[B-PT04] Biotic History

[BPT04-P05] Buckman’s rule revisited: correlation between whorl shape and coiling geometry in ammonoids

*Takao Ubukata¹ (1.Division of Geology & Mineralogy, Department of Earth & Planetary Sciences, Kyoto University)

Keywords:theoretical morphology, ammonoid, Buckman's rule

It has long been known that heavily ornamented individuals tend to have laterally compressed and involute conchs in ammonoids. This pattern is often observed for intraspecific variation (known as Buckman’s Law of Covariation) and has also been documented within a higher taxonomic group. The covariation between sculpture and shell shape has been explained from the morphogenetic viewpoint. However, the correlation between whorl shape and manner of shell coiling is not yet fully understood. It is also known that species with a narrow umbilicus tend to have a laterally compressed shell with a larger whorl expansion rate. The present study tries to explain the correlation between the morphological parameters observed in ammonoids based on a theoretical morphologic model representing planispiral shell forms. The present model utilized consists of increases in length of the helicospiral, radius of the spiral, and height and breadth of the aperture. The growth of each dimension follows a logistic growth model which is defined by its initial value, intrinsic growth rate, and timing of growth offset. Anisomorphic shell growth can be represented by the theoretical model when the intrinsic growth rate or the timing of growth offset is different among dimensions. Computer-generated shell shapes based on the present model show that variation in timing of growth offset of apertural height produces a negative correlation between whorl expansion rate and umbilical width and a positive one between relative whorl breadth and umbilical width. An early offset of growth for apertural height relative to all other dimensions tends to form a tightly coiled shell shape with a wide umbilicus, whereas a late offset readily results in a loosely coiled and laterally compressed shell shape with a narrow umbilicus. The morphological correlations between the parameters were commonly found also in ontogenetic variation in ammonoids as well as in interspecific variation. The results suggest that different timing of growth cessation among dimensions involving the ontogenetic variation may be a cause of the biased distribution of adult shape in the morphospace.