Stochastic stability and the evolution of coordination in spatially structured populations.

Animals can often coordinate their actions to achieve mutually beneficial outcomes. However, this can result in a social dilemma when uncertainty about the behavior of partners creates multiple fitness peaks. Strategies that minimize risk ("risk dominant") instead of maximizing reward ("payoff dominant") are favored in economic models when individuals learn behaviors that increase their payoffs. Specifically, such strategies are shown to be "stochastically stable" (a refinement of evolutionary stability). Here, we extend the notion of stochastic stability to biological models of continuous phenotypes at a mutation-selection-drift balance. This allows us to make a unique prediction for long-term evolution in games with multiple equilibria. We show how genetic relatedness due to limited dispersal and scaled to account for local competition can crucially affect the stochastically-stable outcome of coordination games. We find that positive relatedness (weak local competition) increases the chance the payoff dominant strategy is stochastically stable, even when it is not risk dominant. Conversely, negative relatedness (strong local competition) increases the chance that strategies evolve that are neither payoff nor risk dominant. Extending our results to large multiplayer coordination games we find that negative relatedness can create competition so extreme that the game effectively changes to a hawk-dove game and a stochastically stable polymorphism between the alternative strategies evolves. These results demonstrate the usefulness of stochastic stability in characterizing long-term evolution of continuous phenotypes: the outcomes of multiplayer games can be reduced to the generic equilibria of two-player games and the effect of spatial structure can be analyzed readily.

El reto del paisaje urbano en China, del Mall Comercial al espacio público

Las categorías del espacio introvertido y extrovertido definen por excelencia la estructura espacial, que ordena el ámbito de lo privado y lo público en la ciudad. La dualidad del espacio abierto y cerrado, vinculado a la estructura espacial de la ciudad clásica China, quedaba ordenado, justificado y vinculado mediante una estructura espacial muy definida. Sin embargo en el modelo de ciudad contemporánea, aflora la cuestión de la integración de estas categorías espaciales y su articulación dentro de una estructura urbana heterogénea y fuertemente alterada. ¿Cuáles serán los factores de cambio de la transición de un espacio comunitario introvertido a un espacio cívico abierto? Este proceso es un proceso que debe discurrir a un doble nivel espacial y político. Debe discurrir en paralelo a la transición de las categorías espaciales que ordenan identitariamente el ámbito urbano y la progresiva transición socio-cultural y política de una sociedad que debe gradualmente identificar y adoptar como propias las instituciones de gobierno local y su escenario, la ciudad.

Peak and persistent excess of genetic diversity following an abrupt migration increase.

Genetic diversity is essential for population survival and adaptation to changing environments. Demographic processes (e.g., bottleneck and expansion) and spatial structure (e.g., migration, number, and size of populations) are known to shape the patterns of the genetic diversity of populations. However, the impact of temporal changes in migration on genetic diversity has seldom been considered, although such events might be the norm. Indeed, during the millions of years of a species' lifetime, repeated isolation and reconnection of populations occur. Geological and climatic events alternately isolate and reconnect habitats. We analytically document the dynamics of genetic diversity after an abrupt change in migration given the mutation rate and the number and sizes of the populations. We demonstrate that during transient dynamics, genetic diversity can reach unexpectedly high values that can be maintained over thousands of generations. We discuss the consequences of such processes for the evolution of species based on standing genetic variation and how they can affect the reconstruction of a population's demographic and evolutionary history from genetic data. Our results also provide guidelines for the use of genetic data for the conservation of natural populations.

Evolutionary games on complex networks : the emergence and maintenance of cooperation

Abstract The object of game theory lies in the analysis of situations where different social actors have conflicting requirements and where their individual decisions will all influence the global outcome. In this framework, several games have been invented to capture the essence of various dilemmas encountered in many common important socio-economic situations. Even though these games often succeed in helping us understand human or animal behavior in interactive settings, some experiments have shown that people tend to cooperate with each other in situations for which classical game theory strongly recommends them to do the exact opposite. Several mechanisms have been invoked to try to explain the emergence of this unexpected cooperative attitude. Among them, repeated interaction, reputation, and belonging to a recognizable group have often been mentioned. However, the work of Nowak and May (1992) showed that the simple fact of arranging the players according to a spatial structure and only allowing them to interact with their immediate neighbors is sufficient to sustain a certain amount of cooperation even when the game is played anonymously and without repetition. Nowak and May's study and much of the following work was based on regular structures such as two-dimensional grids. Axelrod et al. (2002) showed that by randomizing the choice of neighbors, i.e. by actually giving up a strictly local geographical structure, cooperation can still emerge, provided that the interaction patterns remain stable in time. This is a first step towards a social network structure. However, following pioneering work by sociologists in the sixties such as that of Milgram (1967), in the last few years it has become apparent that many social and biological interaction networks, and even some technological networks, have particular, and partly unexpected, properties that set them apart from regular or random graphs. Among other things, they usually display broad degree distributions, and show small-world topological structure. Roughly speaking, a small-world graph is a network where any individual is relatively close, in terms of social ties, to any other individual, a property also found in random graphs but not in regular lattices. However, in contrast with random graphs, small-world networks also have a certain amount of local structure, as measured, for instance, by a quantity called the clustering coefficient. In the same vein, many real conflicting situations in economy and sociology are not well described neither by a fixed geographical position of the individuals in a regular lattice, nor by a random graph. Furthermore, it is a known fact that network structure can highly influence dynamical phenomena such as the way diseases spread across a population and ideas or information get transmitted. Therefore, in the last decade, research attention has naturally shifted from random and regular graphs towards better models of social interaction structures. The primary goal of this work is to discover whether or not the underlying graph structure of real social networks could give explanations as to why one finds higher levels of cooperation in populations of human beings or animals than what is prescribed by classical game theory. To meet this objective, I start by thoroughly studying a real scientific coauthorship network and showing how it differs from biological or technological networks using divers statistical measurements. Furthermore, I extract and describe its community structure taking into account the intensity of a collaboration. Finally, I investigate the temporal evolution of the network, from its inception to its state at the time of the study in 2006, suggesting also an effective view of it as opposed to a historical one. Thereafter, I combine evolutionary game theory with several network models along with the studied coauthorship network in order to highlight which specific network properties foster cooperation and shed some light on the various mechanisms responsible for the maintenance of this same cooperation. I point out the fact that, to resist defection, cooperators take advantage, whenever possible, of the degree-heterogeneity of social networks and their underlying community structure. Finally, I show that cooperation level and stability depend not only on the game played, but also on the evolutionary dynamic rules used and the individual payoff calculations. Synopsis Le but de la théorie des jeux réside dans l'analyse de situations dans lesquelles différents acteurs sociaux, avec des objectifs souvent conflictuels, doivent individuellement prendre des décisions qui influenceront toutes le résultat global. Dans ce cadre, plusieurs jeux ont été inventés afin de saisir l'essence de divers dilemmes rencontrés dans d'importantes situations socio-économiques. Bien que ces jeux nous permettent souvent de comprendre le comportement d'êtres humains ou d'animaux en interactions, des expériences ont montré que les individus ont parfois tendance à coopérer dans des situations pour lesquelles la théorie classique des jeux prescrit de faire le contraire. Plusieurs mécanismes ont été invoqués pour tenter d'expliquer l'émergence de ce comportement coopératif inattendu. Parmi ceux-ci, la répétition des interactions, la réputation ou encore l'appartenance à des groupes reconnaissables ont souvent été mentionnés. Toutefois, les travaux de Nowak et May (1992) ont montré que le simple fait de disposer les joueurs selon une structure spatiale en leur permettant d'interagir uniquement avec leurs voisins directs est suffisant pour maintenir un certain niveau de coopération même si le jeu est joué de manière anonyme et sans répétitions. L'étude de Nowak et May, ainsi qu'un nombre substantiel de travaux qui ont suivi, étaient basés sur des structures régulières telles que des grilles à deux dimensions. Axelrod et al. (2002) ont montré qu'en randomisant le choix des voisins, i.e. en abandonnant une localisation géographique stricte, la coopération peut malgré tout émerger, pour autant que les schémas d'interactions restent stables au cours du temps. Ceci est un premier pas en direction d'une structure de réseau social. Toutefois, suite aux travaux précurseurs de sociologues des années soixante, tels que ceux de Milgram (1967), il est devenu clair ces dernières années qu'une grande partie des réseaux d'interactions sociaux et biologiques, et même quelques réseaux technologiques, possèdent des propriétés particulières, et partiellement inattendues, qui les distinguent de graphes réguliers ou aléatoires. Entre autres, ils affichent en général une distribution du degré relativement large ainsi qu'une structure de "petit-monde". Grossièrement parlant, un graphe "petit-monde" est un réseau où tout individu se trouve relativement près de tout autre individu en termes de distance sociale, une propriété également présente dans les graphes aléatoires mais absente des grilles régulières. Par contre, les réseaux "petit-monde" ont, contrairement aux graphes aléatoires, une certaine structure de localité, mesurée par exemple par une quantité appelée le "coefficient de clustering". Dans le même esprit, plusieurs situations réelles de conflit en économie et sociologie ne sont pas bien décrites ni par des positions géographiquement fixes des individus en grilles régulières, ni par des graphes aléatoires. De plus, il est bien connu que la structure même d'un réseau peut passablement influencer des phénomènes dynamiques tels que la manière qu'a une maladie de se répandre à travers une population, ou encore la façon dont des idées ou une information s'y propagent. Ainsi, durant cette dernière décennie, l'attention de la recherche s'est tout naturellement déplacée des graphes aléatoires et réguliers vers de meilleurs modèles de structure d'interactions sociales. L'objectif principal de ce travail est de découvrir si la structure sous-jacente de graphe de vrais réseaux sociaux peut fournir des explications quant aux raisons pour lesquelles on trouve, chez certains groupes d'êtres humains ou d'animaux, des niveaux de coopération supérieurs à ce qui est prescrit par la théorie classique des jeux. Dans l'optique d'atteindre ce but, je commence par étudier un véritable réseau de collaborations scientifiques et, en utilisant diverses mesures statistiques, je mets en évidence la manière dont il diffère de réseaux biologiques ou technologiques. De plus, j'extrais et je décris sa structure de communautés en tenant compte de l'intensité d'une collaboration. Finalement, j'examine l'évolution temporelle du réseau depuis son origine jusqu'à son état en 2006, date à laquelle l'étude a été effectuée, en suggérant également une vue effective du réseau par opposition à une vue historique. Par la suite, je combine la théorie évolutionnaire des jeux avec des réseaux comprenant plusieurs modèles et le réseau de collaboration susmentionné, afin de déterminer les propriétés structurelles utiles à la promotion de la coopération et les mécanismes responsables du maintien de celle-ci. Je mets en évidence le fait que, pour ne pas succomber à la défection, les coopérateurs exploitent dans la mesure du possible l'hétérogénéité des réseaux sociaux en termes de degré ainsi que la structure de communautés sous-jacente de ces mêmes réseaux. Finalement, je montre que le niveau de coopération et sa stabilité dépendent non seulement du jeu joué, mais aussi des règles de la dynamique évolutionnaire utilisées et du calcul du bénéfice d'un individu.

BME-based uncertainty assessment of the Chernobyl fallout

The vast territories that have been radioactively contaminated during the 1986 Chernobyl accident provide a substantial data set of radioactive monitoring data, which can be used for the verification and testing of the different spatial estimation (prediction) methods involved in risk assessment studies. Using the Chernobyl data set for such a purpose is motivated by its heterogeneous spatial structure (the data are characterized by large-scale correlations, short-scale variability, spotty features, etc.). The present work is concerned with the application of the Bayesian Maximum Entropy (BME) method to estimate the extent and the magnitude of the radioactive soil contamination by 137Cs due to the Chernobyl fallout. The powerful BME method allows rigorous incorporation of a wide variety of knowledge bases into the spatial estimation procedure leading to informative contamination maps. Exact measurements (?hard? data) are combined with secondary information on local uncertainties (treated as ?soft? data) to generate science-based uncertainty assessment of soil contamination estimates at unsampled locations. BME describes uncertainty in terms of the posterior probability distributions generated across space, whereas no assumption about the underlying distribution is made and non-linear estimators are automatically incorporated. Traditional estimation variances based on the assumption of an underlying Gaussian distribution (analogous, e.g., to the kriging variance) can be derived as a special case of the BME uncertainty analysis. The BME estimates obtained using hard and soft data are compared with the BME estimates obtained using only hard data. The comparison involves both the accuracy of the estimation maps using the exact data and the assessment of the associated uncertainty using repeated measurements. Furthermore, a comparison of the spatial estimation accuracy obtained by the two methods was carried out using a validation data set of hard data. Finally, a separate uncertainty analysis was conducted that evaluated the ability of the posterior probabilities to reproduce the distribution of the raw repeated measurements available in certain populated sites. The analysis provides an illustration of the improvement in mapping accuracy obtained by adding soft data to the existing hard data and, in general, demonstrates that the BME method performs well both in terms of estimation accuracy as well as in terms estimation error assessment, which are both useful features for the Chernobyl fallout study.

Viability and Management of an Endangered Capercaillie (Tetrao urogallus) Metapopulation in the Jura Mountains, Western Switzerland

The populations of Capercaillie (Tetrao urogallus), the largest European grouse, have seriously declined during the last century over most of their distribution in western and central Europe. In the Jura mountains, the relict population is now isolated and critically endangered (about 500 breeding adults). We developed a simulation software (TetrasPool) that accounts for age and spatial structure as well as stochastic processes, to perform a viability analysis and explore management scenarios for this population, capitalizing on a 24 years-long series of field data. Simulations predict a marked decline and a significant extinction risk over the next century, largely due to environmental and demographic stochasticity (average values of life-history parameters would otherwise allow stability). Variances among scenarios mainly stem from uncertainties about the shape and intensity of density dependence. Uncertainty analyses suggest to focus conservation efforts on enhancing, not only adult survival (as often advocated for long-lived species), but also recruitment. The juvenile stage matters when local populations undergo extinctions, because it ensures connectivity and recolonization. Besides limiting human perturbations, a silvicultural strategy aimed at opening forest structure should improve the quality and surface of available patches, independent of their size and localization. Such measures are to be taken urgently, if the population is to be saved.

A diagram of public spaces within urban landscape as a strategy for sustainable urban planning in Chinese cities

Destruction of historical urban fabric in many Chinese cities and towns, without the possibility of its recovery as an urban asset, leads us to consider alternative strategies and criteria for formulating new urban projects, using creative urban planning instruments and strategies to provide a sense of place and identity to the urban landscape. The challenge is to set up an urban structure that constitutes a spatial reference system, a structure consisting of a set of urban landmarks that construct a system of related public spaces, endowed with collective significance and identity. Such a network could include a wide variety of urban typologies and natural elements. An important result of this strategy would be the recovery of the social and cultural values attached to the natural landscape in Chinese civilization. Hangzhou city will be analyzed as a case study

Potencial de mercado y estructura espacial de los salarios en las regiones españolas, 1955-1995

En este artículo se examina la relación existente entre los salarios de las regiones españolas y su potencial de mercado en el período 1955-1995. Se prueba la existencia de una estructura espacial de los salarios, en la que los salarios disminuyen al alejarnos de las regiones de renta elevada. Este resultado refuerza la hipótesis de la existencia de una dinámica aglomerativa en España durante la segunda mitad del siglo XX. Sin embargo, el efecto del potencial de mercado sobre los salarios disminuye en la segunda parte del período (1975-1995). Este resultado es consistente con la apertura de una senda de dispersión en la localización de la actividad industrial a partir de mediados de los setenta

Potencial de mercado y estructura espacial de los salarios en las regiones españolas, 1955-1995

En este artículo se examina la relación existente entre los salarios de las regiones españolas y su potencial de mercado en el período 1955-1995. Se prueba la existencia de una estructura espacial de los salarios, en la que los salarios disminuyen al alejarnos de las regiones de renta elevada. Este resultado refuerza la hipótesis de la existencia de una dinámica aglomerativa en España durante la segunda mitad del siglo XX. Sin embargo, el efecto del potencial de mercado sobre los salarios disminuye en la segunda parte del período (1975-1995). Este resultado es consistente con la apertura de una senda de dispersión en la localización de la actividad industrial a partir de mediados de los setenta

Contribution of Topography and Incident Solar Radiation to Variation of Soil and Plant Litter at an Area with Heterogeneous Terrain

Natural processes that determine soil and plant litter properties are controlled by multiple factors. However, little attention has been given to distinguishing the effects of environmental factors from the effects of spatial structure of the area on the distribution of soil and litter properties in tropical ecosystems covering heterogeneous topographies. The aim of this study was to assess patterns of soil and litter variation in a tropical area that intercepts different levels of solar radiation throughout the year since its topography has slopes predominantly facing opposing geographic directions. Soil data (pH, C, N, P, H+Al, Ca, Mg, K, Al, Na, sand, and silt) and plant litter data (N, K, Ca, P, and Mg) were gathered together with the geographic coordinates (to model the spatial structure) of 40 sampling units established at two sites composed of slopes predominantly facing northwest and southeast (20 units each). Soil and litter chemical properties varied more among slopes within similar geographic orientations than between the slopes facing opposing directions. Both the incident solar radiation and the spatial structure of the area were relevant in explaining the patterns detected in variation of soil and plant litter. Individual contributions of incident solar radiation to explain the variation in the properties evaluated suggested that this and other environmental factors may play a particularly relevant role in determining soil and plant litter distribution in tropical areas with heterogeneous topography. Furthermore, this study corroborates that the spatial structure of the area also plays an important role in the distribution of soil and litter within this type of landscape, which appears to be consistent with the action of water movement mechanisms in such areas.

Potencial de mercado y estructura espacial de los salarios en las regiones españolas, 1955-1995

En este artículo se examina la relación existente entre los salarios de las regiones españolas y su potencial de mercado en el período 1955-1995. Se prueba la existencia de una estructura espacial de los salarios, en la que los salarios disminuyen al alejarnos de las regiones de renta elevada. Este resultado refuerza la hipótesis de la existencia de una dinámica aglomerativa en España durante la segunda mitad del siglo XX. Sin embargo, el efecto del potencial de mercado sobre los salarios disminuye en la segunda parte del período (1975-1995). Este resultado es consistente con la apertura de una senda de dispersión en la localización de la actividad industrial a partir de mediados de los setenta

Potencial de mercado y estructura espacial de los salarios en las regiones españolas, 1955-1995

En este artículo se examina la relación existente entre los salarios de las regiones españolas y su potencial de mercado en el período 1955-1995. Se prueba la existencia de una estructura espacial de los salarios, en la que los salarios disminuyen al alejarnos de las regiones de renta elevada. Este resultado refuerza la hipótesis de la existencia de una dinámica aglomerativa en España durante la segunda mitad del siglo XX. Sin embargo, el efecto del potencial de mercado sobre los salarios disminuye en la segunda parte del período (1975-1995). Este resultado es consistente con la apertura de una senda de dispersión en la localización de la actividad industrial a partir de mediados de los setenta

Multifractal portrayal of the distribution of the Swiss population

The present research studies the spatial patterns of the distribution of the Swiss population (DSP). This description is carried out using a wide variety of global spatial structural analysis tools such as topological, statistical and fractal measures, which enable the estimation of the spatial degree of clustering of a point pattern. A particular attention is given to the analysis of the multifractality to characterize the spatial structure of the DSP at different scales. This will be achieved by measuring the generalized q-dimensions and the singularity spectrum. This research is based on high quality data of the Swiss Population Census of the Year 2000 at a hectometric resolution (grid 100 x 100 m) issued by the Swiss Federal Statistical Office (FSO).

Multiscale assessment of plant diversity in wooded pastures of the Jura mountains

Résumé La diminution de la biodiversité, à toutes les échelles spatiales et sur l'ensemble de la planète, compte parmi les problèmes les plus préoccupants de notre époque. En terme de conservation, il est aujourd'hui primordial de mieux comprendre les mécanismes qui créent et maintiennent la biodiversité dans les écosystèmes naturels ou anthropiques. La présente étude a pour principal objectif d'améliorer notre compréhension des patrons de biodiversité végétale et des mécanismes sous jacents, dans un écosystème complexe, riche en espèces et à forte valeur patrimoniale, les pâturages boisés jurassiens. Structure et échelle spatiales sont progressivement reconnues comme des dimensions incontournables dans l'étude des patrons de biodiversité. De plus, ces deux éléments jouent un rôle central dans plusieurs théories écologiques. Toutefois, peu d'hypothèses issues de simulations ou d'études théoriques concernant le lien entre structure spatiale du paysage et biodiversité ont été testées de façon empirique. De même, l'influence des différentes composantes de l'échelle spatiale sur les patrons de biodiversité est méconnue. Cette étude vise donc à tester quelques-unes de ces hypothèses et à explorer les patrons spatiaux de biodiversité dans un contexte multi-échelle, pour différentes mesures de biodiversité (richesse et composition en espèces) à l'aide de données de terrain. Ces données ont été collectées selon un plan d'échantillonnage hiérarchique. Dans un premier temps, nous avons testé l'hypothèse élémentaire selon laquelle la richesse spécifique (le nombre d'espèces sur une surface donnée) est liée à l'hétérogénéité environnementale quelque soit l'échelle. Nous avons décomposé l'hétérogénéité environnementale en deux parties, la variabilité des conditions environnementales et sa configuration spatiale. Nous avons montré que, en général, la richesse spécifique augmentait avec l'hétérogénéité de l'environnement : elle augmentait avec le nombre de types d'habitats et diminuait avec l'agrégation spatiale de ces habitats. Ces effets ont été observés à toutes les échelles mais leur nature variait en fonction de l'échelle, suggérant une modification des mécanismes. Dans un deuxième temps, la structure spatiale de la composition en espèces a été décomposée en relation avec 20 variables environnementales et 11 traits d'espèces. Nous avons utilisé la technique de partition de la variation et un descripteur spatial, récemment développé, donnant accès à une large gamme d'échelles spatiales. Nos résultats ont montré que la structure spatiale de la composition en espèces végétales était principalement liée à la topographie, aux échelles les plus grossières, et à la disponibilité en lumière, aux échelles les plus fines. La fraction non-environnementale de la variation spatiale de la composition spécifique avait une relation complexe avec plusieurs traits d'espèces suggérant un lien avec des processus biologiques tels que la dispersion, dépendant de l'échelle spatiale. Dans un dernier temps, nous avons testé, à plusieurs échelles spatiales, les relations entre trois composantes de la biodiversité : la richesse spécifique totale d'un échantillon (diversité gamma), la richesse spécifique moyenne (diversité alpha), mesurée sur des sous-échantillons, et les différences de composition spécifique entre les sous-échantillons (diversité beta). Les relations deux à deux entre les diversités alpha, beta et gamma ne suivaient pas les relations attendues, tout du moins à certaines échelles spatiales. Plusieurs de ces relations étaient fortement dépendantes de l'échelle. Nos résultats ont mis en évidence l'importance du rapport d'échelle (rapport entre la taille de l'échantillon et du sous-échantillon) lors de l'étude des patrons spatiaux de biodiversité. Ainsi, cette étude offre un nouvel aperçu des patrons spatiaux de biodiversité végétale et des mécanismes potentiels permettant la coexistence des espèces. Nos résultats suggèrent que les patrons de biodiversité ne peuvent être expliqués par une seule théorie, mais plutôt par une combinaison de théories. Ils ont également mis en évidence le rôle essentiel joué par la structure spatiale dans la détermination de la biodiversité, quelque soit le composant de la biodiversité considéré. Enfin, cette étude souligne l'importance de prendre en compte plusieurs échelles spatiales et différents constituants de l'échelle spatiale pour toute étude relative à la diversité spécifique. Abstract The world-wide loss of biodiversity at all scales has become a matter of urgent concern, and improving our understanding of local drivers of biodiversity in natural and anthropogenic ecosystems is now crucial for conservation. The main objective of this study was to further our comprehension of the driving forces controlling biodiversity patterns in a complex and diverse ecosystem of high conservation value, wooded pastures. Spatial pattern and scale are central to several ecological theories, and it is increasingly recognized that they must be taken -into consideration when studying biodiversity patterns. However, few hypotheses developed from simulations or theoretical studies have been tested using field data, and the evolution of biodiversity patterns with different scale components remains largely unknown. We test several such hypotheses and explore spatial patterns of biodiversity in a multi-scale context and using different measures of biodiversity (species richness and composition), with field data. Data were collected using a hierarchical sampling design. We first tested the simple hypothesis that species richness, the number of species in a given area, is related to environmental heterogeneity at all scales. We decomposed environmental heterogeneity into two parts: the variability of environmental conditions and its spatial configuration. We showed that species richness generally increased with environmental heterogeneity: species richness increased with increasing number of habitat types and with decreasing spatial aggregation of those habitats. Effects occurred at all scales but the nature of the effect changed with scale, suggesting a change in underlying mechanisms. We then decomposed the spatial structure of species composition in relation to environmental variables and species traits using variation partitioning and a recently developed spatial descriptor, allowing us to capture a wide range of spatial scales. We showed that the spatial structure of plant species composition was related to topography at the coarsest scales and insolation at finer scales. The non-environmental fraction of the spatial variation in species composition had a complex relationship with several species traits, suggesting a scale-dependent link to biological processes, particularly dispersal. Finally, we tested, at different spatial scales, the relationships between different components of biodiversity: total sample species richness (gamma diversity), mean species .richness (alpha diversity), measured in nested subsamples, and differences in species composition between subsamples (beta diversity). The pairwise relationships between alpha, beta and gamma diversity did not follow the expected patterns, at least at certain scales. Our result indicated a strong scale-dependency of several relationships, and highlighted the importance of the scale ratio when studying biodiversity patterns. Thus, our results bring new insights on the spatial patterns of biodiversity and the possible mechanisms allowing species coexistence. They suggest that biodiversity patterns cannot be explained by any single theory proposed in the literature, but a combination of theories is sufficient. Spatial structure plays a crucial role for all components of biodiversity. Results emphasize the importance of considering multiple spatial scales and multiple scale components when studying species diversity.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.