Species diversity

Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant). Species diversity consists of three components: species richness, taxonomic or phylogenetic diversity and species evenness. Species richness is a simple count of species, taxonomic or phylogenetic diversity is the genetic relationship between different groups of species,whereas species evenness quantifies how equal the abundances of the species are. Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant). Species diversity consists of three components: species richness, taxonomic or phylogenetic diversity and species evenness. Species richness is a simple count of species, taxonomic or phylogenetic diversity is the genetic relationship between different groups of species,whereas species evenness quantifies how equal the abundances of the species are. Species diversity in a dataset can be calculated by first taking the weighted average of species proportional abundances in the dataset, and then taking the inverse of this. The equation is: The denominator equals mean proportional species abundance in the dataset as calculated with the weighted generalized mean with exponent q - 1. In the equation, S is the total number of species (species richness) in the dataset, and the proportional abundance of the ith species is p i {displaystyle p_{i}} . The proportional abundances themselves are used as weights.The equation is often written in the equivalent form: The value of q defines which kind of mean is used. q = 0 corresponds to the weighted harmonic mean, which is 1/S because the p i {displaystyle p_{i}} values cancel out. q = 1 is undefined, except that the limit as q approaches 1 is well defined: q = 2 corresponds to the arithmetic mean. As q approaches infinity, the generalized mean approaches the maximum p i {displaystyle p_{i}} value. In practice, q modifies species weighting, such that increasing q increases the weight given to the most abundant species, and fewer equally abundant species are hence needed to reach mean proportional abundance. Consequently, large values of q lead to smaller species diversity than small values of q for the same dataset. If all species are equally abundant in the dataset, changing the value of q has no effect, but species diversity at any value of q equals species richness. Negative values of q are not used, because then the effective number of species (diversity) would exceed the actual number of species (richness). As q approaches negative infinity, the generalized mean approaches the minimum p i {displaystyle p_{i}} value. In many real datasets, the least abundant species is represented by a single individual, and then the effective number of species would equal the number of individuals in the dataset. The same equation can be used to calculate the diversity in relation to any classification, not only species. If the individuals are classified into genera or functional types, p i {displaystyle p_{i}} represents the proportional abundance of the ith genus or functional type, and qD equals genus diversity or functional type diversity, respectively. Often researchers have used the values given by one or more diversity indices to quantify species diversity. Such indices include species richness, the Shannon index, the Simpson index, and the complement of the Simpson index (also known as the Gini-Simpson index). When interpreted in ecological terms, each one of these indices corresponds to a different thing, and their values are therefore not directly comparable. Species richness quantifies the actual rather than effective number of species. The Shannon index equals log(qD), and in practice quantifies the uncertainty in the species identity of an individual that is taken at random from the dataset. The Simpson index equals 1/qD and quantifies the probability that two individuals taken at random from the dataset (with replacement of the first individual before taking the second) represent the same species. The Gini-Simpson index equals 1 - 1/qD and quantifies the probability that the two randomly taken individuals represent different species.