abundance_jaccard: Chao's abundance-weighted indices

In kylebittinger/abdiv: Alpha and Beta Diversity Measures

Chao's abundance-weighted indices

Description

These indices were first developed and introduced as probabilistic, abundance-weighted versions of the Jaccard and Sorenson indices. The abundance information is summarized by two quantities, named U and V in the literature. Each quantity indicates the total abundance of species that are common to both samples: U is the total abundance of such species in the first sample, and V the total in the second sample.

Usage

abundance_jaccard(x, y)

abundance_sorenson(x, y)

Arguments

x, y	Numeric vectors

Details

In addition to defining the quantities U and V, the articles provide formulas for estimating the value U and V if more sampling was to be performed. In other software packages where these indices are implemented, it is the estimated quantities, U_{est} and V_{est} that are used to calculate the distance. For example, the chaodist function in Vegan uses the estimators. In this package, we use the observed values of U and V, rather than the estimated values. Thus, the distances returned here may differ from other software packages that use the estimators rather than the observed values of U and V. In general, the estimators increase U and V, resulting in greater estimated abundance of shared species and thus a smaller distance between samples.

The abundance-weighted Jaccard distance is 1 - UV / (U + V - UV). Relation of abundance_jaccard() to other definitions:

• Differs vegdist() with method = "chao". We use the observed values, not the estimators.

• Differs from the jabund calculator in Mothur. We use the observed values, not the estimators.

The abundance-weighted Sorenson distance is 1 - 2UV / (U + V). Relation of abundance_sorenson() to other definitions:

• Differs from the sabund calculator in Mothur. We use the observed values, not the estimators.

Value

The dissimilarity between x and y

References

Chao A, Chazdon RL, Colwell R, Shen TJ. A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecology Letters 2005;8:148-159.

Examples

x <- c(5, 2, 3) # u = 0.5
y <- c(0, 5, 5) # v = 1
abundance_jaccard(x, y) # should be 1 - 0.5 / (1 + 0.5 - 0.5) = 0.5
abundance_sorenson(x, y) # should be 1 - 2 * 0.5 / (1 + 0.5) = 0.3333

kylebittinger/abdiv documentation built on Nov. 22, 2023, 8:16 p.m.