Mahalanobis Distance Classifier for Ecological Niche Modeling

A custom caret model specification implementing a Mahalanobis distance-based classifier for ecological niche modeling (ENM) and species distribution modeling (SDM). This implementation supports both parametric (chi-squared) and nonparametric (empirical cumulative distribution function; ECDF) transformations of Mahalanobis distances into suitability scores.

Usage

mahal.dist

Format

An object of class list of length 12.

Details

The model is trained using presence-only data to estimate the centroid and covariance structure of environmental conditions associated with species occurrences. Suitability is then derived as the inverse tail probability of the Mahalanobis distance between new observations and the estimated niche centroid.

Two approaches are available to transform Mahalanobis distances into probabilities:

• "chisq": assumes distances follow a chi-squared distribution with degrees of freedom equal to the number of predictors.

• "ecdf": uses the empirical cumulative distribution function of training distances, providing a nonparametric estimate of suitability.

The ECDF-based approach is particularly useful when the assumption of multivariate normality is violated, which is common in ecological data.

This model can be used within the caret::train() framework, enabling resampling, tuning, and ensemble modeling workflows for ecological niche modeling.

Model Parameters

abs

Logical. If TRUE, predictions are binarized using a fixed threshold (default: 0.05). If FALSE, the class with the highest predicted probability is returned.

method

Character. Method used to convert Mahalanobis distances into suitability values. Options are "chisq" or "ecdf".

Details

The Mahalanobis distance defines an ellipsoidal niche in environmental space. Under the chi-squared formulation, suitability decreases as the distance from the niche centroid increases. The ECDF formulation relaxes distributional assumptions by estimating suitability directly from the empirical distribution of distances observed in presence data.

Predictions return class probabilities for "presence" and "pseudoabsence", allowing flexible thresholding and ensemble integration.

Usage in caret

This object can be supplied to caret::train() as a custom model:

library(caret)

model <- train(
  x = predictors,
  y = response,
  method = mahal.dist,
  trControl = trainControl(classProbs = TRUE)
)

You can also run only ECDF by adjusting the tuning grid:

library(caret)

grid <- expand.grid(
  abs = c(TRUE, FALSE),
  method = "ecdf"
)

model <- train(
  x = predictors,
  y = response,
  method = mahal.dist,
  tuneGrid = grid,
  trControl = trainControl(classProbs = TRUE)
)

See also

mahalanobis, ecdf, train