MFdiv: Calculate Multifunctionality Divergence (MFdiv)

In emf: Ecosystem Multifunctionality: Richness, Divergence, and Regularity

Calculate Multifunctionality Divergence (MFdiv)

Description

Multifunctionality divergence (MFdiv) was calculated to quantify the degree of difference between different functions of an ecosystem. MFdiv was calculated by the mean pairwise distance method.

Usage

MFdiv(data, weights = NULL, cor = FALSE)

Arguments

data	A data frame or matrix where rows represent observations and columns represent functions.
weights	A numeric vector of weights for each function (column). If NULL, equal weights are assigned.
cor	Logical. If TRUE, calculates MFdiv with redundancy correction based on correlation between functions. If FALSE, calculates uncorrected MFdiv.

Details

To measure MFdiv quantitatively, we employ the mean pairwise distance method (Webb et al., 2002).

For uncorrected MFdiv, the formula is:

MFdiv = \frac{\sum_{i=1}^{n}\sum_{j=i+1}^{n}{w_i w_j D_{ij}}}{\sum_{i=1}^{n}\sum_{j=i+1}^{n}{w_i w_j}}

where D_{ij} = |f_i - f_j|

When redundancy correction is applied ('cor = TRUE'), the function accounts for correlations between ecosystem functions. The correction process involves:

1. Calculating a distance matrix based on correlations: d_{ij} = \sqrt{1 - |r_{ij}|}

2. Applying threshold-based correction: d_{ij}(\tau) = \min(d_{ij}, \tau)

3. Computing effective function values: F_i(\tau) = \sum_{j=1}^{L}(1 - \frac{d_{ij}(\tau)}{\tau})f_j

4. Calculating the corrected MFdiv using these effective function values:

D_{ij}(\tau) = |F_i - F_j|

MFdiv = \frac{\sum_{i=1}^{n}\sum_{j=i+1}^{n}{w_i w_j D_{ij}(\tau)}}{\sum_{i=1}^{n}\sum_{j=i+1}^{n}{w_i w_j}}

5. The final result is the area under the curve (AUC) of MFdiv values across different tau thresholds.

Value

A data frame with MFdiv values for each observation (row) in the input data.

Examples

data(forestfunctions)
head(forestfunctions)
MFdiv(forestfunctions[,6:31], cor = FALSE)

emf documentation built on June 8, 2025, 1:26 p.m.