is difficult to estimate how much more or less diverse one site is from another. 

Effective Number of Species or Hill Numbers account for this non-linearity. The theory hinges on this assertion, "When all abundances are equal, diversity is then proportional to the number of species." Hill numbers can be calculated and integrated into estimates of Shannon and Simpsons.

As cautioned by Ricotta and Feoli 2024, the decision to use Effective Number of Species vs Species Richness ultimately depends on your system and questions. In some cases, a non-linear assumption (richness) may be preferred to a linear assumption (effective number of species) and studies should understand the limitations of either. In all cases, interpreting results in the context of their richness, evenness, and composition can lead to better management decisions and scientific conclusions. 


Further Reading:

Simpson Diversity SIMPSON, E. Measurement of Diversity. Nature 163, 688 (1949). https://doi.org/10.1038/163688a0
Jost 2006 Entropy and Diversity - https://nsojournals.onlinelibrary.wiley.com/doi/abs/10.1111/j.2006.0030-1299.14714.x
Opinion from Jost on diversity indices: http://www.loujost.com/Statistics%20and%20Physics/Diversity%20and%20Similarity/EffectiveNumberOfSpecies.htm
Jost 2007 PARTITIONING DIVERSITY INTO INDEPENDENT ALPHA AND BETA COMPONENTS https://esajournals.onlinelibrary.wiley.com/doi/abs/10.1890/06-1736.1
Strong 2016 on biases in Shannon-Weiner https://www.sciencedirect.com/science/article/abs/pii/S1470160X16301479
Ricotta and Feoli 2024 on critique of Hill Numbers https://www.sciencedirect.com/science/article/pii/S1470160X2400428X#b0040
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