Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics

In this paper, by using a stochastic reaction-diffusion-taxis model, we analyze the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters. The model includes intraspecific competition of picophytoplankton for light and nutrients. The multiplicative noise sources present in the model account for random fluctuations of environmental variables. Phytoplankton distributions obtained from the model show a good agreement with experimental data sampled in two different sites of the Sicily Channel. The results could be extended to analyze data collected in different sites of the Mediterranean Sea and to devise predictive models for phytoplankton dynamics in oligotrophic waters.     

Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion Model

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values.     

SUMMER DISTRIBUTION OF PICOPHYTOPLANKTON IN THE NORTH YELLOW SEA

 利用荧光显微技术(Epifluorescence microscopy, EFM)对2006年夏季北黄海水域80个站点的微微型浮游植物进行了检测, 并对其在平面和垂直分布上的变化以及昼夜变化情况进行了研究。检测到聚球藻(Synechococcus, Syn)和真核球藻(Picoeukaryotes, Euk)两类微微型浮游植物, 未检测到原绿球藻(Prochlorococcus, Pro), 其中Syn以富含藻红素的Syn细胞(PE细胞)为优势种类, 而富含藻蓝素的Syn细胞(PC细胞)数量较少。在荣城湾以东的水域, 各水层Syn和Euk的丰度都较其它水域的高。Syn在北黄海冷水团及附近水域下30 m深处和底层水体中出现明显的低值区, Euk丰度受冷水团影响不明显。在垂直分布上, 水表层和水下10 m深处Syn的丰度高于水下30 m深处和底层, 而Euk在垂直分布上无明显差异。在昼夜变化上, 各水层Syn、Euk丰度的白昼与夜间变化趋势无明显区别。     

Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia

Two multiscale (hybrid) stochastic reaction–diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction–diffusion models. The first hybrid model is based on the models previously developed in the literature. The second hybrid model is based on the application of a recently developed two-regime method (TRM) to a fully molecular-based model, which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model.     

How Diffusivity,Thermocline and Incident Light Intensity Modulate the Dynamics of Deep Chlorophyll Maximum in Tyrrhenian Sea

During the last few years theoretical works have shed new light and proposed new hypotheses on the mechanisms which regulate the spatio-temporal behaviour of phytoplankton communities in marine pelagic ecosystems. Despite this, relevant physical and biological issues, such as effects of the time-dependent mixing in the upper layer, competition between groups, and dynamics of non-stationary deep chlorophyll maxima, are still open questions. In this work, we analyze the spatio-temporal behaviour of five phytoplankton populations in a real marine ecosystem by using a one-dimensional reaction-diffusion-taxis model. The study is performed, taking into account the seasonal variations of environmental variables, such as light intensity, thickness of upper mixed layer and profiles of vertical turbulent diffusivity, obtained starting from experimental findings. Theoretical distributions of phytoplankton cell concentration was converted in chlorophyll concentration, and compared with the experimental profiles measured in a site of the Tyrrhenian Sea at four different times (seasons) of the year, during four different oceanographic cruises. As a result we find a good agreement between theoretical and experimental distributions of chlorophyll concentration. In particular, theoretical results reveal that the seasonal changes of environmental variables play a key role in the phytoplankton distribution and determine the properties of the deep chlorophyll maximum. This study could be extended to other marine ecosystems to predict future changes in the phytoplankton biomass due to global warming, in view of devising strategies to prevent the decline of the primary production and the consequent decrease of fish species.     

Kinetics of target site localization of a protein on DNA: a stochastic approach

It is widely recognized that the cleaving rate of a restriction enzyme on target DNA sequences is several orders-of-magnitude faster than the maximal one calculated from the diffusion-limited theory. It was therefore commonly assumed that the target site interaction of a restriction enzyme with DNA has to occur via two steps: one-dimensional diffusion along a DNA segment, and long-range jumps coming from association-dissociation events. We propose here a stochastic model for this reaction which comprises a series of one-dimensional diffusions of a restriction enzyme on nonspecific DNA sequences interrupted by three-dimensional excursions in the solution until the target sequence is reached. This model provides an optimal finding strategy which explains the fast association rate. Modeling the excursions by uncorrelated random jumps, we recover the expression of the mean time required for target site association to occur given by Berg et al. in 1981, and we explicitly give several physical quantities describing the stochastic pathway of the enzyme. For competitive target sites we calculate two quantities: processivity and preference. By comparing these theoretical expressions to recent experimental data obtained for EcoRV-DNA interaction, we quantify: 1), the mean residence time per binding event of EcoRV on DNA for a representative one-dimensional diffusion coefficient; 2), the average lengths of DNA scanned during the one-dimensional diffusion (during one binding event and during the overall process); and 3), the mean time and the mean number of visits needed to go from one target site to the other. Further, we evaluate the dynamics of DNA cleavage with regard to the probability for the restriction enzyme to perform another one-dimensional diffusion on the same DNA substrate following a three-dimensional excursion.     

Patterns of patchy spread in multi-species reaction–diffusion models

Spread of populations in space often takes place via formation, interaction and propagation of separated patches of high species density, without formation of continuous fronts. This type of spread is called a ‘patchy spread’. In earlier models, this phenomenon was considered to be a result of a pronounced environmental or/and demographic stochasticity. Recently, it was found that a patchy spread can arise in a fully deterministic predator–prey system and in models of infectious diseases; in each case the process takes place in a homogeneous environment. It is well recognized that the observed patterns of patchy spread in nature are a result of interplay between stochastic and deterministic factors. However, the models considering deterministic mechanism of patchy spread are developed and studied much less compared to those based on stochastic mechanisms. A further progress in the understanding of the role of deterministic factors in the patchy spread would be extremely helpful. Here we apply multi-species reaction–diffusion models of two spatial dimensions in a homogeneous environment. We demonstrate that patterns of patchy spread are rather common for the considered approach, in particular, they arise both in mutualism and competition models influenced by predation. We show that this phenomenon can occur in a system without a strong Allee effect, contrary to what was assumed to be crucial in earlier models. We show, as well, a pattern of patchy spread having significantly different speeds in different spatial directions. We analyze basic features of spatiotemporal dynamics of patchy spread common for the reaction–diffusion approach. We discuss in which ecosystems we would observe patterns of deterministic patchy spread due to the considered mechanism.     

Growth and grazing mortality rates of Prochlorococcus, Synechococcus and eukaryotic picophytoplankton in a bay of the Uwa Sea, Japan

Growth and grazing mortality rates of Synechococcus, Prochlorococcusand eukaryotic picophytoplankton were determined using dilutionexperiments in a bay of the Uwa Sea, Japan. Seasonal changesin the vertical distribution of each picophytoplankter wereinterpreted based on previous physico-chemical measurementsand potential ecophysiological differences. Significant relationshipsbetween dilution and picophytoplankton growth rate were foundonly during the stratified period, suggesting that food linkagebetween the picophytoplankton and grazers was active duringthe stratified period. We found an almost 1:1 balance betweengrowth and grazing mortality rates of Prochlorococcus and Synechococcusin the presence of both nanoflagellates and ciliates, suggestingthat the abundance of the cyanobacteria is in a quasi-steady-statesystem with grazing losses compensated by growth. The relationshipbetween growth and grazing mortality rate of eukaryotic picophytoplanktonwas unclear. We discuss the dynamics of each picophytoplankterabundance with special reference to the characteristics of themicrobial food web in the bay, together with two physical eventsresponsible for matter cycling within the bay.     

The use of DGGE analyses to explore eastern Mediterranean and Red Sea marine picophytoplankton assemblages

In vast areas of the oceans, most marine photosynthetic production is performed by cells smaller than 2-3 microm (picoplankton). Here, we report on denaturing gradient gel electrophoresis (DGGE) analyses of naturally occurring marine oxygenic picophytoplankton using the conserved photosynthetic psbA gene. The psbA gene proved to be a good indicator for picophytoplankton presence and was shown to work with DGGE. The DGGE results show the distribution of photosynthetic marine groups belonging to cyanobacteria and the eukaryotic prasinophytes (green algae) in the Red and eastern Mediterranean Seas in the seasons examined. The present study demonstrates the value of DGGE as a tool for rapid analyses of natural marine communities of picophytoplankton.     

A Comparison of Bimolecular Reaction Models for Stochastic Reaction–Diffusion Systems

Stochastic reaction–diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary spatially-continuous models that have been used in recent studies: the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching a fixed separation (called the reaction-radius). The Doi model uses reaction potentials, whereby two molecules react with a fixed probability per unit time, λ, when separated by less than the reaction radius. In this work, we study the rigorous relationship between the two models. For the special case of a protein diffusing to a fixed DNA binding site, we prove that the solution to the Doi model converges to the solution of the Smoluchowski model as λ→∞, with a rigorous $O(\lambda^{-\frac{1}{2} + \epsilon})$ error bound (for any fixed ?>0). We investigate by numerical simulation, for biologically relevant parameter values, the difference between the solutions and associated reaction time statistics of the two models. As the reaction-radius is decreased, for sufficiently large but fixed values of λ, these differences are found to increase like the inverse of the binding radius.     

Diffusion models for chemotaxis: a statistical analysis of noninteractive unicellular movement.

A program is developed for applying stochastic differential equations to models for chemotaxis. First a few of the experimental and theoretical models for chemotaxis both for swimming bacteria and for cells migrating along a substrate are reviewed. In physical and biological models of deterministic systems, finite difference equations are often replaced by a limiting differential equation in order to take advantage of the ease in the use of calculus. A similar but more intricate methodology is developed here for stochastic models for chemotaxis. This exposition is possible because recent work in probability theory gives ease in the use of the stochastic calculus for diffusions and broad applicability in the convergence of stochastic difference equations to a stochastic differential equation. Stochastic differential equations suggest useful data for the model and provide statistical tests. We begin with phenomenological considerations as we analyze a one-dimensional model proposed by Boyarsky, Noble, and Peterson in their study of human granulocytes. In this context, a theoretical model consists in identifying which diffusion best approximates a model for cell movement based upon theoretical considerations of cell physiology. Such a diffusion approximation theorem is presented along with discussion of the relationship between autocovariance and persistence. Both the stochastic calculus and the diffusion approximation theorem are described in one dimension. Finally, these tools are extended to multidimensional models and applied to a three-dimensional experimental setup of spherical symmetry.     

Evaluation of genes involved in Norway lobster (<Emphasis Type="Italic">Nephrops norvegicus</Emphasis>) female sexual maturation using transcriptomic analysis

In marine ecosystems, the most significant migration observed in terms of biomass distribution is the one connected with the vertical movements in the water column. In the present study, the vertical profiles of the mesopelagic shrimps Gennadas elegans, Eusergestes arcticus, Sergia robusta, and the epipelagic Parasergestes vigilax in the Balearic Sea (western Mediterranean), during the stratified (summer) and non-stratified (autumn) hydrographic conditions, were investigated through their ontogeny, from the larval to adult stages. The mesopelagic adults were observed to move down to the deeper layers during the night more than during the daylight hours. Most larvae aggregated within the limits of the upper water column. The P. vigilax larvae were collected only during the stratified period. The first two larval stages vertical distribution indicates that the mesopelagic crustacean spawning could occur at greater depths. During the non-stratified period, the larvae of the mesopelagic species tended to remain at about 500 m depth at night, rising towards the upper layers at sunrise. Vertical patterns are discussed, as strategies associated with predator–prey trade-offs. To our knowledge, the present study is the first such attempt to jointly analyze the vertical migrations of the developmental stages of the pelagic shrimps in the Mediterranean Sea.     

Predicting reef fish connectivity from biogeographic patterns and larval dispersal modelling to inform the development of marine reserve networks

Developing networks of no-take marine reserves is often hindered by uncertainty in the extent to which local marine populations are connected to one another through larval dispersal and recruitment (connectivity). While patterns of connectivity can be predicted by larval dispersal models and validated by empirical methods, biogeographic approaches have rarely been used to investigate connectivity at spatial scales relevant to reserve networks (10's–100's of km). Here, species assemblage patterns in coral reef fish were used together with an individual-based model of dispersal of reef fish larvae to infer patterns of connectivity in a ∼300 km wide region in the Philippines that included the Bohol Sea and adjacent bodies of water. A dominant current flows through the study region, which may facilitate connectivity among >100 no-take reserves. Connectivity was first investigated by analysing data on the presence/absence of 216 species of reef fish and habitat variables across 61 sites. Hierarchical clustering of sites reflecting species assemblage patterns distinguished a major group of sites in the Bohol Sea (Bray–Curtis similarity >70%) from sites situated in adjacent bodies of water (bays, channels between islands and a local sea). The grouping of sites could be partly explained by a combination of degree of embayment, % cover of sand and % cover of rubble (Spearman rank correlation, ρ_w = 0.42). The individual-based model simulated dispersal of reef fish larvae monthly for three consecutive years in the region. The results of simulations, using a range of pelagic larval durations (15–45 days), were consistent with the species assemblage patterns. Sites in the model that showed strongest potential connectivity corresponded to the majority of sites that comprised the Bohol Sea group suggested by hierarchical clustering. Most sites in the model that exhibited weak connectivity were groups of sites which had fish assemblages that were least similar to those in the Bohol Sea group. Concurrent findings from the two approaches suggest a strong influence of local oceanography and geography on broad spatial patterns of connectivity. The predictions can be used as an initial basis to organise existing reserves to form ecologically meaningful networks. This study showed that species assemblage patterns could be a viable supplementary indicator of connectivity if used together with predictions from a larval dispersal model and if the potential effect of habitat on the structuring of species assemblages is taken into consideration.     

Ammonium adsorption in sediments of a tropical mangrove forest (Thailand) and a temperate Wadden Sea area (Denmark)

Dimensionless ammonium adsorption coefficients (K) were determined for tropical mangrove forest sediments and temperate Wadden Sea sediments. The K values were obtained from ammonium adsorption isotherms of KCl (2 M) extractable ammonium versus dissolved ammonium in the porewater; relationships that can be described by a linear model. Linearity was evident even at low porewater concentrations for mangrove sediment, according to isotherms based on KCl extractions on untreated sediment profiles. K-values were low in mangrove forest sediments (0.04–0.10), and higher in Wadden Sea sediments (0.17–1.12). The vertical range in K-values was larger at the vegetated sites, with highest values in subsurface sediments, which suggests differences in quantity and quality of the fine organic and inorganic fractions. The low ammonium adsorption in the mangrove sediments can be explained by a higher concentration of competitive cations, especially iron, in this iron-rich environment. The low adsorption of ammonium in mangrove sediments and vegetated surface sediment of the Wadden Sea was negatively related to the organic content of the sediments, which is in contrast to findings for other marine sediments. We suggest that organic material may have a diluting effect on the exchange capacity in fine-grained sediments, and that organic coatings may block ion exchange sites on clay surfaces. Thus, there may be a organic-rich ‘wetland’ versus organic-poor ‘sediment’ effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stochastic effects in intercellular calcium spiking in hepatocytes

We carry out a Monte Carlo simulation of stochastic effects for two models of intercellular calcium wave propagation in rat hepatocytes. Both models involve gap junction diffusion by a second messenger. We find that, in general, the stochastic effects improve agreement with experiment, for a reasonable choice of model parameters. Both stochastic models exhibit baseline fluctuations and variations in the peak heights of Ca(2+). In addition, we find for one model that there is a distribution of latency times, rather than a single latency time, with a distribution width which is comparable to the experimental observation of spike widths. We also find for the other model with low gap junction diffusion that it is possible for cell multiplets to oscillate independently initially, but to subsequently become synchronized.     

Eukaryotic picophytoplankton community response to copper enrichment in a metal‐perturbed coastal environment

Copper is an essential micronutrient, especially for photosynthetic organisms, but can be toxic at high concentrations. In the past years, coastal waters have been exposed to an increase in copper concentration due to anthropogenic inputs. One well known case is the Chañaral area (Easter South Pacific coast), where a long term coastal copper enrichment event has occurred. That event strongly affected benthic marine diversity, including microbial communities. In this work, microcosm experiments were carried out to address the changes on picophytoplankton community composition of the disturbed area, when challenged to copper additions. Eukaryotic picophytoplankton communities from two areas were analyzed: one in the most copper‐perturbed area and another at the north edge of the perturbed area. Flow cytometry data showed that 25 μg L^?1 of copper addition exerted a positive effect in the growth kinetics on part of the eukaryotic picophytoplankton communities, independently of the site. 16S‐plastid terminal restriction fragment length polymorphisms analysis suggested that eukaryotic picophytoplankton display a short and directional response to high copper levels. Members of the Prasinophyceae class, a Coscinodiscophyceae diatom, as well as Phaeocystis, respond in a short time to the environmental disturbance, making them excellent candidates for further studies to evaluate phytoplanktonic species as sentinels for copper disturbances in coastal marine ecosystems.     

Spatial pattern analysis in forest dynamics: deviation from power law and direction of regeneration waves

Grid-based models have been used to understand spatial heterogeneity of the vegetation height in forests and to analyze spatio-temporal dynamics of the forest regeneration process. In this report, we present two methods of identifying lattice models when spatio-temporal data are given. The first method detects directionality of regeneration waves based on the timing of local disturbance events. The second evaluates the forest pattern by recording the fraction of high and low vegetation areas at multiple spatial scales. We illustrate these methods by applying them to patterns generated using three simple stochastic lattice models: (1) two-state model, distinguishing sites with high and low vegetation, (2) three-state model, in which sites can be in an additional disturbed state, and (3) Shimagare model, which considers a continuous range of states. The combination of the two methods provides efficient means of distinguishing the models. The first method has a more direct ecological meaning, while the second is useful when forest data are limited in time.     

The Lagrangian stochastic model for estimating footprint and water vapor fluxes over inhomogeneous surfaces

This study investigated a two-dimensional Lagrangian stochastic dispersion model for estimating water vapor fluxes and footprint over homogeneous and inhomogeneous surfaces. Over the homogeneous surface, particle trajectories were computed from a 2-D Lagrangian model forced by Eulerian velocity statistics determined by Monin–Obukhov similarity theory (MOST). For an inhomogeneous surface, the velocity and atmospheric stability profiles were computed using a second-order Eulerian closure model, and these local profiles were then used to drive the Lagrangian model. The model simulations were compared with water vapor flux measurements carried out above an irrigated bare soil site and an irrigated potato site. The inhomogeneity involved a step change in surface roughness, humidity, and temperature. Good agreement between eddy-correlation-measured and Lagrangian-model-predicted water vapor fluxes was found for both sites. Hence, this analysis demonstrates the practical utility of second-order closure models in conjunction with Lagrangian analysis to estimate the scalar footprint in planar inhomogeneous flows.