MFK: Calculate Composite Multifunctionality Index (MFK)

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

Calculate Composite Multifunctionality Index (MFK)

Description

Calculates a composite multifunctionality index based on the K index approach (Wojcik 2024), integrating three facets of multifunctionality: richness (MFric), regularity (MFreg), and divergence (MFdiv) using their geometric mean.

Usage

MFK(data, weights = NULL)

Arguments

data	A data frame or matrix where rows represent observations and columns represent ecosystem functions. Function values should be normalized to a common scale (e.g., 0-1).
weights	A numeric vector of weights for each function (column). If NULL, equal weights are assigned to all functions. Default is NULL.

Details

The composite index MFK is calculated as the geometric mean of three facets:

MFK = \sqrt[3]{MFric \times MFreg \times MFdiv}

This approach follows the K index methodology (Wojcik 2024), where the geometric mean combines multiple facets of diversity into a single integrated measure. The three facets represent:

• MFric: Multifunctionality richness

• MFreg: Multifunctionality regularity

• MFdiv: Multifunctionality divergence

Value

A data frame containing:

• MFric: Multifunctionality richness values

• MFreg: Multifunctionality regularity values

• MFdiv: Multifunctionality divergence values

• MFK: Composite multifunctionality index values

References

Wojcik, L. A., Gaedke, U., van Velzen, E., & Klauschies, T. (2025). Measuring overall functional diversity by aggregating its multiple facets: Functional richness, biomass evenness, trait evenness and dispersion. Methods in Ecology and Evolution, 16, 215–227.

See Also

MFric, MFreg, MFdiv

Examples

# Example with sample data
data <- data.frame(
  func1 = c(0.5, 0.3, 0.2),
  func2 = c(0.2, 0.4, 0.4),
  func3 = c(0.3, 0.3, 0.4)
)
rownames(data) <- c("Site1", "Site2", "Site3")

# Calculate MFK with equal weights
MFK(data)

# Calculate MFK with custom weights (emphasizing func2)
MFK(data, weights = c(1, 2, 1))

emf documentation built on Jan. 8, 2026, 5:10 p.m.