Table 1.
Summary of fundamental, commonly used diversity measures. The variable q indicates the order of the corresponding Hill number qD as defined in equation (16).
| Measure | Interpretation | Application | Advantages | Disadvantages |
|---|---|---|---|---|
| Species number ni | Number of entities of type i | Evolutionary and population models | Straightforward interpretation in models | Keeping track of species identity may be unrealistic |
| Species abundance (clone count) ck. | Number of species of size k | Models of self-assembly/nucleation [52-54]; characterization of population in barcoding studies [55] | Directly related to richness, useful when clone identity is not important | No clone identity information, insensitive to exchange of populations between clones |
| Richness (0D) | Total number of distinguishable species | Conservation planning; assessment of ecosystems [3] | Straightforward mathematical definition and interpretation | Maximally affected by small sampling; all species are treated equally |
| Evenness (1D) | Uniformity of relative abundances of species in a population | Characterization of ecosystems and inequity in societies; Theil index [3, 168-170] | Straightforward mathematical definition and interpretation; similar to entropy | Affected by sampling |
| Simpson’s diversity (2D) | Probability that two randomly drawn entities are of the same species | Characterization of cell populations [147, 179] | Less affected by sampling | More intricate mathematical definition & Less interpretability |
| qD, q > 2 | N/A | Characterization of more frequent species in a population; Berger–Parker index [90] | Significantly less affected by sampling | No intuitive interpretation |
| Lorenz curve | Cumulative relative wealth | Economics, wealth distributions | Fundamental mathematical object | No identity information (like ordered clone counts) |
| Gini index | Deviation of Lorenz curves from absolute equality | Population-level wealth inequality | Easily understood | No identity information, Values are subjectively interpreted |
| Hoover/Robin Hood index | KS statistic between Lorenz curve and equality line | Population-level wealth inequality | Easily understood | No identity information, values are subjectively interpreted |