Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.

Rapid radiation in spiny lobsters (Palinurus spp) as revealed by classic and ABC methods using mtDNA and microsatellite data

Background: Molecular tools may help to uncover closely related and still diverging species from a wide variety of taxa and provide insight into the mechanisms, pace and geography of marine speciation. There is a certain controversy on the phylogeography and speciation modes of species-groups with an Eastern Atlantic-Western Indian Ocean distribution, with previous studies suggesting that older events (Miocene) and/or more recent (Pleistocene) oceanographic processes could have influenced the phylogeny of marine taxa. The spiny lobster genus Palinurus allows for testing among speciation hypotheses, since it has a particular distribution with two groups of three species each in the Northeastern Atlantic (P. elephas, P. mauritanicus and P. charlestoni) and Southeastern Atlantic and Southwestern Indian Oceans (P. gilchristi, P. delagoae and P. barbarae). In the present study, we obtain a more complete understanding of the phylogenetic relationships among these species through a combined dataset with both nuclear and mitochondrial markers, by testing alternative hypotheses on both the mutation rate and tree topology under the recently developed approximate Bayesian computation (ABC) methods. Results Our analyses support a North-to-South speciation pattern in Palinurus with all the South-African species forming a monophyletic clade nested within the Northern Hemisphere species. Coalescent-based ABC methods allowed us to reject the previously proposed hypothesis of a Middle Miocene speciation event related with the closure of the Tethyan Seaway. Instead, divergence times obtained for Palinurus species using the combined mtDNA-microsatellite dataset and standard mutation rates for mtDNA agree with known glaciation-related processes occurring during the last 2 my. Conclusion The Palinurus speciation pattern is a typical example of a series of rapid speciation events occurring within a group, with very short branches separating different species. Our results support the hypothesis that recent climate change-related oceanographic processes have influenced the phylogeny of marine taxa, with most Palinurus species originating during the last two million years. The present study highlights the value of new coalescent-based statistical methods such as ABC for testing different speciation hypotheses using molecular data.

Tracking Invasion Histories in the Sea: Facing Complex Scenarios Using Multilocus Data

In recent years, new analytical tools have allowed researchers to extract historical information contained in molecular data, which has fundamentally transformed our understanding of processes ruling biological invasions. However, the use of these new analytical tools has been largely restricted to studies of terrestrial organisms despite the growing recognition that the sea contains ecosystems that are amongst the most heavily affected by biological invasions, and that marine invasion histories are often remarkably complex. Here, we studied the routes of invasion and colonisation histories of an invasive marine invertebrate Microcosmus squamiger (Ascidiacea) using microsatellite loci, mitochondrial DNA sequence data and 11 worldwide populations. Discriminant analysis of principal components, clustering methods and approximate Bayesian computation (ABC) methods showed that the most likely source of the introduced populations was a single admixture event that involved populations from two genetically differentiated ancestral regions - the western and eastern coasts of Australia. The ABC analyses revealed that colonisation of the introduced range of M. squamiger consisted of a series of non-independent introductions along the coastlines of Africa, North America and Europe. Furthermore, we inferred that the sequence of colonisation across continents was in line with historical taxonomic records - first the Mediterranean Sea and South Africa from an unsampled ancestral population, followed by sequential introductions in California and, more recently, the NE Atlantic Ocean. We revealed the most likely invasion history for world populations of M. squamiger, which is broadly characterized by the presence of multiple ancestral sources and non-independent introductions within the introduced range. The results presented here illustrate the complexity of marine invasion routes and identify a cause-effect relationship between human-mediated transport and the success of widespread marine non-indigenous species, which benefit from stepping-stone invasions and admixture processes involving different sources for the spread and expansion of their range.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Computation of an integral basis of a quartic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Computation of an integral basis of quartic number field

"Vegeu el resum a l'inici del document del fitxer ajunt."

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

The analysis of approximate quickselect and related problems

Approximate Quickselect, a simple modification of the well known Quickselect algorithm for selection, can be used to efficiently find an element with rank k in a given range [i..j], out of n given elements. We study basic cost measures of Approximate Quickselect by computing exact and asymptotic results for the expected number of passes, comparisons and data moves during the execution of this algorithm. The key element appearing in the analysis of Approximate Quickselect is a trivariate recurrence that we solve in full generality. The general solution of the recurrence proves to be very useful, as it allows us to tackle several related problems, besides the analysis that originally motivated us. In particular, we have been able to carry out a precise analysis of the expected number of moves of the ith element when selecting the jth smallest element with standard Quickselect, where we are able to give both exact and asymptotic results. Moreover, we can apply our general results to obtain exact and asymptotic results for several parameters in binary search trees, namely the expected number of common ancestors of the nodes with rank i and j, the expected size of the subtree rooted at the least common ancestor of the nodes with rank i and j, and the expected distance between the nodes of ranks i and j.

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Compositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials

Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data.Many of the issues that are discussed with reference to the statistical analysis of compositionaldata have a natural counterpart in the construction of a Bayesian statistical model for categoricaldata.This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986)in his seminal book on compositional data. Particular emphasis is put on the problem of whatparameterization to use

Omnidirectional Depth Computation from a Single Image

Omnidirectional cameras offer a much wider field of view than the perspective ones and alleviate the problems due to occlusions. However, both types of cameras suffer from the lack of depth perception. A practical method for obtaining depth in computer vision is to project a known structured light pattern on the scene avoiding the problems and costs involved by stereo vision. This paper is focused on the idea of combining omnidirectional vision and structured light with the aim to provide 3D information about the scene. The resulting sensor is formed by a single catadioptric camera and an omnidirectional light projector. It is also discussed how this sensor can be used in robot navigation applications