A simple generative model of trilobite segmentation and growth

Abstract

Generative growth models have been the basis for numerous studies of morphological diversity and evolution. Most work has focused on modeling accretionary growth systems, with much less attention to discrete growth systems. Generative growth models for molting organisms, such as arthropods, have remained particularly elusive. However, our understanding of post-embryonic growth in trilobite species is sufficiently mature that it is now possible to model growth in a way that incorporates the addition of new parts as well as differential growth rates for existing parts across the trilobite body plan. Furthermore, body size data for a large sample of specimens of the trilobite species Aulacopleura koninckii (Barrande, 1846) make it possible to generate robust estimates for model parameters. Although the generative model described here was based on a relatively simple segmentation schedule, a diverse array of observed body sizes and relative proportions of body regions can be attained by altering only a few parameters at a time. Notably, small changes in growth rates can have large effects on body size (e.g. an increase of 4% increases body size by 350%). Subsampling of the empirical dataset indicates that parameters describing the growth gradient in the trunk are more sensitive to sample size than input parameters. Increasing the number of stages represented improves parameter estimates more quickly than increasing number of specimens per stage.

Absolute axial growth and trunk segmentation in the early Cambrian trilobite Oryctocarella duyunensis

“…Again, this may be an artifact of the almost flat gradient in the anterior of the trunk combined with the possibly nonexistent gradient in the cephalon. In the only other published work reporting on trilobite continuous growth gradients (Hopkins 2020), the shape of the meraspid trunk gradient of the Cambrian aulacopleurid Elrathia kingii , normalizing for the average trunk growth rate, is very similar to that in A. koninckii .…”

“…Although all such cases have limitations, including the rather specific set of paleoenvironments represented, these studies do offer important insight into how ancient developmental processes were regulated in this early euarthropod clade. In parallel, and building on this descriptive and analytical work, investigations have begun on mechanistic modeling of growth and segmentation, in which ontogeny reconstruction is based on the application of estimated growth and segmentation parameters, rather than on simple data fitting (Hughes et al 2017; Hopkins 2020). These works suggest the promise of trilobite studies for the discipline of “paleo-evo-devo” (Minelli and Fusco 2008: p. 216).…”

Ontogeny of the trilobite Elrathia kingii (Meek) and comparison of growth rates between Elrathia kingii and Aulacopleura koninckii (Barrande)

“… Parameters are compared with those estimated from Aulacopleura koninckii using data from Hughes et al . (2017; see also Hopkins 2020b). The average body length at the meraspid–holaspid transition was estimated as the average length of specimens with 12 thoracic tergites in Elrathia kingii , which is the penultimate number of thoracic tergites.…”

“…A function (par.est.R) for estimating the above parameters in the statistical programming language R (R Core Team 2019) is described in Hopkins (2020b). The procedure described above was followed to estimate growth rates and other parameters for Aulacopleura koninckii , using data available from Hughes et al .…”

Deep insights into trilobite development

“…A recommendation of Hopkins MJ (2020). A simple generative model of trilobite segmentation and growth.…”