The Geometry of Macroevolution: Phenotypic Evolution on Non-Euclidean Manifolds.

Area of Science:

• Evolutionary biology
• Macroevolutionary studies
• Quantitative genetics

Background:

• Phylogenetic comparative methods commonly assume phenotypes evolve in Euclidean space.
• This assumption may be biologically unrealistic due to developmental and genetic constraints.
• Curved, non-Euclidean geometries are proposed as a more accurate model for phenotypic evolution.

Purpose of the Study:

• To advocate for the explicit consideration of the 'geometry of macroevolution'.
• To demonstrate how Euclidean metrics can artifactually underestimate evolutionary divergence on curved manifolds.
• To offer a novel explanation for observed patterns like age-rate scaling.

Main Methods:

• Theoretical modeling of evolutionary paths on curved manifolds.
• Demonstration of analytical artifacts caused by inappropriate metric assumptions.
• Discussion of data-driven manifold learning using phenomic datasets and machine learning.

Main Results:

• Euclidean metrics systematically underestimate path lengths on curved manifolds.
• Geometric distortion can create the appearance of declining evolutionary rates over time.
• This provides a complementary explanation for age-rate scaling patterns.

Conclusions:

• Explicitly characterizing the geometry of macroevolution is crucial for accurate inference.
• Moving beyond implicit geometric assumptions ensures macroevolutionary patterns reflect biological reality.
• Advances in data and machine learning facilitate empirical inference of evolutionary geometry.