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1.
The water and the ecosystem dynamics of the Ria de Aveiro, a shallow, multi-branch lagoon located on the northwest coast of Portugal, are simulated using a new fully coupled 3D modeling system. This model couples the hydrodynamic model SELFE (semi-implicit Eulerian-Lagrangian finite element) and an ecological model extended from EcoSim 2.0 to represent zooplankton dynamics. The model application is based on an unstructured grid spatial discretization, which is particularly appropriate for this system given its complex geometry. The baroclinic circulation is calibrated and validated for different environmental conditions, leading to velocity errors smaller than 5 cm/s across the lagoon. Ecological simulations, focused on zooplankton dynamics represented by a site-specific formulation, are then presented and compared against field data for two contrasting environmental conditions: Autumn 2000 and Spring 2001. Results show that the fully coupled model is able to reproduce the dynamics of the ecosystem in the Spring 2001, fitting the model results inside the range of data variation. During this period zooplankton differences between data and model results are of about 0.005 mg C/l (60%), while other ecological tracers’ differences are generally smaller than 20–30% along the several branches of the lagoon. In the Autumn 2000, the model tends to overestimate zooplankton by a factor of 10 and to underestimate phytoplankton and ammonium, with discrepancies of about 0.1 mg C/l and 4.8 μmol N/l, respectively. Factors like the ecological conditions imposed at the boundaries, the input parameters of the ecological model and the simplification of the ecosystem structure, since phytoplankton is the only primary producer considered, may explain the observed differences.  相似文献   

2.
Barnett A  Beisner BE 《Ecology》2007,88(7):1675-1686
While empirical studies linking biodiversity to local environmental gradients have emphasized the importance of lake trophic status (related to primary productivity), theoretical studies have implicated resource spatial heterogeneity and resource relative ratios as mechanisms behind these biodiversity patterns. To test the feasibility of these mechanisms in natural aquatic systems, the biodiversity of crustacean zooplankton communities along gradients of total phosphorus (TP) as well as the vertical heterogeneity and relative abundance of their phytoplankton resources were assessed in 18 lakes in Quebec, Canada. Zooplankton community richness was regressed against TP, the spatial distribution of phytoplankton spectral groups, and the relative biomass of spectral groups. Since species richness does not adequately capture ecological function and life history of different taxa, features which are important for mechanistic theories, relationships between zooplankton functional diversity (FD) and resource conditions were examined. Zooplankton species richness showed the previously established tendency to a unimodal relationship with TP, but functional diversity declined linearly over the same gradient. Changes in zooplankton functional diversity could be attributed to changes in both the spatial distribution and type of phytoplankton resource. In the studied lakes, spatial heterogeneity of phytoplankton groups declined with TP, even while biomass of all groups increased. Zooplankton functional diversity was positively related to increased heterogeneity in cyanobacteria spatial distribution. However, a smaller amount of variation in functional diversity was also positively related to the ratio of biomass in diatoms/chrysophytes to cyanobacteria. In all observed relationships, a greater variation of functional diversity than species richness measures was explained by measured factors, suggesting that functional measures of zooplankton communities will benefit ecological research attempting to identify mechanisms behind environmental gradients affecting diversity.  相似文献   

3.
《Ecological modelling》2007,200(1-2):33-44
In modelling spatial distribution of species, ignoring spatial autocorrelation (SA) and multicollinearity may lead to false ecological conclusions. Here we take into account both issues for examining and modelling the spatial pattern of abundance of the globally threatened lesser kestrel (Falco naumanni) during summer in a 38,400 ha area of northwestern Spain where large premigratory aggregations of the species occur. Spatial pattern was examined using Moran's correlogram, and models were built including geographical coordinates and autocovariate terms (which account for SA) in generalized linear models (GLM) and hierarchical partitioning (HP) models. HP models allow to alleviate multicollinearity. A grid-based approach was used by dividing the study area in 24 contiguous 4 km × 4 km squares where birds were counted in 2–3 visits per square (response variable). Environmental coarse-grained variables were extracted from a geographic information system (GIS) at three spatial extents. Moran's correlogram showed that lesser kestrel mean abundance per square was spatially autocorrelated up to 4–8 km. The results from both GLM and HP analyses were roughly compatible. The GLM models explained 80.0% of the variation in kestrel abundance and were the same at the three spatial extents. Lesser Kestrel abundance was not significantly explained by landscape variables, but was negatively related to both the distance to the nearest communal roost and distance to the nearest breeding colony with more of 10 breeding pairs of lesser kestrel. An autocovariate term added later in the GLM models improved both their explanatory power (from 74.5 to 80.0%) and model residuals, which were not longer spatially autocorrelated, fulfilling thus the statistical assumption of independent errors. Findings suggest that the spatial distribution of abundance of summering lesser kestrel is, at least, partially driven by endogenous causes, such as conspecific attraction. Exogenous causes such as finer-scale variables (e.g. type of crops and food available) are yet likely needed for lesser kestrel-environment relationships.  相似文献   

4.
In planktonic food webs, the conversion rate of plant material to herbivore biomass is determined by a variety of factors such as seston biochemical/elemental composition, phytoplankton cell morphology, and colony architecture. Despite the overwhelming heterogeneity characterizing the plant–animal interface, plankton population models usually misrepresent the food quality constraints imposed on zooplankton growth. In this study, we reformulate the zooplankton grazing term to include seston food quality effects on zooplankton assimilation efficiency and examine its ramifications on system stability. Using different phytoplankton parameterizations with regards to growth strategies, light requirements, sinking rates, and food quality, we examined the dynamics induced in planktonic systems under varying zooplankton mortality/fish predation, light conditions, nutrient availability, and detritus food quality levels. In general, our analysis suggests that high food quality tends to stabilize the planktonic systems, whereas unforced oscillations (limit cycles) emerge with lower seston food quality. For a given phytoplankton specification and resource availability, the amplitude of the plankton oscillations is primarily modulated from zooplankton mortality and secondarily from the nutritional quality of the alternative food source (i.e., detritus). When the phytoplankton community is parameterized as a cyanobacterium-like species, conditions of high nutrient availability combined with high zooplankton mortality led to phytoplankton biomass accumulation, whereas a diatom-like parameterization resulted in relatively low phytoplankton to zooplankton biomass ratios highlighting the notion that high phytoplankton food quality allows the zooplankton community to sustain relatively high biomass and to suppress phytoplankton biomass to low levels. During nutrient and light enrichment conditions, both phytoplankton and detritus food quality determine the extent of the limit cycle region, whereas high algal food quality increases system resilience by shifting the oscillatory region towards lower light attenuation levels. Detritus food quality seems to regulate the amplitude of the dynamic oscillations following enrichment, when algal food quality is low. These results highlight the profitability of the alternative food sources for the grazer as an important predictor for the dynamic behavior of primary producer–grazer interactions in nature.  相似文献   

5.
To extend coupled human–environment systems research and include the ecological effects of land-use and land-cover change and policy scenarios, we present an analysis of the effects of forest patch size and shape and landscape pattern on carbon storage estimated by BIOME-BGC. We evaluate the effects of including within-patch and landscape-scale heterogeneity in air temperature on carbon estimates using two modelling experiments. In the first, we combine fieldwork, spatial analysis, and BIOME-BGC at a 15-m resolution to estimate carbon storage in the highly fragmented and human-dominated landscape of Southeastern Michigan, USA. In the second, we perform the same analysis on 12 hypothetical landscapes that differ only in their degree of fragmentation. For each experiment we conduct four air-temperature treatments, three guided by field-based data and one empirically informed by local National Weather Service station data. The three field data sets were measured (1) exterior to a forest patch, (2) from the patch edge inward to 60 m on east-, south-, and west-facing aspects, separately, and (3) interior to that forest patch. Our field-data analysis revealed a decrease in maximum air temperature from the forest patch edge to a depth of 80 m. Within-patch air-temperature values were significantly different (α = 0.01) among transects (c.v. = 13.28) and for all measurement locations (c.v. = 30.58). Results from the first experiment showed that the interior treatment underestimated carbon storage by ~8000 Mg C and the exterior treatment overestimated carbon storage by 30,000 Mg C within Dundee Township, Southeastern Michigan, when compared to a treatment that included within-patch heterogeneity. In the second experiment we found a logarithmic increase in carbon storage with increasing fragmentation (r2 = 0.91). While a number of other processes (e.g. altered disturbance frequency or severity) remain to be included in future experiments, this combined field and modelling study clearly demonstrated that the inclusion of within-patch and landscape heterogeneity, and landscape fragmentation, each have a strong effect on forest carbon cycling and storage as simulated by a widely used ecosystem process model.  相似文献   

6.
Riverine reservoirs have a short water retention time, which is ecologically more similar to that of rivers. Generally, phytoplankton-based approaches are used for lakes and periphytic diatom-based approach for rivers. To understand the differences in the responses of phytoplankton and periphytic diatoms to environmental variables for riverine reservoirs, we collected periphytic diatom samples on artificial substrata as well as phytoplankton samples from a tropical reservoir with a resident time less than 10 days. Our results showed that 131 phytoplankton species and 138 periphytic diatoms were detected; the variation of phytoplankton community was mainly reflected by the dominant species with a strong response to the environmental variables at a time scale, whereas the variation of periphytic diatom community was noted in both the species composition and the dominant species, with a strong response at spatial-temporal scales. The multivariate regression analysis and redundancy analysis showed that environmental factors have higher explanations for the variance of the periphytic diatom community (R2 = 0.27). Temperature was the key explanatory variable for phytoplankton, planktonic diatoms and periphytic diatoms (P < 0.01). However, dissolved oxygen and nitrate were also detected as significant explanatory factors associated with periphytic diatom community (P < 0.01). Thus, the periphytic diatoms were concluded to be more sensitive to environmental change and were associated with more environmental variables than phytoplankton. Periphytic diatoms appear to provide more ecological information than phytoplankton for riverine reservoirs. © 2018 Science Press. All rights reserved.  相似文献   

7.
《Ecological modelling》2007,200(1-2):193-206
An object-oriented model of environment–mussel aquaculture interactions and mussel carrying-capacity within Lagune de la Grande-Entrée (GEL), Iles-de-la-Madeleine, Québec, was constructed to assist in development of sustainable mussel culture in this region. A multiple box ecosystem model for GEL tied to the output of a hydrodynamic model was constructed using Simile software, which has inherent ability to represent spatial elements and specify water exchange between modelled regions. Mussel growth and other field data were used for model validation. Plackett–Burman sensitivity analysis demonstrated that a variety of bioenergetic parameters of zooplankton and phytoplankton submodels were important in model outcomes. Model results demonstrated that mussel aquaculture can be further developed throughout the lagoon. At present culture densities, phytoplankton depletion is minimal, and there is little food limitation of mussel growth. Results indicated that increased stocking density of mussels in the existing farm will lead to decreased mass per individual mussel. Depending on the location of new farm emplacement within the lagoon, implementation of new aquaculture sites either reduced mussel growth in the existing farm due to depletion of phytoplankton, or exhibited minimum negative impact on the existing farm. With development throughout GEL, an excess of phytoplankton was observed during the year in all modelled regions, even at stocking densities as high as 20 mussels m−3. Although mussels cultured at this density do not substantially impact the ecosystem, their growth is controlled by the flux of phytoplankton food and abundance of zooplankton competitors. This model provides an effective tool to examine expansion of shellfish farming to new areas, balancing culture location and density.  相似文献   

8.
9.
近年来,随着茂名经济迅猛发展及涉海工程建设,其近海海域遭到日益严重的污染,海域环境日趋恶化。为更好地了解茂名近岸海域中小型浮游动物群落结构及其与环境因子的关系,摸清中小型浮游动物的种类组成及其空间分布状况,保护近岸海域生物多样性,分别于2019年夏季(6月)和秋季(9月)对茂名近海浮游动物进行调查。调查共发现浮游动物52种,以桡足类为主(达到40种,占比76.92%)。秋季浮游动物平均丰度和平均生物量(分别为29.82 ind·m-3和282.08 mg·m-3)均高于夏季(分别为15.71×103 ind·m-3和110.23 mg·m-3)。短角长腹剑水蚤(Oithona brevicornis)、小长腹剑水蚤(Oithona nana)、强额拟哲水蚤(Paracalanus crassirostris)和小拟哲水蚤(Paracalanus parvus)为茂名近岸海域春、夏季优势种。夏季和秋季浮游植物物种多样性指数平均值分别为3.06和2.69,丰富度指数平均值分别为3.65和3.38,均匀度指数平均值分别为0.71和0.66。运用BIO-ENV方法分析了浮游动物群落结构以及与浮游植物丰度、环境因子之间的关系,结果表明浮游植物丰度、溶解氧、盐度、水温、水深是影响夏季浮游动物群落的主要环境因子,水深、浮游植物丰度是影响秋季浮游动物群落的主要环境因子。  相似文献   

10.
Process representations critical to the phytoplankton and zooplankton submodels are described. These include constructs for: light- and nutrient-limitations and their interaction, temperature, consumption, and population-age structure. Values for key parameters are documented with reference to the literature on aquatic ecology and ecological modelling. Time-course relationships of the processes affecting the phytoplankton, zooplankton, phosphorus and nitrogen compartments are presented and discussed. These serve as additional documentation and are an important result of modelling synthesis.  相似文献   

11.
Diez JM  Pulliam HR 《Ecology》2007,88(12):3144-3152
Abiotic and biotic processes operate at multiple spatial and temporal scales to shape many ecological processes, including species distributions and demography. Current debate about the relative roles of niche-based and stochastic processes in shaping species distributions and community composition reflects, in part, the challenge of understanding how these processes interact across scales. Traditional statistical models that ignore autocorrelation and spatial hierarchies can result in misidentification of important ecological covariates. Here, we demonstrate the utility of a hierarchical modeling framework for testing hypotheses about the importance of abiotic factors at different spatial scales and local spatial autocorrelation for shaping species distributions and abundances. For the two orchid species studied, understory light availability and soil moisture helped to explain patterns of presence and abundance at a microsite scale (<4 m2), while soil organic content was important at a population scale (<400 m2). The inclusion of spatial autocorrelation is shown to alter the magnitude and certainty of estimated relationships between abundance and abiotic variables, and we suggest that such analysis be used more often to explore the relationships between species life histories and distributions. The hierarchical modeling framework is shown to have great potential for elucidating ecological relationships involving abiotic and biotic processes simultaneously at multiple scales.  相似文献   

12.
Few numerical simulations have attempted to include a high degree of biological detail for several trophic levels. Typically, in planktonic ecosystem models, if the dynamics of nutrients, phytoplankton and herbivorous zooplankton are formulated with ecological complexity, then carnivores are ignored, forced or modeled in an extremely simplified manner. Extensive mechanistic detail for important carnivores is difficult to represent because reliable and relevant ecological data are rarely available for appropriate species and local populations. Further, the wide temporal and spatial differences between life histories of lower plankton and carnivores may be technically difficult to model.In Narragansett Bay, Rhode Island, the ctenophore Mnemiopsis leidyi is an important carnivore to which these objections do not apply. A detailed carbon-based simulation model of this population of ctenophores was developed independently from an ecosystem model of Narragansett Bay which included detailed interactions between phytoplankton, primarily herbivorous zooplankton and nutrients. The interfacing of these two models without changing any of the formulations or values of the coefficients provided a test of the commonly used practice of forcing certain components. Both models were originally constructed with the biomass of a critical compartment forced according to observed data; in the plankton model, ctenophores were forced, and in the ctenophore model, zooplankton were forced.Predicted biomasses for zooplankton and ctenophores in the combined model were similar to the results of the two parent models, but improved relative to the actual field observations. From the findings it appears that the strategy of forcing is valid provided the forced patterns are appropriate and reasonable.  相似文献   

13.
Termination of harmful algal blooms (HABs) and coexistence of phytoplankton–zooplankton populations are of great importance to human health, ecosystem, environment, tourism and fisheries. In this paper, we propose a three component model consisting of non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP) and zooplankton (Z). The growth of zooplankton species is assume to reduce due to toxic chemicals released by TPP population. We have extended the model proposed by Chattopadhyay et al. [Chattopadhyay, J., Sarkar, R.R., Pal, S., 2004. Mathematical modelling of harmful algal blooms supported by experimental findings. Ecol. Comp. 1, 225–235] by including competition terms between TPP and NTP. We observe the effect of competition factors both in the presence and absence of the environmental fluctuation. From our field as well as model analysis we observe that competition helps in the coexistence of the species, but if the effect of competition is very high on the TPP population, it results in planktonic bloom. It is shown that the coexistence equilibrium loses its stability when the competition coefficient crosses a critical value and resulting Hopf-bifurcation around the positive equilibrium depicting oscillations phenomena of the populations.  相似文献   

14.
A computer simulation model of oceanic Langmuir circulations illustrates the role of these vortical water movements as physical forcing mechanisms affecting the horizontal and vertical distributions of planktonic organisms. The diel migration of omnivorous and herbivorous zooplankton (approximately by literature values for the swimming speeds of Meganyctiphanes norvegica and Calanus finmarchicus, respectively) and the sinking of phytoplankton interact with the Langmuir cells, resulting in a spatially heterogeneous community. The patchy distributions, in turn, affect the prey—predator interactions in this simple food web. Situations involving threshold and non-threshold feeding strategies as well as constant and changing circulations are investigated. The simulations are restricted to twilight and nocturnal events.  相似文献   

15.
We assessed the relative roles of local environmental conditions and dispersal on community structure in a landscape of lakes for the major trophic groups. We use taxonomic presence-absence and abundance data for bacteria, phytoplankton, zooplankton, and fish from 18 lakes in southern Quebec, Canada. The question of interest was whether communities composed of organisms with more limited dispersal abilities, because of size and life history (zooplankton and fish) would show a different effect of lake distribution than communities composed of good dispersers (bacteria and phytoplankton). We examine the variation in structure attributable to local environmental (i.e., lake chemical and physical variables) vs. dispersal predictors (i.e., overland and watercourse distances between lakes) using variation partitioning techniques. Overall, we show that less motile species (crustacean zooplankton and fish) are better predicted by spatial factors than by local environmental ones. Furthermore, we show that for zooplankton abundances, both overland and watercourse dispersal pathways are equally strong, though they may select for different components of the community, while for fish, only watercourses are relevant dispersal pathways. These results suggest that crustacean zooplankton and fish are more constrained by dispersal and therefore more likely to operate as a metacommunity than are bacteria and phytoplankton within this studied landscape.  相似文献   

16.
A mechanistic model was applied to study the influence of diurnal vertical migration (DVM) of planktonic crustaceans on the succession and composition of the phytoplankton community. While zooplankton was restricted to only one functional group, the phytoplankton community was divided into two functional groups which are distinguished by their maximum growth rates and vulnerability to zooplankton grazing. DVM causes a pulsed grazing regime and may also entail a corresponding reduction of the cumulative daily rates of ingestion and losses of zooplankton. To study the relative importance of these two mechanisms of DVM to phytoplankton we performed a scenario analysis consisting of 5 different scenarios. The results show that DVM has a strong influence on the phytoplankton community. Well edible algae benefit during the first 3–4 weeks of summer stratification by reduced daily grazing. The typical shift from small, well edible algae to larger, poorly or non-edible phytoplankton is distinctly delayed. Under the assumption of unchanged daily grazing, however, a pulsed grazing regime has nearly no influence on the resulting phytoplankton composition. As similar effects are also found for completely non-edible phytoplankton, indirect effects via phosphorus availability must be assumed. Thus, the scenario analysis reveals that the observed effects of DVM on phytoplankton can be explained by a combination of two mechanisms: (1) reduction of the daily zooplankton grazing, and (2) changed assimilation and remineralisation of phosphorus. Surprisingly and in contradiction to earlier reports there is almost no DVM effect on phytoplankton due to the sole action of a pulsed grazing regime.  相似文献   

17.
Abstract: Due to the structuring forces and large-scale physical processes that shape our biosphere, we often find that environmental and ecological data are either spatially or temporally—or both spatially and temporally—dependent. When these data are analyzed, statistical techniques and models are frequently applied that were developed for independent data. We describe some of the detrimental consequences, such as inefficient parameter estimators, biased hypothesis test results, and inaccurate predictions, of ignoring spatial and temporal data dependencies, and we cite an example of adverse statistical results occurring when spatial dependencies were disregarded. We also discuss and recommend available techniques used to detect and model spatial and temporal dependence, including variograms, covariograms, autocorrelation and partial autocorrelation plots, geostatistical techniques, Gaussian autoregressive models, K functions, and ARIMA models, in environmental and ecological research to avoid the aforementioned difficulties.  相似文献   

18.
Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.  相似文献   

19.
《Ecological modelling》2005,186(1):43-54
The extinction of solar UV (290–400 nm) radiation in aquatic ecosystems is a complex phenomena. In this paper, we examine and model the attenuation of UV radiation in a shallow lake ecosystem. In particular we focus our analysis on the specific role of the fractions of dissolved and particulate matter in the water column in the attenuation of radiation. This analysis is aimed by representing the spatial distribution of each fraction making it possible to evidence the spatial variation in habitat quality. In situ and laboratory measurement are used to elaborate a UV attenuation model. The attenuation model distinguishes between the contribution of particulate and dissolved matter in the attenuation of the solar UV flux. In the studied wetland lake (Laguna Iberá, sub-tropical latitude, Argentina) the importance of dissolved matter is dominated in the UVB solar spectrum (290–320 nm) but the effects of the particulate fraction are not negligible, in particular in UVA (320–400 nm). The spatial representation of model results demonstrate the non homogeneous nature between attenuation of the two fractions. Local and global environmental change can have important impacts on dissolved and particulate matter concentrations, which cam have ecological consequences in relation to the high flux of incoming UV radiation. The model developed to examine the relative attenuation of the dissolved and particulate fractions and is a useful instrument to identify the role that these fractions have on the optical characteristics of aquatic ecosystems.  相似文献   

20.
Phytoplankton concentration in Lake Kinneret (Israel) has varied up to 10-fold in space and time, with horizontal patches ranging from a couple of kilometres to a basin scale. Previous studies have used a 1D model to reproduce the temporal evolution of physical and biogeochemical variables in this lake. The question that arises then is how appropriate is a 1D approach to represent the dynamic of a spatially heterogeneous system, where there are non-linear dependencies between variables. Field data, a N-P-Z model coupled to both a 1D and a 3D hydrodynamic model, a 1D diffusion-reaction equation and scaling analysis are used to understand the role of spatial variability, expressed as phytoplankton patchiness, in the modelling of primary production. The analysis and results are used to investigate the effect of horizontal variability in the forcing and in the free mechanisms that affect the growth of patterns. The study shows that the use of averaged properties in a 1D approach may produce misleading results in the presence of localised patches, in terms of both concentration and composition of phytoplankton. The reason lies in the fact that the calibration process of ecological parameters in the 1D model appears to be site and process specific. That is, it depends on the pattern's characteristics and the underlying physical processes causing them. And this is a critical point for the success of numerical simulations under spatial variability. In this study, it is also shown that a length scale based on diffusion and growth rate of phytoplankton could be used as a criterion to assess the appropriateness of the 1D assumption.  相似文献   

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