BackgroundFollowing recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To use this data to address evolutionary and ecological questions, an array of tools has been developed to conduct shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose a new ‘alpha-shapes’ method for quantifying 3D shape complexity.MethodsWe 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 size differences, a suite of alpha-shapes was fitted per specimen. An alpha shape is 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 refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall ‘complexity’.ResultsOur 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 ‘complexity’. Alpha-shapes agrees with other measures of complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as being most complex, contrasting with other shape metrics. 3D fractal dimension is identified as an inappropriate metric of complexity when applied to bacula.ConclusionsAlpha-shapes is 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. We interpret alpha-shapes as being particularly sensitive to concavities in surface topology, potentially distinguishing it from other shape complexity metrics. Beyond genital shape, the alpha-shapes technique holds considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.

Bird necks display unparalleled levels of morphological diversity compared to other vertebrates, yet it is unclear what factors have structured this variation. Using three-dimensional geometric morphometrics and multivariate statistics, we show that the avian cervical column is a hierarchical morpho-functional appendage, with varying magnitudes of ecologically driven osteological variation at different scales of organization. Contrary to expectations given the widely varying ecological functions of necks in different species, we find that regional modularity of the avian neck is highly conserved, with an overall structural blueprint that is significantly altered only by the most mechanically demanding ecological functions. Nevertheless, the morphologies of vertebrae within subregions of the neck show more prominent signals of adaptation to ecological pressures. We also find that both neck length allometry and the nature of neck elongation in birds are different from other vertebrates. In contrast with mammals, neck length scales isometrically with head mass and, contrary to previous work, we show that neck elongation in birds is achieved predominantly by increasing vertebral lengths rather than counts. Birds therefore possess a cervical spine that may be unique in its versatility among extant vertebrates, one that, since the origin of flight, has adapted to function as a surrogate forelimb in varied ecological niches.

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The baculum is an enigmatic bone within the mammalian glans penis, and the driving forces behind its often bizarre shape have captivated evolutionary biologists for over a century. Hypotheses for the function of the baculum include aiding in intromission, stimulating females and assisting with prolonged mating. Previous attempts to test these hypotheses have focused on the gross size of the baculum and have failed to reach a consensus. We conducted three-dimensional imaging and apply a new method to quantify three-dimensional shape complexity in the carnivoran baculum. We show that socially monogamous species are evolving towards complex-shaped bacula, whereas group-living species are evolving towards simple bacula. Overall three-dimensional baculum shape complexity is not related to relative testes mass, but tip complexity is higher in induced ovulators and species engaging in prolonged copulation. Our study provides evidence of postcopulatory sexual selection pressures driving three-dimensional shape complexity in the carnivore baculum.

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.

Wind tunnel tests conducted on a model based on the long-eared bat Plecotus auritus indicated that the positioning of the tail membrane (uropatagium) can significantly influence flight control. Adjusting tail position by increasing the angle of the legs ventrally relative to the body has a two-fold effect; increasing leg-induced wing camber (i.e., locally increased camber of the inner wing surface) and increasing the angle of attack of the tail membrane. We also used our model to examine the effects of flying with and without a tail membrane. For the bat model with a tail membrane increasing leg angle increased the lift, drag and pitching moment (nose-down) produced. However, removing the tail membrane significantly reduced the change in pitching moment with increasing leg angle, but it had no significant effect on the level of lift produced. The drag on the model also significantly increased with the removal of the tail membrane. The tail membrane, therefore, is potentially important for controlling the level of pitching moment produced by bats and an aid to flight control, specifically improving agility and manoeuvrability. Although the tail of bats is different from that of birds, in that it is only divided from the wings by the legs, it nonetheless, may, in addition to its prey capturing function, fulfil a similar role in aiding flight control.

Most studies relating bat morphology to flight ecology have concentrated on the wing membrane. Here, canonical variance analysis showed that the ear and tail morphologies of bats also strongly relate to foraging strategy, which in turn is correlated with flight style. Variations in tail membrane morphology are likely to be a trade-off between increases in the mechanical cost of flight and improvements in foraging and flight performance. Flying with large ears is also potentially energetically expensive, particularly at high flight speeds. Large ears, therefore, are only likely to be affordable for slow foraging gleaning bat species. Bats with faster foraging flight styles tend to have smaller ears, possibly to cut the overall drag produced and reduce the power required for flight. Variations in the size of ears and tail membranes appear to be driven primarily by foraging strategy and not by body size, because the scaling relationships found are either weak or not significant. Ear size in bats may be a result of a trade-off between acoustic and aerodynamic performance.

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