Alpha shapes: Determining 3D shape complexity across morphologically diverse structures

Background. Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To utilise this data to address evolutionary and ecological questions, an array of tools has been developed to conduct 3D shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose the new ‘alpha-shapes’ method for quantifying 3D shape complexity. Methods. We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute differences in size, a suite of alpha-shapes was fitted to each specimen. An alpha shape is a formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. ‘Optimal’ alpha was defined as the degree of refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall shape ‘complexity’. Results Our results show that alpha-shapes can be used to quantify interspecific variation in shape ‘complexity’ within biological structures of disparate geometry. The ‘stepped’ nature of alpha curves is informative with regards to the contribution of specific morphological features to overall shape ‘complexity’. Alpha-shapes agrees with other measures of topographic complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as possessing the highest topographic complexity, contrasting with other shape metrics. 3D fractal dimension is found to be an inappropriate metric of complexity when applied to bacula. Conclusions. The alpha-shapes methodology can be used to calculate ‘optimal’ alpha refinement as a proxy for shape ‘complexity’ without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. Beyond genital shape, we consider the alpha-shapes technique to hold considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines

The Gene Ontology resource: enriching a GOld mine

The Gene Ontology Consortium (GOC) provides the most comprehensive resource currently available for computable knowledge regarding the functions of genes and gene products. Here, we report the advances of the consortium over the past two years. The new GO-CAM annotation framework was notably improved, and we formalized the model with a computational schema to check and validate the rapidly increasing repository of 2838 GO-CAMs. In addition, we describe the impacts of several collaborations to refine GO and report a 10% increase in the number of GO annotations, a 25% increase in annotated gene products, and over 9,400 new scientific articles annotated. As the project matures, we continue our efforts to review older annotations in light of newer findings, and, to maintain consistency with other ontologies. As a result, 20 000 annotations derived from experimental data were reviewed, corresponding to 2.5% of experimental GO annotations. The website (http://geneontology.org) was redesigned for quick access to documentation, downloads and tools. To maintain an accurate resource and support traceability and reproducibility, we have made available a historical archive covering the past 15 years of GO data with a consistent format and file structure for both the ontology and annotations