MFric: Calculate Multifunctionality Richness (MFric)

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

Calculate Multifunctionality Richness (MFric)

Description

This function calculates the Multifunctionality Richness (MFric) for each row in a dataset. MFric represents the average level of multiple ecosystem function indicators, reflecting the overall performance of an ecosystem across various functional metrics.

Usage

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

Arguments

data	A numeric data frame or matrix where rows represent observations (e.g., sites, plots) and columns represent different ecosystem functions.
weights	A numeric vector of weights for each function (column) in the data. If NULL (default), equal weights of 1 are assigned to all functions.
cor	Logical. If FALSE (default), calculates uncorrected MFric. If TRUE, calculates correlation-corrected MFric accounting for redundancy among functions.

Details

The uncorrected MFric is calculated as:

MFric = \frac{\sum_{i=1}^{n} w_i f_i}{\sum_{i=1}^{n} w_i}

where fi represents the normalized performance level of function i, and wi denotes the weight assigned to function i.

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 MFric using these effective function values:

MFric = \frac{\sum_{i=1}^{n} w_i F_i}{\sum_{i=1}^{n} w_i}

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

Value

A data frame with a single column named "MFric" containing the calculated Multifunctionality Richness values for each row in the input data. Row names are preserved from the input data if available.

Examples

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

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