Including Distorted Specimens in Allometric Studies: Linear Mixed Models Account for Deformation

Area of Science:

• Paleontology
• Evolutionary Biology
• Biometrics

Background:

• Allometry, the study of relative growth, is crucial for understanding evolutionary constraints and ontogenetic patterns.
• Fossilization often deforms specimens, complicating accurate allometric reconstructions.
• Traditional methods like OLS regression struggle with datasets containing both distorted and undistorted fossil measurements.

Purpose of the Study:

• To evaluate the efficacy of generalized linear mixed models (GLMMs) for reconstructing allometry in datasets with fossil specimens.
• To compare GLMM performance against traditional OLS regression when dealing with post-burial deformation.
• To provide a more robust method for analyzing allometric patterns in extinct taxa.

Main Methods:

• A simulation study based on the extinct cynodont *Exaeretodon argentinus* was conducted.
• Generalized linear mixed models (GLMMs) were employed to analyze allometric data, accounting for additional sources of variation.
• The GLMM approach was applied to empirical datasets of *E. argentinus* cranial measurements and *Tawa hallae* femoral measurements.

Main Results:

• GLMMs provided more accurate allometric estimates using full datasets (including distorted specimens) compared to using only undistorted data.
• GLMMs demonstrated superior performance over OLS regression in reconstructing allometry from datasets containing fossil specimens.
• The study confirmed that GLMMs can effectively handle variation introduced by fossilization-induced deformation.

Conclusions:

• Generalized linear mixed models (GLMMs) are a more reliable method for reconstructing allometry in paleontological datasets, especially those with deformed specimens.
• The adoption of GLMMs should become standard protocol for analyzing allometry in fossil taxa.
• This approach enhances the study of evolutionary patterns and ontogenetic growth in extinct organisms.