The geometry of morphospaces: lessons from the classic Raup shell coiling model

Area of Science:

• Evolutionary biology
• Palaeontology
• Theoretical morphology

Background:

• Morphospaces visualize morphological variation but often lack metric properties like distance and direction.
• Raup's iconic morphospace for coiled shells, widely used for ammonoids, is not Euclidean, limiting interpretation of evolutionary patterns.
• Existing morphospaces vary in geometry, complicating comparisons and analyses of morphological differences.

Purpose of the Study:

• To address the limitations of non-Euclidean morphospaces, specifically Raup's model for coiled shells.
• To introduce and validate a landmark-based morphospace with metric properties for analyzing morphological disparity.
• To compare the properties and relationships of Raup's morphospace and the proposed landmark-based morphospace.

Main Methods:

• Development of a landmark-based morphospace using the same measurements as Raup's parameters.
• Simulations to compare the properties of different morphospaces.
• Reanalysis of Palaeozoic ammonoid shell disparity using both morphospace frameworks.

Main Results:

• Raup's morphospace, while useful for shell description, does not guarantee meaningful interpretation of taxon spread and spacing due to its non-Euclidean structure.
• The proposed landmark-based morphospace provides a geometrically sound framework for quantitative analyses of morphological patterns.
• The study highlights algebraic and geometric relationships between Raup's and the landmark-based morphospaces.

Conclusions:

• Quantitative analyses of morphological patterns, particularly shell disparity, should be conducted within the validated landmark-based morphospace.
• Raup's model remains valuable for describing shell coiling geometry but not for rigorous disparity analysis.
• Researchers using diverse morphospaces in evolutionary morphology must exercise caution when interpreting and comparing results.