Comparative analysis of shell occupation by two southern populations of the hermit crab Loxopagurus loxochelis (Decapoda, Diogenidae)

The present study aimed to comparatively verify the relation between the hermit crabs and the shells they use in two populations of Loxopagurus loxochelis. Samples were collected monthly from July 2002 to June 2003, at Caraguatatuba and Ubatuba Bay, Sao Paulo, Brazil. The animals sampled had their sex identified, were weighed and measured; their shells were identified, measured and weighed, and their internal volume determined. To relate the hermit crab's characteristics and the shells' variables, principal component analysis (PCA) and a regression tree were used. According to the PCA analysis, the three gastropod shells most frequently used by L. loxochelis varied in size. The regression tree successfully explained the relationship between the hermit crab's characteristics and the internal volume of the inhabited shell. It can be inferred that the relationship between the morphometry of an individual hermit crab and its shell is not straightforward and it is impossible to explain only on the basis of direct correlations between the body's and the shell's attributes. Several factors (such as the morphometry and the availability of the shell, environmental conditions and inter- and intraspecific competition) interact and seem to be taken into consideration by the hermit crabs when they choose a shell, resulting in the diversified pattern of shell occupancy shown here and elsewhere.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Comparative analysis of shell occupation by two southern populations of the hermit crab Loxopagurus loxochelis (Decapoda, Diogenidae)

The present study aimed to comparatively verify the relation between the hermit crabs and the shells they use in two populations of Loxopagurus loxochelis. Samples were collected monthly from July 2002 to June 2003, at Caraguatatuba and Ubatuba Bay, São Paulo, Brazil. The animals sampled had their sex identified, were weighed and measured; their shells were identified, measured and weighed, and their internal volume determined. To relate the hermit crab's characteristics and the shells' variables, principal component analysis (PCA) and a regression tree were used. According to the PCA analysis, the three gastropod shells most frequently used by L. loxochelis varied in size. The regression tree successfully explained the relationship between the hermit crab's characteristics and the internal volume of the inhabited shell. It can be inferred that the relationship between the morphometry of an individual hermit crab and its shell is not straightforward and it is impossible to explain only on the basis of direct correlations between the body's and the shell's attributes. Several factors (such as the morphometry and the availability of the shell, environmental conditions and inter- and intraspecific competition) interact and seem to be taken into consideration by the hermit crabs when they choose a shell, resulting in the diversified pattern of shell occupancy shown here and elsewhere.