FunRed

R package for computing functional redundancy and functional interdependency measures for a single trait using relative entropy.

Relative Entropy is calculated using the KL function of the philentropy package with the following parameters: test.na = TRUE (to handle missing values), unit = "log" (to compute divergence using the natural logarithm), est.prob = NULL (indicating that empirical probabilities were used), and epsilon = 1e-05 (a value to address cases when division by zero occurs).

Installation

You can install this package from GitHub using the devtools package:

# Install required dependencies first
install.packages("philentropy")

# Install devtools if not already installed
if (!requireNamespace("devtools", quietly = TRUE)) {
  install.packages("devtools")
}

# Install FunRed package from GitHub
devtools::install_github("SysPsyHertel/FunRed")

Functions

1. fredundancy(functions, abundance, n_reference)

Compute measures of functional redundancy and functional interdependency.

Arguments

• abundance: A vector of abundances representing each species in the community. The vector is checked to ensure the abundances sum to 1. If they do not, the vector is normalized, provided the sum is within an acceptable tolerance (|1 - sum(abundances)| < 1e-5). If the sum falls outside this tolerance, an error message is returned. Note that the vector can also have zero values, although absolute continuity must hold (from a non abundant species that species cannot have any function).
• functions: The paired vector of functions of the abundance vector. Needs to be the same length as the abundance vector. Gets transformed into relative frequencies.
• n_reference: Integer value, corresponding to the number of species in the reference that can perform the function (optional).

Returns

• sample_based: A coefficient corresponding to taxon sample-based functional redundancy.
• reference_based: A coefficient corresponding to taxon reference-based functional (optional, if n_reference is set).
• abundance_based: A coefficient corresponding to abundance-based functional redundancy.
• interdependency: A coefficient corresponding to functional interdependency.

Example Usage

# Assuming 'functions' and 'abundance' are defined:
result <- fredundancy(functions, abundance, n_reference = 7)

Toy Example and description

Below is a toy example to demonstrate how the fredundancy function works.

functions <- c(0.8, 0.1, 0.05, 0.05, 0)
abundance <- c(0.2, 0.1, 0.05, 0.05, 0.6)
n_reference <- 7

result <- fredundancy(functions, abundance, n_reference)
print(result)

Output:

$sample_based
[1] -0.9010913

$reference_based
[1] -1.237564

$abundance_based
[1] -1.109035

$interdependency
[1] 0.1927448

Description

Note that, except when computing functional interdependency, the Kullback-Leibler divergence is negated in all calculations.

• To compute sample taxon-based functional redundancy, we calculate the Kullback-Leibler divergence between the function vector and a uniformly distributed vector of the same length as the number of species in a sample, i.e. the number of nonzero elements in the abundance vector.
  In the toy example, we compute the Kullback-Leibler divergence for sample taxon-based redundancy between (0.8, 0.1, 0.05, 0.05, 0) and (1/5, 1/5, 1/5, 1/5, 1/5).
• For the calculation of reference taxon-based functional redundancy, the parameter n_reference corresponds to the total number of species in the reference that can perform the function. The nonzero values in the function vector remain unchanged, while zeros are added until its total length equals n_reference. Then, the Kullback-Leibler divergence is computed between this padded vector and a uniform distribution of the same length as n_reference.
  In the toy example, we compute the Kullback-Leibler divergence for sample taxon-based redundancy between (0.8, 0.1, 0.05, 0.05, 0, 0 ,0) and (1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7).
• To compute abundance-based functional redundancy, we calculate the Kullback-Leibler divergence between the function vector and the abundance vector.
  In the toy example, we compute the Kullback-Leibler divergence for abundance-based redundancy between (0.8, 0.1, 0.05, 0.05, 0) and (0.2, 0.1, 0.05, 0.05, 0.6).
• For the computation of functional interdependency only non-zero values of the function vector are considered. For the abundance vector, only the abundances of species that have non-zero function are considered. The abundance vector is then divided by the sum of the restricted vector, such that its components sum up to 1. In the toy example, we compute the Kullback-Leibler divergence for sample functional interdependency between (0.8, 0.1, 0.05, 0.05) and (0.2, 0.1, 0.05, 0.05)/(0.2+0.1+0.05+0.05).