Shape classification based on interpoint distance distributions

According to Kendall (1989), in shape theory, The idea is to filter out effects resulting from translations, changes of scale and rotations and to declare that shape is “what is left”.While this statement applies in principle to classical shape theory based on landmarks, the basic idea remains also when other approaches are used. For example, we might consider, for every shape, a suitable associated function which, to a large extent, could be used to characterize the shape. This finally leads to identify the shapes with the elements of a quotient space of sets in such a way that all the sets in the same equivalence class share the same identifying function. In this paper, we explore the use of the interpoint distance distribution (i.e. the distribution of the distance between two independent uniform points) for this purpose. This idea has been previously proposed by other authors [e.g., Osada et al. (2002), Bonetti and Pagano (2005)]. We aim at providing some additional mathematical support for the use of interpoint distances in this context. In particular, we show the Lipschitz continuity of the transformation taking every shape to its corresponding interpoint distance distribution. Also, we obtain a partial identifiability result showing that, under some geometrical restrictions, shapes with different planar area must have different interpoint distance distributions. Finally, we address practical aspects including a real data example on shape classification in marine biologyThis work has been partially supported by Spanish Grants MTM2013-44045-P (Berrendero and Cuevas) and MTM2013-41383-P (Pateiro-López

Adaptive Radiation within Marine Anisakid Nematodes: A Zoogeographical Modeling of Cosmopolitan, Zoonotic Parasites

Parasites of the nematode genus Anisakis are associated with aquatic organisms. They can be found in a variety of marine hosts including whales, crustaceans, fish and cephalopods and are known to be the cause of the zoonotic disease anisakiasis, a painful inflammation of the gastro-intestinal tract caused by the accidental consumptions of infectious larvae raw or semi-raw fishery products. Since the demand on fish as dietary protein source and the export rates of seafood products in general is rapidly increasing worldwide, the knowledge about the distribution of potential foodborne human pathogens in seafood is of major significance for human health. Studies have provided evidence that a few Anisakis species can cause clinical symptoms in humans. The aim of our study was to interpolate the species range for every described Anisakis species on the basis of the existing occurrence data. We used sequence data of 373 Anisakis larvae from 30 different hosts worldwide and previously published molecular data (n = 584) from 53 field-specific publications to model the species range of Anisakis spp., using a interpolation method that combines aspects of the alpha hull interpolation algorithm as well as the conditional interpolation approach. The results of our approach strongly indicate the existence of species-specific distribution patterns of Anisakis spp. within different climate zones and oceans that are in principle congruent with those of their respective final hosts. Our results support preceding studies that propose anisakid nematodes as useful biological indicators for their final host distribution and abundance as they closely follow the trophic relationships among their successive hosts. The modeling might although be helpful for predicting the likelihood of infection in order to reduce the risk of anisakiasis cases in a given area