Quantifying individual variation in reaction norms: Mind the residual

Area of Science:

• Ecology and Evolution
• Quantitative Genetics
• Behavioral Ecology

Background:

• Phenotypic plasticity, the ability of an organism to change its phenotype in response to environmental changes, is a key concept in ecology and evolution.
• Individual-by-environment (I × E) interactions quantify variation in plasticity among individuals, influencing population adaptation.
• Random regression models (RRMs) are widely used to study I × E, but results are inconsistent, potentially due to unaddressed heterogeneity in residual variance (heteroscedasticity).

Purpose of the Study:

• To investigate the impact of residual variance structures on the estimation of I × E interactions using RRMs.
• To evaluate how heteroscedasticity, plasticity levels, sample size, and environmental variability affect RRM performance.
• To provide guidelines for selecting appropriate residual variance structures in RRM analyses.

Main Methods:

• Simulated data with varying degrees of heteroscedasticity, plasticity, sample size, and environmental variability were analyzed using RRMs with different residual variance structures.
• Model comparison using information criteria was employed to select the best-fitting residual structure.
• Real data from two populations of great tits (Parus major) were analyzed to validate the findings.

Main Results:

• The choice of residual variance structure in RRMs significantly influenced the precision of I × E estimates and statistical power.
• Substantial lack of precision and high false-positive rates were observed when sample size, environmental variability, and plasticity were low.
• Model comparison effectively identified appropriate residual structures, as demonstrated by analyses of simulated and real data.

Conclusions:

• Ignoring heteroscedasticity in RRMs can lead to biased estimates of I × E interactions and reduced statistical power.
• Using information criteria for model selection helps in choosing appropriate residual variance structures, improving the reliability of plasticity studies.
• Standardizing RRM methodology by addressing residual variance is essential for reducing bias and advancing our understanding of phenotypic plasticity in evolutionary biology.