Proposing an information criterion for individual-based models developed in a pattern-oriented modelling framework

Individual-based models (IBMs) have been improved in quality and reliability in recent years with an approach called pattern-oriented modelling (POM). POM proposes guidelines to develop models reproducing multiple patterns observed on the field and to test systematically how well the IBMs reproduce them. POM studies used generally traditional methods of goodness of fit such as the sum of squares evaluation or ad hoc comparisons of fitting errors and variations. Model selection, however, can be a rigorous statistical approach based on information theory and information criteria such as the Akaike's information criterion (AIC) or the deviance information criterion (DIC). So far, it has not been tried to link POM to these rigorous techniques. The main problems to achieve that are: (a) the difficulty to have likelihood functions for IBMs’ parameters and (b) the possibility to obtain posterior distributions of IBMs’ parameters given the patterns to reproduce. In a first part, this paper answers problem (a) by proposing and explaining how to calculate a deviance measure (POMDEV) for models developed in a context of POM. And while answering the second problem, a second part of the paper proposes an information criterion for model selection in a POM context (the pattern-oriented modelling information criterion: POMIC). This criterion does not yet have the same theoretical foundation as, e.g., AIC, but uses formal analogies to the DIC. In a third part POMIC is tested with a modelling exercise. This exercise shows the potential of POMIC to use multiple patterns for selecting among multiple potential submodels and eventually select the most parsimonious and well fitting model version. We conclude that POMIC, although being a heuristically derived approach, can greatly improve the POM framework.     

Charles Darwin, beetles and phylogenetics

Here, we review Charles Darwin’s relation to beetles and developments in coleopteran systematics in the last two centuries. Darwin was an enthusiastic beetle collector. He used beetles to illustrate different evolutionary phenomena in his major works, and astonishingly, an entire sub-chapter is dedicated to beetles in “The Descent of Man”. During his voyage on the Beagle, Darwin was impressed by the high diversity of beetles in the tropics, and he remarked that, to his surprise, the majority of species were small and inconspicuous. However, despite his obvious interest in the group, he did not get involved in beetle taxonomy, and his theoretical work had little immediate impact on beetle classification. The development of taxonomy and classification in the late nineteenth and earlier twentieth century was mainly characterised by the exploration of new character systems (e.g. larval features and wing venation). In the mid-twentieth century, Hennig’s new methodology to group lineages by derived characters revolutionised systematics of Coleoptera and other organisms. As envisioned by Darwin and Ernst Haeckel, the new Hennigian approach enabled systematists to establish classifications truly reflecting evolution. Roy A. Crowson and Howard E. Hinton, who both made tremendous contributions to coleopterology, had an ambivalent attitude towards the Hennigian ideas. The Mickoleit school combined detailed anatomical work with a classical Hennigian character evaluation, with stepwise tree building, comparatively few characters and a priori polarity assessment without explicit use of the outgroup comparison method. The rise of cladistic methods in the 1970s had a strong impact on beetle systematics. Cladistic computer programs facilitated parsimony analyses of large data matrices, mostly morphological characters not requiring detailed anatomical investigations. Molecular studies on beetle phylogeny started in the 1990s with modest taxon sampling and limited DNA data. This has changed dramatically. With very large data sets and high throughput sampling, phylogenetic questions can be addressed without prior knowledge of morphological characters. Nevertheless, molecular studies have not lead to the great breakthrough in beetle systematics—yet. Especially the phylogeny of the extremely species rich suborder Polyphaga remains incompletely resolved. Coordinated efforts of molecular workers and of morphologists using innovative techniques may lead to more profound insights in the near future. The final aim is to develop a well-founded phylogeny, which truly reflects the evolution of this immensely species rich group of organisms.