5:15 PM - 7:15 PM
[BPT04-P05] Assessment of morphological diversity of ammonoid shell form based on a Euclidian morphospace
Keywords:Euclidian morphospace, morphological diversity, ammonoids
Change in morphological diversity across Phanerozoic has been attracted attention as a clue for understanding mode of mass extinction and subsequent recovery as well as its relation to taxonomic diversity in the fossil records. The measure of morphological diversity has commonly been based on the amount of the morphospace occupied by a taxonomic group. The most widely applied morphospace is Raup’s (1966) theoretical morphospace constructed on the basis of parameters of a theoretical morphologic model. The Raup’s morphospace has been used for the analyses of morphological disparity of ammonoids (Villier and Korn, 2004; Simon et al., 2011; Korn et al., 2013). The Raup's morphospace is conventionally depicted as a Euclidian space in which a particular shell form is plotted with orthogonal axes representing the model parameters. However, Raup’s parameters, such as whorl expansion rate and relative width of umbilicus, are defined as ratios of two distance measures and are consequently not commensurable measures with a common unit. Therefore, the Raup’s morphospace lacks properties of Euclidian spaces and should be understood as an affine space in which distances in different directions are incommensurable (Budd, 2021; Contreas-Figueroa and Aragón, 2023). This means that Raup’s morphospace is not useful to assess morphological variation and diversity based on commensurable measures. In geometric morphometrics, the Euclidian distance between two sets of shape coordinates, an approximate value of Procrustes distance, can be used as a distance metrics in the shape space. Geometric morphomatrics is applicable to coiling geometry of ammonoids (Geber, 2008), and is potentially useful to represent ontogenetic variation in shell shape if a radial shell section of a completed adult specimen is available. However, specimens preserving the entire ontogenetic series of shell form without deformation are generally unavailable in ammonoids.
The present study introduces an analytical method for assessing morphological diversity of ammonoids based on Procrustes distances. It is based on a theoretical morphologic model which represents anisometric growth of ammonoid shell. The conch geometry is defined by the relationship among the amounts of increases of growth components such as spiral radius, spiral length and whorl radius each of which follows a logistic growth model. The parameters of the theoretical morphologic model are optimized using Bayesian inference. A hypothetical model of the radial cross section of the shell is generated to define landmarks on the section and to calculate their coordinates. Shape coordinates of the landmarks are computed through a generalized least-square superimposition and then Procrustes distances between pairs of the individuals are used to assess morphological diversity. This method requires to produce an idealized synthetic form of radial cross section of the species of interest through measurements of fossil specimens at various growth stages. The theoretical morphologic model of anisometric shell growth and inverse estimation of its parameter values allow us to carry out the procedures.
The present study introduces an analytical method for assessing morphological diversity of ammonoids based on Procrustes distances. It is based on a theoretical morphologic model which represents anisometric growth of ammonoid shell. The conch geometry is defined by the relationship among the amounts of increases of growth components such as spiral radius, spiral length and whorl radius each of which follows a logistic growth model. The parameters of the theoretical morphologic model are optimized using Bayesian inference. A hypothetical model of the radial cross section of the shell is generated to define landmarks on the section and to calculate their coordinates. Shape coordinates of the landmarks are computed through a generalized least-square superimposition and then Procrustes distances between pairs of the individuals are used to assess morphological diversity. This method requires to produce an idealized synthetic form of radial cross section of the species of interest through measurements of fossil specimens at various growth stages. The theoretical morphologic model of anisometric shell growth and inverse estimation of its parameter values allow us to carry out the procedures.