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Mahalanobis distances and ecological niche modelling: correcting a chi-squared probability error.

Thomas R Etherington¹

¹Manaaki Whenua-Landcare Research, Lincoln, New Zealand.

|April 12, 2019

Summary

This study corrects an error in using Mahalanobis distance for ecological modeling. It demonstrates the correct method for calculating probabilities, improving species distribution and habitat suitability models.

Keywords:

Chi-squared distribution Ecological niche modelling Habitat suitability modelling Mahalanobis distance Multivarite normal distribution Presence-only Probability Resource selection functions Species distribution modelling Virtual ecology

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Area of Science:

Ecology
Statistics
Ecological Modeling

Background:

Mahalanobis distance is used in ecology to model species distributions and habitat suitability.
An error in converting Mahalanobis distances to probabilities using chi-squared distribution exists in the literature and software.
This error can impact the accuracy of ecological models.

Purpose of the Study:

To correct a long-standing error in the application of Mahalanobis distance for ecological modeling.
To provide a clear explanation of Mahalanobis distance calculation and probability conversion.
To demonstrate the correct application through a virtual ecology experiment.

Main Methods:

Explanation of Mahalanobis distance calculation.
Demonstration of correct probability conversion using a virtual ecology experiment.
Discussion of the implications of the error on previous studies.

Main Results:

The study identifies and corrects an error in Mahalanobis distance probability calculation.
A virtual experiment validates the corrected method for ecological applications.
Previous ecological models using the erroneous method may require re-evaluation.

Conclusions:

Accurate Mahalanobis distance probability calculation is crucial for reliable ecological modeling.
The corrected methodology enhances the utility of Mahalanobis distance for niche and distribution modeling.
This work aims to improve the application of Mahalanobis distance in ecological research.