Distinguishing within- from between-individual effects: How to use the within-individual centring method for...

Area of Science:

• Ecology
• Evolutionary Biology
• Quantitative Biology

Background:

• Population-level patterns can obscure individual-level processes.
• Distinguishing between within- and among-individual processes is vital for ecological and evolutionary dynamics.
• The within-individual centering method is established for analyzing linear and quadratic patterns.

Purpose of the Study:

• To highlight two alternative equations for investigating quadratic within-individual patterns.
• To explain the distinct assumptions and constraints of these equations.
• To guide researchers in selecting the appropriate equation for their specific biological context.

Main Methods:

• Comparative analysis of two equations for quadratic within-individual patterns.
• Literature review on the application of these equations in ecological studies.
• Simulation studies to assess the impact of equation choice on inference.

Main Results:

• One equation has been predominantly used, but may not always be appropriate.
• The two equations differ in their assumptions regarding absolute versus relative individual processes.
• Incorrect equation selection can lead to biased estimates and flawed model selection.

Conclusions:

• The choice of equation for quadratic within-individual patterns depends on the underlying biological process.
• Careful selection of the analysis equation is essential to avoid flawed inference.
• Guidelines are provided to aid researchers in choosing the appropriate equation for nonlinear relationship analysis.