Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

Distribution of diatom communities in agricultural and mining watersheds of Southwest Spain

Els sistemes aquàtics continental representen un dels ecosistemes més amenaçats a nivell mundial, com a conseqüència de l'ús intensiu quel'home en fa. La conca del Guadiana no està lliure d'aquestes pressions antròpiques. Les grans infraestructures hidràuliques i l'escorrentia provinent de l'agricultura són només exemples dels greus problemes que pateix la conca. Aquests problemes es fan especialment palesos en la zona alta de la conca, on l'escassetat d'aigua no fa més que agreujar el problema.Tot això ha generat la necessitat urgent d'avaluar l'estat de conservació d'aquests ecosistemes aquàtics continentals, poder determinar la mesura i la magnitud de les pertorbacions que els estan afectant i així proposar mesures de gestió destinades a restaurar-ne la integritat ecològica. El principal objectiu que presenta aquest és determinar els patrons de distribució de les comunitats de algals (amb una menció especial en el grup de les diatomees) i de les seves causes en la conca del Guadiana i associades, amb la finalitat d'establir i proposar eines que permetin avaluar l'estat de conservació de les masses d'aigua d'aquestes conques.