Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Aquatic community patterns across environmental gradients in a Mediterranean floodplain and their application to ecosystem restoration

El presente estudio tiene como objetivo proporcionar una base de conocimiento sólida para la restauración ecológica de ríos, basada en la respuesta de comunidades acuáticas a cambios en la conectividad hídrica, factores medioambientales y presión antrópica. La conectividad hídrica lateral resultó ser el factor principal que estructura hábitats y comunidades acuáticas en el Ebro; mientras que la turbidez, salinidad y concentración de nutrientes fueron factores secundarios. La combinación de estos factores establece un marco ecológico que permite realizar predicciones acerca de los patrones taxonómicos y funcionales con más probabilidades de ocurrir en la llanura del Ebro. La posibilidad de que se creen nuevos humedales de forma natural en el Ebro es muy baja, mientras los que quedan están amenazados por una baja renovación del agua. El objetivo de la restauración ecológica debe por tanto consistir en re-establecer un amplio rango de condiciones hídricas, de acuerdo con el potencial sostenible del ecosistema.