calcDiv {chemodiv}

Calculate various diversity measures

Description

Function to calculate different common measures of diversity, and components (richness, evenness, disparity) thereof. Types of measures that can be calculated includes Hill diversity, Functional Hill diversity, Mean Pairwise Dissimilarity (MPD), Shannon's diversity, Simpson diversity, Rao's Q, Pielou's evenness and Hill evenness.

Usage

calcDiv(sampleData, compDisMat = NULL, type = "HillDiv", q = 1)

Arguments

sampleData

Data frame with the relative concentration of each compound (column) in every sample (row).

compDisMat

Compound dissimilarity matrix, as calculated by compDis. Has to be supplied for calculations of Functional Hill Diversity and Rao's Q.

type

Type(s) of diversity or component(s) thereof to calculate. Any of "Shannon", "Simpson", "HillDiv", "FuncHillDiv", "MPD", "RaoQ", "PielouEven", "HillEven".

q

Diversity order to use for Hill diversity, Functional Hill Diversity and Hill Evenness. q should be equal to or larger than zero. This parameter determines the sensitivity of the (Functional) Hill Diversity measure to the relative frequencies of compounds. Commonly set to 0, 1 or 2, although any value > 0 may be used. For q = 0 compound proportions are not taken into account. For q = 1 (default) compounds are weighed according to their proportion in the sample. For q = 2, more weight is put on compounds with high proportions.

Details

The function calculates diversity and/or components thereof for each sample in sampleData. It can calculate the following indices:

• Shannon. Shannon's Diversity.

• Simpson. Simpson Diversity, often referred to as the Inverse Simpson Index.

• HillDiv. Hill Diversity. Equation 4a/4b in Chao et al. 2014. Also referred to as the Hill number or the effective number of species (here compounds). The parameter q determines the sensitivity of the measure to the relative frequencies of compounds (see above for details). For q = 0, this equals the number of compounds in a sample, i.e. the richness. For q = 1, this equals the exponential of Shannon's Diversity. For q = 2, this equals the Simpson Diversity.

• FuncHillDiv. Functional Hill Diversity. There are different versions of this. Here, the most common version is calculated. This is the FD(Q), called "total functional diversity", calculated in equation 4b/6b in Chiu & Chao 2014. This measure quantifies the effective total dissimilarity between compounds in the sample. Calculation of Functional Hill Diversity requires a compound dissimilarity matrix. The parameter q determines the sensitivity of the measure to the relative frequencies of compounds (see above for details). For q = 1, this is a measure sensitive to compound richness, evenness and dissimilarity, and is therefore the most comprehensive measure of diversity. For q = 0, this is equal to Functional Attribute Diversity (FAD) which is the sum of all dissimilarities in the dissimilarity matrix.

• MPD. Mean Pairwise Dissimilarity. As the name suggests, this is equal to the mean of the pairwise dissimilarities in the compound dissimilarity matrix (excluding the 0 values in the diagonal). Therefore, in contrast to FAD (see above) this measure is not dependent on the number of compounds, and hence represents the disparity component of diversity. Practically, MPD is calculated as Functional Hill Diversity at q = 0, divided by n(n-1), where n is the number of compounds, i.e. Hill Diversity at q = 0.

• RaoQ. Rao's quadratic entropy index Q. The perhaps most common measure of functional diversity. Requires a compound dissimilarity matrix. Rao's Q represents the average dissimilarity of two randomly selected (weighed by their proportions) compounds in the sample.

• PielouEven. Pielou's Evenness, also referred to as Shannon's equitability. This is perhaps the most common evenness measure. Equal to the Shannon's Diversity divided by the natural logarithm of the number of compounds. In other words, it expresses evenness with the observed Shannon's diversity as a proportion of the maximum Shannon's diversity where all compounds are equally abundant. Therefore, this is a relative measure with a minimum value of 0 and a maximum value of 1. This measure of evenness is not replication invariant.

• HillEven. Hill Evenness, as defined by equation 8 in Tuomisto 2012. This is equal to the Hill Diversity, at a given value of q, divided by the number of compounds, and therefore has a minimum value of 1 / number of compounds and maximum value of 1. This measure of evenness is replication invariant. This measure can be normalized to range from 0 to 1 (equation 13 in Tuomisto 2012).

Value

Data frame with calculated diversity values for each sample.

References

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: 297-324.

Chiu C-H, Chao A. 2014. Distance-Based Functional Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers. PLoS ONE 9: e100014.

Hill MO. 1973. Diversity and Evenness: A Unifying Notation and Its Consequences. Ecology 54: 427-432.

Petren H, Koellner TG, Junker RR. 2023. Quantifying chemodiversity considering biochemical and structural properties of compounds with the R package chemodiv. New Phytologist 237: 2478-2492.

Petren H, Anaia RA, Aragam KS, Braeutigam A, Eckert S, Heinen R, Jakobs R, Ojeda L, Popp M, Sasidharan R, Schnitzler J-P, Steppuhn A, Thon F, Tschikin S, Unsicker SB, van Dam NM, Weisser WW, Wittmann MJ, Yepes S, Ziaja D, Meuller C, Junker RR. 2023. Understanding the phytochemical diversity of plants: Quantification, variation and ecological function. bioRxiv doi: 10.1101/2023.03.23.533415.

Tuomisto H. 2012. An updated consumer's guide to evenness and related indices. Oikos 121: 1203-1218

Examples

data(minimalSampData)
data(minimalCompDis)
calcDiv(sampleData = minimalSampData)
calcDiv(sampleData = minimalSampData, type = c("HillDiv", "HillEven"))
calcDiv(sampleData = minimalSampData, compDisMat = minimalCompDis,
type = "FuncHillDiv", q = 2)

data(alpinaSampData)
data(alpinaCompDis)
calcDiv(sampleData = alpinaSampData, compDisMat = alpinaCompDis,
type = "FuncHillDiv")