A simple generative model of trilobite segmentation and growth

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.