5:15 PM - 6:45 PM
[BPT03-P03] Evolutionary conservativeness and variability of ontogenetic trajectories of conch geometry in ammonoids
Keywords:ammonoids, ontogenetic trajectories, heterochrony
In evolutionary biology, heterochrony, changes in the rate or timing of development, has been invoked to explain morphological differences between closely related species because it allows evolutionary changes in morphology without modification of growth pathway or ontogenetic trajectory. Heterochrony is commonly identified by comparing ontogenetic trajectories in age-shape space. However, age information is often unavailable for fossil specimens. Consequently, paleontologists tend to focus on the size of onset/offset of development of a morphological feature rather than growth trajectories of continuous characters. For example, ontogenetic variation in shell ornament commonly found in ammonoids is one of the popular targets for heterochrony research, but ontogenetic trajectories of ammonoid conch geometries have been rarely discussed in the context of heterochrony. The present study focuses on ontogenetic variation in conch geometry often seen in ammonoids and tries to compare the growth trajectories among species.
For this purpose, ontogenetic trajectories of shell shape in a “time”-shape space were reconstructed for each species using a theoretical morphologic model of a planispiral tube which mimics an ammonoid shell form. The growth components considered herein are expansion of spiral radius, elongation of spiral length, and dilation of the whorl. The coiling geometry of the spiral is defined by the relationship between the amounts of increases in spiral radius and spiral length. The patterns of ontogenetic changes in whorl cross-sectional shape depend on the relationship between the amounts of increases in height and breadth of the whorl. A relative time interval over the duration of growth is defined based on a logistic growth model of the spiral radius of the shell. The growth curves for the spiral length and the height and breadth of the whorl are defined as logistic functions of the relative time with respect to radius expansion with a set of given parameter values of the logistic growth. The parameters of the logistic model for each growth component were estimated by using Bayesian inference. The parameters were then used to reconstruct the growth curves and ontogenetic trajectories of shell shape that were calculated as the ratio of the spiral length, the whorl height, and the whorl breadth with respect to the spiral radius.
As a result, the patterns of the ontogenetic trajectories tend to be similar among closely related species particularly in the relative spiral length as well as in the relative whorl height. When focusing on the results on the manner of shell coiling, a heterochronic relationship seems common among species within a genus. However, the patterns of the ontogenetic trajectories were more or less variable within a single genus and some intrageneric variation in whorl shape cannot be explained by heterochrony. The results suggest that evolutionary conservativeness of ontogenetic trajectories is different among traits in ammonoids.
For this purpose, ontogenetic trajectories of shell shape in a “time”-shape space were reconstructed for each species using a theoretical morphologic model of a planispiral tube which mimics an ammonoid shell form. The growth components considered herein are expansion of spiral radius, elongation of spiral length, and dilation of the whorl. The coiling geometry of the spiral is defined by the relationship between the amounts of increases in spiral radius and spiral length. The patterns of ontogenetic changes in whorl cross-sectional shape depend on the relationship between the amounts of increases in height and breadth of the whorl. A relative time interval over the duration of growth is defined based on a logistic growth model of the spiral radius of the shell. The growth curves for the spiral length and the height and breadth of the whorl are defined as logistic functions of the relative time with respect to radius expansion with a set of given parameter values of the logistic growth. The parameters of the logistic model for each growth component were estimated by using Bayesian inference. The parameters were then used to reconstruct the growth curves and ontogenetic trajectories of shell shape that were calculated as the ratio of the spiral length, the whorl height, and the whorl breadth with respect to the spiral radius.
As a result, the patterns of the ontogenetic trajectories tend to be similar among closely related species particularly in the relative spiral length as well as in the relative whorl height. When focusing on the results on the manner of shell coiling, a heterochronic relationship seems common among species within a genus. However, the patterns of the ontogenetic trajectories were more or less variable within a single genus and some intrageneric variation in whorl shape cannot be explained by heterochrony. The results suggest that evolutionary conservativeness of ontogenetic trajectories is different among traits in ammonoids.