Evaluating hypotheses of instar-grouping in arthropods: a maximum likelihood approach

The ontogeny of arthropod exoskeletons is punctuated by short periods of growth following each molt, separated by longer stages of unchanging morphology called instars. The recognition of instar clusters in size distributions has been important in understanding the growth and evolution of fossil arthropods. Generally, these clusters have been identified by inspection, but this approach has been criticized for its subjectivity. In this paper, we describe a statistical framework for evaluating hypotheses of clustering based on maximum likelihood analysis of mixture models. The approach assumes that individuals are normally distributed within instars; thus an arthropod size distribution can be considered a mixture of normal distributions. This methodology provides an objective framework to compare various plausible hypotheses of grouping, including the possibility that there is no significant grouping at all. We apply this method to evaluate clustering in two trilobite species, Ampyxina bellatula and Piochaspis sellata. Both of these data sets show statistically significant evidence of clustering, a phenomenon rarely documented for holaspid-stage trilobites. After consideration of alternative causes of clustering, we argue that the observed groupings are best explained as instar groups. In these two species, growth increments between molts were similar throughout the observed portion of ontogeny, although subtle yet significant variation can be seen within the ontogeny of Ampyxina bellatul