On the use of principal components in contemporany population genetics: a case study

In human Population Genetics, routine applications of principal component techniques are often required. Population biologists make widespread use of certain discrete classifications of human samples into haplotypes, the monophyletic units of phylogenetic trees constructed from several single nucleotide bimorphisms hierarchically ordered. Compositional frequencies of the haplotypes are recorded within the different samples. Principal component techniques are then required as a dimension-reducing strategy to bring the dimension of the problem to a manageable level, say two, to allow for graphical analysis. Population biologists at large are not aware of the special features of compositional data and normally make use of the crude covariance of compositional relative frequencies to construct principal components. In this short note we present our experience with using traditional linear principal components or compositional principal components based on logratios, with reference to a specific dataset

Characterization and mechanism of action of the biological control agent Pantoea agglomerans EPS125

La soca EPS125 ha mostrat ser un efectiu agent de control biològic de diferents patògens fúngics de postcollita en diferents fruits. Degut a la seva elevada eficàcia, es va plantejar desenvolupar aquesta soca comercialment i per aquest motiu en el present treball es plantejà complementar la informació necessària pel seu registre. D'acord amb els resultats obtinguts mitjançant proves fenotípiques i genotípiques, la soca EPS125 queda inclosa dins l'espècie Pantoea agglomerans (Enterobacter agglomerans-Erwinia herbicola). En relació a la utilització de fonts de carboni, en el perfil i contingut d'àcids grassos cel·lulars i en el polimorfisme en la longitud dels fragments de macrorestricció genòmica (MRFLP), la soca EPS125 mostrà trets característics que la diferencien d'altres soques. Els dos marcadors moleculars (125.2 i 125.3) específics per la soca EPS125 dissenyats en el present treball mostraren ser semiespecífics per la seva detecció mitjançant la tècnica PCR i Real Time PCR. Quedant pendent l'anàlisi d'especificitat de l'ús combinat dels dos marcadors moleculars en una reacció PCR multiplex. P. agglomerans EPS125 ha mostrat ser molt efectiva en el control de Penicillium expansum en poma amb una dosi efectiva mitjana de 2.7x105 a 7x105 ufc/ml, i una ratio de 25-101 cèl·lules de la soca EPS125 per inactivar una espora del patogen segons el model de saturació hiperbòlica. Segons les aproximacions fenotípiques i estudis genotípics realitzats, sembla que els mecanismes de biocontrol utilitzats per la soca EPS125 contra P. expansum en poma estan directament relacionats amb la capacitat de formació de biofilm per aquesta soca.

Availability and use of organic matter in stream ecosystems: the role of biofilms

La comunitat bentònica dels ecosistemes fluvials processa una gran quantitat de la matèria orgànica que arriba als rius. L'origen de les entrades de material (autòctones o al·lòctones), la seva composició química i la seva quantitat (freqüència de les entrades i concentració assolida en el riu), determinen l'estructura de la comunitat bentònica autotròfica i heterotròfica, les seves relacions tròfiques i les seves interaccions potencials (competència, sinergisme). L'objectiu d'aquesta tesi és posar de manifest la utilització de la matèria orgànica dissolta (MOD) per part dels biofilms bacterians bentònics fluvials i determinar l'eficiència del sistema fluvial en l'ús dels diferents materials que hi circulen. Amb aquesta finalitat s'han portat a terme diversos experiments, tant de camp com de laboratori, per tal de conèixer els efectes de la disponibilitat de la matèria orgànica (quantitat) i la seva qualitat (composició química i biodegradabilitat) i els efectes deguts a l'augment de temperatura de l'aigua del riu.

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

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Fast calculation of the CAC convolution algorithm using the multinomial distribution function

The authors focus on one of the methods for connection acceptance control (CAC) in an ATM network: the convolution approach. With the aim of reducing the cost in terms of calculation and storage requirements, they propose the use of the multinomial distribution function. This permits direct computation of the associated probabilities of the instantaneous bandwidth requirements. This in turn makes possible a simple deconvolution process. Moreover, under certain conditions additional improvements may be achieved