adiv_functions: Alpha Diversity Metrics

In ecodive: Parallel and Memory-Efficient Ecological Diversity Metrics

Alpha Diversity Metrics

Description

Alpha Diversity Metrics

Usage

ace(counts, cutoff = 10L, margin = 1L, cpus = n_cpus())

berger(counts, norm = "percent", margin = 1L, cpus = n_cpus())

brillouin(counts, margin = 1L, cpus = n_cpus())

chao1(counts, margin = 1L, cpus = n_cpus())

faith(counts, tree = NULL, margin = 1L, cpus = n_cpus())

fisher(counts, digits = 3L, margin = 1L, cpus = n_cpus())

inv_simpson(counts, norm = "percent", margin = 1L, cpus = n_cpus())

margalef(counts, margin = 1L, cpus = n_cpus())

mcintosh(counts, margin = 1L, cpus = n_cpus())

menhinick(counts, margin = 1L, cpus = n_cpus())

observed(counts, margin = 1L, cpus = n_cpus())

shannon(counts, norm = "percent", margin = 1L, cpus = n_cpus())

simpson(counts, norm = "percent", margin = 1L, cpus = n_cpus())

squares(counts, margin = 1L, cpus = n_cpus())

Arguments

counts	A numeric matrix of count data where each column is a feature, and each row is a sample. Any object coercible with as.matrix() can be given here, as well as phyloseq, rbiom, SummarizedExperiment, and TreeSummarizedExperiment objects. For optimal performance with very large datasets, see the guide in vignette('performance').
cutoff	The maximum number of observations to consider "rare". Default: 10.
margin	If your samples are in the matrix's rows, set to 1L. If your samples are in columns, set to 2L. Ignored when counts is a phyloseq, rbiom, SummarizedExperiment, or TreeSummarizedExperiment object. Default: 1L
cpus	How many parallel processing threads should be used. The default, n_cpus(), will use all logical CPU cores.
norm	Normalize the incoming counts. Options are: norm = "percent" - Relative abundance (sample abundances sum to 1). norm = "binary" - Unweighted presence/absence (each count is either 0 or 1). norm = "clr" - Centered log ratio. norm = "none" - No transformation. Default: 'percent', which is the expected input for these formulas.
tree	A phylo-class object representing the phylogenetic tree for the OTUs in counts. The OTU identifiers given by colnames(counts) must be present in tree. Can be omitted if a tree is embedded with the counts object or as attr(counts, 'tree').
digits	Precision of the returned values, in number of decimal places. E.g. the default digits=3 could return 6.392.

Value

A numeric vector.

Formulas

Prerequisite: all counts are whole numbers.

Given:

• n : The number of features (e.g. species, OTUs, ASVs, etc).

• X_i : Integer count of the i-th feature.

• X_T : Total of all counts (i.e. sequencing depth). X_T = \sum_{i=1}^{n} X_i

• P_i : Proportional abundance of the i-th feature. P_i = X_i / X_T

• F_1 : Number of features where X_i = 1 (i.e. singletons).

• F_2 : Number of features where X_i = 2 (i.e. doubletons).

Abundance-based Coverage Estimator (ACE) ace()	See below.
Berger-Parker Index berger()	\max(P_i)
Brillouin Index brillouin()	\displaystyle \frac{\ln{[(\sum_{i = 1}^{n} X_i)!]} - \sum_{i = 1}^{n} \ln{(X_i!)}}{\sum_{i = 1}^{n} X_i}
Chao1 chao1()	\displaystyle n + \frac{(F_1)^2}{2 F_2}
Faith's Phylogenetic Diversity faith()	See below.
Fisher's Alpha (\alpha) fisher()	\displaystyle \frac{n}{\alpha} = \ln{\left(1 + \frac{X_T}{\alpha}\right)} The value of \alpha must be solved for iteratively.
Gini-Simpson Index simpson()	1 - \sum_{i = 1}^{n} P_i^2
Inverse Simpson Index inv_simpson()	1 / \sum_{i = 1}^{n} P_i^2
Margalef's Richness Index margalef()	\displaystyle \frac{n - 1}{\ln{X_T}}
McIntosh Index mcintosh()	\displaystyle \frac{X_T - \sqrt{\sum_{i = 1}^{n} (X_i)^2}}{X_T - \sqrt{X_T}}
Menhinick's Richness Index menhinick()	\displaystyle \frac{n}{\sqrt{X_T}}
Observed Features observed()	n
Shannon Diversity Index shannon()	-\sum_{i = 1}^{n} P_i \times \ln(P_i)
Squares Richness Estimator squares()	\displaystyle n + \frac{(F_1)^2 \sum_{i=1}^{n} (X_i)^2}{X_T^2 - nF_1}

Abundance-based Coverage Estimator (ACE)

Given:

• n : The number of features (e.g. species, OTUs, ASVs, etc).

• r : Rare cutoff. Features with \le r counts are considered rare.

• X_i : Integer count of the i-th feature.

• F_i : Number of features with exactly i counts.

• F_1 : Number of features where X_i = 1 (i.e. singletons).

• F_{rare} : Number of rare features where X_i \le r.

• F_{abund} : Number of abundant features where X_i > r.

• X_{rare} : Total counts belonging to rare features.

• C_{ace} : The sample abundance coverage estimator, defined below.

• \gamma_{ace}^2 : The estimated coefficient of variation, defined below.

• D_{ace} : Estimated number of features in the sample.

\displaystyle C_{ace} = 1 - \frac{F_1}{X_{rare}}

\displaystyle \gamma_{ace}^2 = \max\left[\frac{F_{rare} \sum_{i=1}^{r}i(i-1)F_i}{C_{ace}X_{rare}(X_{rare} - 1)} - 1, 0\right]

\displaystyle D_{ace} = F_{abund} + \frac{F_{rare}}{C_{ace}} + \frac{F_1}{C_{ace}}\gamma_{ace}^2

Faith's Phylogenetic Diversity (Faith's PD)

Given n branches with lengths L and a sample's abundances A on each of those branches coded as 1 for present or 0 for absent:

\sum_{i = 1}^{n} L_i A_i

Examples

    # Example counts matrix
    t(ex_counts)
    
    ace(ex_counts)
    
    chao1(ex_counts)
    
    squares(ex_counts)
    

ecodive documentation built on Jan. 16, 2026, 5:11 p.m.