Independent contrasts and regression through the origin.

Area of Science:

• Phylogenetics
• Evolutionary Biology
• Statistical Modeling

Background:

• Phylogeneticists commonly use regression through the origin for analyzing comparative data with independent contrasts.
• The theoretical underpinnings and necessity of this method for such data have been re-examined.

Purpose of the Study:

• To revisit the rationale for using regression through the origin in phylogenetic comparative analysis.
• To develop and evaluate permutation tests for regression coefficients and coefficient of determination in this context.

Main Methods:

• Formulation of permutation tests for regression through the origin.
• Simulations under two data generation models (regression models I and II) to assess type I error and power.
• Investigation of two permutation strategies: permuting response variable (y) and permuting residuals.
• Application to two biological examples: fish parasite non-specificity and mammal parasite richness.

Main Results:

• Parametric and permutation tests are reliable for normally distributed errors, common in independent contrast studies.
• Permutation of the response variable (y) is recommended for highly asymmetric error distributions.
• Parametric tests are suitable when extreme values are present in covariables.

Conclusions:

• The study validates and extends statistical methods for phylogenetic comparative analysis.
• Provides guidance on selecting appropriate statistical tests based on error distribution and data characteristics.
• Demonstrates the utility of these methods with real-world biological data on host-parasite relationships.