Modelling plant species distribution in alpine grasslands using airborne imaging spectroscopy.

Remote sensing using airborne imaging spectroscopy (AIS) is known to retrieve fundamental optical properties of ecosystems. However, the value of these properties for predicting plant species distribution remains unclear. Here, we assess whether such data can add value to topographic variables for predicting plant distributions in French and Swiss alpine grasslands. We fitted statistical models with high spectral and spatial resolution reflectance data and tested four optical indices sensitive to leaf chlorophyll content, leaf water content and leaf area index. We found moderate added-value of AIS data for predicting alpine plant species distribution. Contrary to expectations, differences between species distribution models (SDMs) were not linked to their local abundance or phylogenetic/functional similarity. Moreover, spectral signatures of species were found to be partly site-specific. We discuss current limits of AIS-based SDMs, highlighting issues of scale and informational content of AIS data.

A multilevel multiscale finite volume method

The Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.

Learning wind fields with multiple kernels

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine region.

What drives invasibility? A multi-model inference test and spatial modelling of alien plant species richness patterns in northern Portugal

Understanding and anticipating biological invasions can focus either on traits that favour species invasiveness or on features of the receiving communities, habitats or landscapes that promote their invasibility. Here, we address invasibility at the regional scale, testing whether some habitats and landscapes are more invasible than others by fitting models that relate alien plant species richness to various environmental predictors. We use a multi-model information-theoretic approach to assess invasibility by modelling spatial and ecological patterns of alien invasion in landscape mosaics and testing competing hypotheses of environmental factors that may control invasibility. Because invasibility may be mediated by particular characteristics of invasiveness, we classified alien species according to their C-S-R plant strategies. We illustrate this approach with a set of 86 alien species in Northern Portugal. We first focus on predictors influencing species richness and expressing invasibility and then evaluate whether distinct plant strategies respond to the same or different groups of environmental predictors. We confirmed climate as a primary determinant of alien invasions and as a primary environmental gradient determining landscape invasibility. The effects of secondary gradients were detected only when the area was sub-sampled according to predictions based on the primary gradient. Then, multiple predictor types influenced patterns of alien species richness, with some types (landscape composition, topography and fire regime) prevailing over others. Alien species richness responded most strongly to extreme land management regimes, suggesting that intermediate disturbance induces biotic resistance by favouring native species richness. Land-use intensification facilitated alien invasion, whereas conservation areas hosted few invaders, highlighting the importance of ecosystem stability in preventing invasions. Plants with different strategies exhibited different responses to environmental gradients, particularly when the variations of the primary gradient were narrowed by sub-sampling. Such differential responses of plant strategies suggest using distinct control and eradication approaches for different areas and alien plant groups.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Modelling hydrodynamics in the Rio Parana, Argentina : an evaluation and inter-comparison of reduced-complexity and physics based models applied to a large sand-bed river

Depth-averaged velocities and unit discharges within a 30 km reach of one of the world's largest rivers, the Rio Parana, Argentina, were simulated using three hydrodynamic models with different process representations: a reduced complexity (RC) model that neglects most of the physics governing fluid flow, a two-dimensional model based on the shallow water equations, and a three-dimensional model based on the Reynolds-averaged Navier-Stokes equations. Row characteristics simulated using all three models were compared with data obtained by acoustic Doppler current profiler surveys at four cross sections within the study reach. This analysis demonstrates that, surprisingly, the performance of the RC model is generally equal to, and in some instances better than, that of the physics based models in terms of the statistical agreement between simulated and measured flow properties. In addition, in contrast to previous applications of RC models, the present study demonstrates that the RC model can successfully predict measured flow velocities. The strong performance of the RC model reflects, in part, the simplicity of the depth-averaged mean flow patterns within the study reach and the dominant role of channel-scale topographic features in controlling the flow dynamics. Moreover, the very low water surface slopes that typify large sand-bed rivers enable flow depths to be estimated reliably in the RC model using a simple fixed-lid planar water surface approximation. This approach overcomes a major problem encountered in the application of RC models in environments characterised by shallow flows and steep bed gradients. The RC model is four orders of magnitude faster than the physics based models when performing steady-state hydrodynamic calculations. However, the iterative nature of the RC model calculations implies a reduction in computational efficiency relative to some other RC models. A further implication of this is that, if used to simulate channel morphodynamics, the present RC model may offer only a marginal advantage in terms of computational efficiency over approaches based on the shallow water equations. These observations illustrate the trade off between model realism and efficiency that is a key consideration in RC modelling. Moreover, this outcome highlights a need to rethink the use of RC morphodynamic models in fluvial geomorphology and to move away from existing grid-based approaches, such as the popular cellular automata (CA) models, that remain essentially reductionist in nature. In the case of the world's largest sand-bed rivers, this might be achieved by implementing the RC model outlined here as one element within a hierarchical modelling framework that would enable computationally efficient simulation of the morphodynamics of large rivers over millennial time scales. (C) 2012 Elsevier B.V. All rights reserved.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

Ensemble methods for environmental data modelling with support vector regression

This paper investigates the use of ensemble of predictors in order to improve the performance of spatial prediction methods. Support vector regression (SVR), a popular method from the field of statistical machine learning, is used. Several instances of SVR are combined using different data sampling schemes (bagging and boosting). Bagging shows good performance, and proves to be more computationally efficient than training a single SVR model while reducing error. Boosting, however, does not improve results on this specific problem.

Modelling Bone Mineral Density in Swiss Breast Cancer Patients Treated with Letrozole, Tamoxifen and Sequences of Letrozole and Tamoxifen in the BIG 1-98 Study (SAKK 21/07).

Background: Bone health is a concern when treating early stage breast cancer patients with adjuvant aromatase inhibitors. Early detection of patients (pts) at risk of osteoporosis and fractures may be helpful for starting preventive therapies and selecting the most appropriate endocrine therapy schedule. We present statistical models describing the evolution of lumbar and hip bone mineral density (BMD) in pts treated with tamoxifen (T), letrozole (L) and sequences of T and L. Methods: Available dual-energy x-ray absorptiometry exams (DXA) of pts treated in trial BIG 1-98 were retrospectively collected from Swiss centers. Treatment arms: A) T for 5 years, B) L for 5 years, C) 2 years of T followed by 3 years of L and, D) 2 years of L followed by 3 years of T. Pts without DXA were used as a control for detecting selection biases. Patients randomized to arm A were subsequently allowed an unplanned switch from T to L. Allowing for variations between DXA machines and centres, two repeated measures models, using a covariance structure that allow for different times between DXA, were used to estimate changes in hip and lumbar BMD (g/cm2) from trial randomization. Prospectively defined covariates, considered as fixed effects in the multivariable models in an intention to treat analysis, at the time of trial randomization were: age, height, weight, hysterectomy, race, known osteoporosis, tobacco use, prior bone fracture, prior hormone replacement therapy (HRT), bisphosphonate use and previous neo-/adjuvant chemotherapy (ChT). Similarly, the T-scores for lumbar and hip BMD measurements were modeled using a per-protocol approach (allowing for treatment switch in arm A), specifically studying the effect of each therapy upon T-score percentage. Results: A total of 247 out of 546 pts had between 1 and 5 DXA; a total of 576 DXA were collected. Number of DXA measurements per arm were; arm A 133, B 137, C 141 and D 135. The median follow-up time was 5.8 years. Significant factors positively correlated with lumbar and hip BMD in the multivariate analysis were weight, previous HRT use, neo-/adjuvant ChT, hysterectomy and height. Significant negatively correlated factors in the models were osteoporosis, treatment arm (B/C/D vs. A), time since endocrine therapy start, age and smoking (current vs. never).Modeling the T-score percentage, differences from T to L were -4.199% (p = 0.036) and -4.907% (p = 0.025) for the hip and lumbar measurements respectively, before any treatment switch occurred. Conclusions: Our statistical models describe the lumbar and hip BMD evolution for pts treated with L and/or T. The results of both localisations confirm that, contrary to expectation, the sequential schedules do not seem less detrimental for the BMD than L monotherapy. The estimated difference in BMD T-score percent is at least 4% from T to L.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.