Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Simulation of interface dynamics across pore discontinuities

We study the dynamics of a water-oil meniscus moving from a smaller to a larger pore. The process is characterised by an abrupt change in the configuration, yielding a sudden energy release. A theoretic study for static conditions provides analytical solutions of the surface energy content of the system. Although the configuration after the sudden energy release is energetically more convenient, an energy barrier must be overcome before the process can happen spontaneously. The energy barrier depends on the system geometry and on the flow parameters. The analytical results are compared to numerical simulations that solve the full Navier-Stokes equation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. First, the numerical simulations of a quasi-static process are validated by comparison with the analytical solutions for a static meniscus, then numerical simulations with varying injection velocity are used to investigate dynamic effects on the configuration change. During the sudden energy jump the system exhibits an oscillatory behaviour. Extension to more complex geometries might elucidate the mechanisms leading to a dynamic capillary pressure and to bifurcations in final distributions of fluid phases in porous

Multiple processes regulate long-term population dynamics of sea urchins on Mediterranean rocky reefs

We annually monitored the abundance and size structure of herbivorous sea urchin populations (Paracentrotus lividus and Arbacia lixula) inside and outside a marine reserve in the Northwestern Mediterranean on two distinct habitats (boulders and vertical walls) over a period of 20 years, with the aim of analyzing changes at different temporal scales in relation to biotic and abiotic drivers. P. lividus exhibited significant variability in density over time on boulder bottoms but not on vertical walls, and temporal trends were not significantly different between the protection levels. Differences in densities were caused primarily by variance in recruitment, which was less pronounced inside the MPA and was correlated with adult density, indicating density-dependent recruitment under high predation pressure, as well as some positive feedback mechanisms that may facilitate higher urchin abundances despite higher predator abundance. Populations within the reserve were less variable in abundance and did not exhibit the hyper-abundances observed outside the reserve, suggesting that predation effects maybe more subtle than simply lowering the numbers of urchins in reserves. A. lixula densities were an order of magnitude lower than P. lividus densities and varied within sites and over time on boulder bottoms but did not differ between protection levels. In December 2008, an exceptionally violent storm reduced sea urchin densities drastically (by 50% to 80%) on boulder substrates, resulting in the lowest values observed over the entire study period, which remained at that level for at least two years (up to the present). Our results also showed great variability in the biological and physical processes acting at different temporal scales. This study highlights the need for appropriate temporal scales for studies to fully understand ecosystem functioning, the concepts of which are fundamental to successful conservation and management.

The population dynamics of Halecium petrosum and Halecium pusillum (Hydrozoa, Cnidaria), epiphytes of Halimeda tuna in the nortwestern Mediterranean

Halecium petrosum and Halecium pusillum on the alga Halimeda tuna from Tossa de Mar, northeastern Spain, were studied. Asexual reproduction of H. petrosum, by stolonisation, occurred throughout the year except for July and August. Asexual reproduction of H. pusillum, by planktonic propagules, occurred throughout the year. Sexual reproduction was limited to the autumn in H. petrosum and spring in H. pusillum. The growth rates of colonies of both species were rapid but declined with increased size. Mean colony size over two consecutive two week periods increased approximately five-fold and three-fold for H. petrosum, and six-fold and four-fold for H. pusillum. Mortality was estimated to be high for both species, especially in summer. The maximum life span of colonies (ramets) of both species was estimated to be only eight weeks. Consequently most colonies do not reproduce sexually. The absence of reproduction of H. petrosum in summer, when the turnover of algal thalli was greatest, probably contributed to the summer decline in its abundance. In both species the genet (clone) survives for unknown, possibly very long, periods by asexual reproduction which facilites colonisation of other substrata.

Marine and transitional Middle/Upper Eocenen units of the Southeastern Pyrenean Foreland Basin (NE Spain)

The stratigraphic basis of this work has allowed the use of larger foraminifers in the biostratigraphic characterisation of the new Shallow Benthic Zones (SBZ). This part of the volume presents a description of the sedimentary cycles formed by the transgressive-regressive systems of the Lutetian and Bartonian in the southeastern sector of the Ebro Foreland Basin. Concerning the Lutetian deposits studied in the Amer-Vic and Empordà areas, four sedimentary cycles have been characterised. The first and second are found within the Tavertet/Girona Limestone Formation (Reguant, 1967; Pallí, 1972), while the third and fourth cycles cover the Coll de Malla Marl Formation (Clavell et al., 1970), the Bracons Formation (Gich, 1969, 1972), the Banyoles Marl Formation (Almela and Ríos, 1943), and the Bellmunt Formation (Gich, 1969, 1972). In the Bartonian deposits studied in the Igualada area, two transgressive-regressive sedimentary cycles have been characterised in the Collbàs Formation (Ferrer, 1971), the Igualada Formation (Ferrer, 1971), and the Tossa Formation (Ferrer, 1971). The Shallow Benthic Zones (SBZs) recognised within the Lutetian are the following: SBZ 13, from the Early Lutetian, in the transgressive system of the first cycle; SBZ 14, from the Middle Lutetian, in the second cycle and the lower part of the transgressive system of the third cycle; SBZ 15, from the Middle Lutetian, in the remaining parts of the third system; SBZ 16, from the Late Lutetian, throughout the fourth cycle. The association of larger foraminifers in the first and second cycles of the Bartonian in the Igualada area has been used as the basis for the definition of SBZs 17 and 18 recognised in the Bartonian of the western Tethys.

Information sharing and social network dynamics : a coevolutionary approach

The capacity to interact socially and share information underlies the success of many animal species, humans included. Researchers of many fields have emphasized the evo¬lutionary significance of how patterns of connections between individuals, or the social networks, and learning abilities affect the information obtained by animal societies. To date, studies have focused on the dynamics either of social networks, or of the spread of information. The present work aims to study them together. We make use of mathematical and computational models to study the dynamics of networks, where social learning and information sharing affect the structure of the population the individuals belong to. The number and strength of the relationships between individuals, in turn, impact the accessibility and the diffusion of the shared information. Moreover, we inves¬tigate how different strategies in the evaluation and choice of interacting partners impact the processes of knowledge acquisition and social structure rearrangement. First, we look at how different evaluations of social interactions affect the availability of the information and the network topology. We compare a first case, where individuals evaluate social exchanges by the amount of information that can be shared by the partner, with a second case, where they evaluate interactions by considering their partners' social status. We show that, even if both strategies take into account the knowledge endowments of the partners, they have very different effects on the system. In particular, we find that the first case generally enables individuals to accumulate higher amounts of information, thanks to the more efficient patterns of social connections they are able to build. Then, we study the effects that homophily, or the tendency to interact with similar partners, has on knowledge accumulation and social structure. We compare the case where individuals who know the same information are more likely to learn socially from each other, to the opposite case, where individuals who know different information are instead more likely to learn socially from each other. We find that it is not trivial to claim which strategy is better than the other. Depending on the possibility of forgetting information, the way new social partners can be chosen, and the population size, we delineate the conditions for which each strategy allows accumulating more information, or in a faster way For these conditions, we also discuss the topological characteristics of the resulting social structure, relating them to the information dynamics outcome. In conclusion, this work paves the road for modeling the joint dynamics of the spread of information among individuals and their social interactions. It also provides a formal framework to study jointly the effects of different strategies in the choice of partners on social structure, and how they favor the accumulation of knowledge in the population. - La capacité d'interagir socialement et de partager des informations est à la base de la réussite de nombreuses espèces animales, y compris les humains. Les chercheurs de nombreux domaines ont souligné l'importance évolutive de la façon dont les modes de connexions entre individus, ou réseaux sociaux et les capacités d'apprentissage affectent les informations obtenues par les sociétés animales. À ce jour, les études se sont concentrées sur la dynamique soit des réseaux sociaux, soit de la diffusion de l'information. Le présent travail a pour but de les étudier ensemble. Nous utilisons des modèles mathématiques et informatiques pour étudier la dynamique des réseaux, où l'apprentissage social et le partage d'information affectent la structure de la population à laquelle les individus appartiennent. Le nombre et la solidité des relations entre les individus ont à leurs tours un impact sur l'accessibilité et la diffusion de l'informa¬tion partagée. Par ailleurs, nous étudions comment les différentes stratégies d'évaluation et de choix des partenaires d'interaction ont une incidence sur les processus d'acquisition des connaissances ainsi que le réarrangement de la structure sociale. Tout d'abord, nous examinons comment des évaluations différentes des interactions sociales influent sur la disponibilité de l'information ainsi que sur la topologie du réseau. Nous comparons un premier cas, où les individus évaluent les échanges sociaux par la quantité d'information qui peut être partagée par le partenaire, avec un second cas, où ils évaluent les interactions en tenant compte du statut social de leurs partenaires. Nous montrons que, même si les deux stratégies prennent en compte le montant de connaissances des partenaires, elles ont des effets très différents sur le système. En particulier, nous constatons que le premier cas permet généralement aux individus d'accumuler de plus grandes quantités d'information, grâce à des modèles de connexions sociales plus efficaces qu'ils sont capables de construire. Ensuite, nous étudions les effets que l'homophilie, ou la tendance à interagir avec des partenaires similaires, a sur l'accumulation des connaissances et la structure sociale. Nous comparons le cas où des personnes qui connaissent les mêmes informations sont plus sus¬ceptibles d'apprendre socialement l'une de l'autre, au cas où les individus qui connaissent des informations différentes sont au contraire plus susceptibles d'apprendre socialement l'un de l'autre. Nous constatons qu'il n'est pas trivial de déterminer quelle stratégie est meilleure que l'autre. En fonction de la possibilité d'oublier l'information, la façon dont les nouveaux partenaires sociaux peuvent être choisis, et la taille de la population, nous déterminons les conditions pour lesquelles chaque stratégie permet d'accumuler plus d'in¬formations, ou d'une manière plus rapide. Pour ces conditions, nous discutons également les caractéristiques topologiques de la structure sociale qui en résulte, les reliant au résultat de la dynamique de l'information. En conclusion, ce travail ouvre la route pour la modélisation de la dynamique conjointe de la diffusion de l'information entre les individus et leurs interactions sociales. Il fournit également un cadre formel pour étudier conjointement les effets de différentes stratégies de choix des partenaires sur la structure sociale et comment elles favorisent l'accumulation de connaissances dans la population.

Roles of astrocytic sodium dynamics in the neurometabolic coupling : a study by cellular imaging

RESUME LARGE PUBLIC Le système nerveux central est principalement composé de deux types de cellules :les neurones et les cellules gliales. Ces dernières, bien que l'emportant en nombre sur les neurones, ont longtemps été considérées comme des cellules sans intérêts par les neuroscientifiques. Hors, les connaissances modernes à leurs sujets indiquent qu'elles participent à la plupart des tâches physiologiques du cerveau. Plus particulièrement, elles prennent part aux processus énergétiques cérébraux. Ceux-ci, en plus d'être vitaux, sont particulièrement intrigants puisque le cerveau représente seulement 2 % de la masse corporelle mais consomme environ 25 % du glucose (substrat énergétique) corporel. Les astrocytes, un type de cellules gliales, jouent un rôle primordial dans cette formidable utilisation de glucose par le cerveau. En effet, l'activité neuronale (transmission de l'influx nerveux) est accompagnée d'une augmentation de la capture de glucose, issu de la circulation sanguine, par les astrocytes. Ce phénomène est appelé le «couplage neurométabolique » entre neurones et astrocytes. L'ion sodium fait partie des mécanismes cellulaires entrant en fonction lors de ces processus. Ainsi, dans le cadre de cette thèse, les aspects dynamiques de la régulation du sodium astrocytaire et leurs implications dans le couplage neurométabolique ont été étudiés par des techniques d'imagerie cellulaires. Ces études ont démontré que les mitochondries, machineries cellulaires convertissant l'énergie contenue dans le glucose, participent à la régulation du sodium astrocytaire. De plus, ce travail de thèse a permis de découvrir que les astrocytes sont capables de se transmettre, sous forme de vagues de sodium se propageant de cellules en cellules, un message donnant l'ordre d'accroître leur consommation d'énergie. Cette voie de signalisation leur permettrait de fournir de l'énergie aux neurones suite à leur activation. RESUME Le glutamate libéré dans la fente synaptique pendant l'activité neuronale, est éliminé par les astrocytes environnants. Le glutamate est co-transporté avec des ions sodiques, induisant une augmentation intracellulaire de sodium (Na+i) dans les astrocytes. Cette élévation de Na+i déclenche une cascade de mécanismes moléculaires qui aboutissent à la production de substrats énergétiques pouvant être utilisés par les neurones. Durant cette thèse, la mesure simultanée du sodium mitochondrial (Na+mit) et cytosolique par des techniques d'imagerie utilisant des sondes fluorescentes spécifiques, a indiqué que les variations de Na+i induites par le transport du glutamate sont transmises aux mitochondries. De plus, les voies d'entrée et de sortie du sodium mitochondrial ont été identifiées. L'échangeur de Na+ et de Ca2+ mitochondrial semble jouer un rôle primordial dans l'influx de Na+mit, alors que l'efflux de Na+mit est pris en charge par l'échangeur de Na+ et de H+ mitochondrial. L'étude du Na+mit a nécessité l'utilisation d'un système de photoactivation. Les sources de lumière ultraviolette (UV) classiques utilisées à cet effet (lasers, lampes à flash) ayant plusieurs désavantages, une alternative efficace et peu coûteuse a été développée. Il s'agit d'un système compact utilisant une diode électroluminescente (LED) à haute puissance et de longueur d'onde de 365nm. En plus de leurs rôles dans le couplage neurométabolique, les astrocytes participent à la signalisation multicellulaire en transmettant des vagues intercellulaires de calcium. Ce travail de thèse démontre également que des vagues intercellulaires de sodium peuvent être évoquées en parallèle à ces vagues calciques. Le glutamate, suite à sa libération par un mécanisme dépendent du calcium, est réabsorbé par les transporteurs au glutamate. Ce mécanisme a pour conséquence la génération de vagues sodiques se propageant de cellules en cellules. De plus, ces vagues sodiques sont corrélées spatialement avec une consommation accrue de glucose par les astrocytes. En conclusion, ce travail de thèse a permis de montrer que le signal sodique astrocytaire, déclenché en réponse au glutamate, se propage à la fois de façon intracellulaire aux mitochondries et de façon intercellulaire. Ces résultats suggèrent que les astrocytes fonctionnent comme un réseau de cellules nécessaire au couplage énergétique concerté entre neurones et astrocytes et que le sodium est un élément clé dans les mécanismes de signalisations cellulaires sous-jacents. SUMMARY Glutamate, released in the synaptic cleft during neuronal activity, is removed by surrounding astrocytes. Glutamate is taken-up with Na+ ions by specific transporters, inducing an intracellular Na+ (Na+i) elevation in astrocytes which triggers a cascade of molecular mechanisms that provides metabolic substrates to neurons. Thus, astrocytic Na+i homeostasis represents a key component of the so-called neurometabolic coupling. In this context, the first part of this thesis work was aimed at investigating whether cytosolic Na+ changes are transmitted to mitochondria, which could therefore influence their function and contribute to the overall intracellular Na+ regulation. Simultaneous monitoring of both mitochondrial Na+ (Na+mit) and cytosolic Na+ changes with fluorescent dyes revealed that glutamate-evoked cytosolic Na+ elevations are indeed transmitted to mitochondria. The mitochondrial Na+/Ca2+ exchangers have a prominent role in the regulation of Na+mit influx pathway, and Na+mit extrusion appears to be mediated by Na+/H+ exchangers. To demonstrate the implication of Na+/Ca2+ exchangers, this study has required the technical development of an UV-flash photolysis system. Because light sources for flash photolysis have to be powerful and in the near UV range, the use of UV lasers or flash lamps is usually required. As an alternative to these UV sources that have several drawbaks, we developped a compact, efficient and lowcost flash photolysis system which employs a high power 365nm light emitting diode. In addition to their role in neurometabolic coupling, astrocytes participate in multicellular signaling by transmitting intercellular Ca2+ waves. The third part of this thesis show that intercellular Na+ waves can be evoked in parallel to Ca2+ waves. Glutamate released by a Ca2+ wave-dependent mechanism is taken up by glutamate transporters, resulting in a regenerative propagation of cytosolic Na+ increases. Na+ waves in turn lead to a spatially correlated increase in glucose uptake. In conclusion, the present thesis demonstrates that glutamate-induced Na+ changes occurring in the cytosol of astrocytes propagate to both the mitochondrial matrix and the astrocytic network. These results furthermore support the view that astrocytic Na+ is a signal coupled to the brain energy metabolism.

Organic matter processing and soil evolution in a braided river system

Traditionally, braided river research has considered flow, sediment transport processes and, recently, vegetation dynamics in relation to river morphodynamics. However, if considering the development of woody vegetated patches over a time scale of decades, we must consider the extent to which soil forming processes, particularly related to soil organic matter, impact the alluvial geomorphic-vegetation system. Here we quantify the soil organic matter processing (humification) that occurs on young alluvial landforms. We sampled different geomorphic units, ranging from the active river channel to established river terraces in a braided river system. For each geomorphic unit, soil pits were used to sample sediment/soil layers that were analysed in terms of grain size (<2mm) and organic matter quantity and quality (RockEval method). A principal components analysis was used to identify patterns in the dataset. Results suggest that during the succession from bare river gravels to a terrace soil, there is a transition from small amounts of external organic matter supply provided by sedimentation processes (e.g. organic matter transported in suspension and deposited on bars), to large amounts of autogenic in situ organic matter production due to plant colonisation. This appears to change the time scale and pathways of alluvial succession (bio-geomorphic succession). However, this process is complicated by: the ongoing possibility of local sedimentation, which can serve to isolate surface layers via aggradation from the exogenic supply; and erosion which tends to create fresh deposits upon which organic matter processing must re-start. The result is a complex pattern of organic matter states as well as a general lack of any clear chronosequence within the active river corridor. This state reflects the continual battle between deposition events that can isolate organic matter from the surface, erosion events that can destroy accumulating organic matter and the early ecosystem processes necessary to assist the co-evolution of soil and vegetation. A key question emerges over the extent to which the fresh organic matter deposited in the active zone is capable of significantly transforming the local geochemical environment sufficiently to accelerate soil development.

Horizontal vestibulo-ocular reflex dynamics in acute vestibular neuritis and viral labyrinthitis: evidence of otolith-canal interaction.

OBJECTIVE: To evaluate the dynamic properties of the horizontal vestibulo-ocular reflex (h-VOR) in the acute stage of two common labyrinthine diseases that provoke severe attacks of vertigo with spontaneous nystagmus: vestibular neuritis (vestibular loss alone) and viral labyrinthitis (cochleovestibular loss). MATERIAL AND METHODS: Sixty-three patients were investigated: 42 were diagnosed with vestibular neuritis and 21 with viral labyrinthitis. The h-VOR function was evaluated by conventional caloric and impulsive testing. A simplified model of vestibular function was used to analyze the vestibulo-ocular response to rotational stimulation. RESULTS: The results showed a significant difference in h-VOR characteristics between the two pathologies. Patients with vestibular neuritis exhibited a strong horizontal semicircular canal deficit, but no h-VOR asymmetry between the two rotational directions. In contrast, patients with viral labyrinthitis demonstrated moderate canal paresis and a marked h-VOR deficit in rotation toward the affected ear. CONCLUSION: These findings support the hypothesis that the h-VOR dynamic asymmetry that occurs after an acute unilateral inner ear lesion is not due to canal dysfunction alone, but involves complex adaptive changes in the central VOR that may implicate the otolith system. Based on histopathologic and clinical differences in the two pathologies reported in the literature, we postulate that this otolith-canal interaction is mainly linked to the loss of saccular function.

Multiple processes regulate long-term population dynamics of sea urchins on Mediterranean rocky reefs

We annually monitored the abundance and size structure of herbivorous sea urchin populations (Paracentrotus lividus and Arbacia lixula) inside and outside a marine reserve in the Northwestern Mediterranean on two distinct habitats (boulders and vertical walls) over a period of 20 years, with the aim of analyzing changes at different temporal scales in relation to biotic and abiotic drivers. P. lividus exhibited significant variability in density over time on boulder bottoms but not on vertical walls, and temporal trends were not significantly different between the protection levels. Differences in densities were caused primarily by variance in recruitment, which was less pronounced inside the MPA and was correlated with adult density, indicating density-dependent recruitment under high predation pressure, as well as some positive feedback mechanisms that may facilitate higher urchin abundances despite higher predator abundance. Populations within the reserve were less variable in abundance and did not exhibit the hyper-abundances observed outside the reserve, suggesting that predation effects maybe more subtle than simply lowering the numbers of urchins in reserves. A. lixula densities were an order of magnitude lower than P. lividus densities and varied within sites and over time on boulder bottoms but did not differ between protection levels. In December 2008, an exceptionally violent storm reduced sea urchin densities drastically (by 50% to 80%) on boulder substrates, resulting in the lowest values observed over the entire study period, which remained at that level for at least two years (up to the present). Our results also showed great variability in the biological and physical processes acting at different temporal scales. This study highlights the need for appropriate temporal scales for studies to fully understand ecosystem functioning, the concepts of which are fundamental to successful conservation and management.

Silene as a model system in ecology and evolution.

The genus Silene, studied by Darwin, Mendel and other early scientists, is re-emerging as a system for studying interrelated questions in ecology, evolution and developmental biology. These questions include sex chromosome evolution, epigenetic control of sex expression, genomic conflict and speciation. Its well-studied interactions with the pathogen Microbotryum has made Silene a model for the evolution and dynamics of disease in natural systems, and its interactions with herbivores have increased our understanding of multi-trophic ecological processes and the evolution of invasiveness. Molecular tools are now providing new approaches to many of these classical yet unresolved problems, and new progress is being made through combining phylogenetic, genomic and molecular evolutionary studies with ecological and phenotypic data.

Ising critical behavior of a non-Halmiltonian lattice system

We study steady states in d-dimensional lattice systems that evolve in time by a probabilistic majority rule, which corresponds to the zero-temperature limit of a system with conflicting dynamics. The rule satisfies detailed balance for d=1 but not for d>1. We find numerically nonequilibrium critical points of the Ising class for d=2 and 3.

Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

Growth of Crassostrea gasar cultured in marine and estuary environments in Brazilian waters

The objective of this work was to evaluate the growth of the mangrove oyster Crassostrea gasar cultured in marine and estuarine environments. Oysters were cultured for 11 months in a longline system in two study sites - São Francisco do Sul and Florianópolis -, in the state of Santa Catarina, Southern Brazil. Water chlorophyll-α concentration, temperature, and salinity were measured weekly. The oysters were measured monthly (shell size and weight gain) to assess growth. At the end of the culture period, the average wet flesh weight, dry flesh weight, and shell weight were determined, as well as the distribution of oysters per size class. Six nonlinear models (logistic, exponential, Gompertz, Brody, Richards, and Von Bertalanffy) were adjusted to the oyster growth data set. Final mean shell sizes were higher in São Francisco do Sul than in Florianópolis. In addition, oysters cultured in São Francisco do Sul were more uniformly distributed in the four size classes than those cultured in Florianópolis. The highest average values of wet flesh weight and shell weight were observed in São Francisco do Sul, whereas dry flesh weight did not differ between the sites. The estuary environment is more promising for the cultivation of oysters.