Pedro Duarte

Mathematical modelling to assess the carrying capacity for multi-species culture within coastal waters

Abstract In the context of aquaculture, carrying capacity is generally understood as the standing stock of a particular species at which production is maximised without negatively affecting growth rates. The estimation of carrying capacity for aquaculture is a complex issue. That complexity stems from the many interactions between and among cultivated and non-cultivated species, as well as between those species and their physical and chemical environments. Mathematical models may help to resolve these interactions, by analysing them in a dynamic manner. Previous carrying capacity models have considered the biogeochemical processes that influence growth of cultivated species in great detail. However, physical processes tend to have been addressed very simplistically. Further, most modelling has been for monocultures, despite the increasing importance of multi-species (=polyculture) systems. We present here a two-dimensional coupled physical–biogeochemical model implemented for Sungo Bay, Shandong Province, People’s Republic of China. Sungo Bay is used for extensive polyculture, where bivalve shellfish and kelp are the most important cultivated species. Data collected over 13 years (1983–2000) was available for modelling. Our main objectives were to implement the model, achieving reasonable calibration and validation with independent data sets, for use in estimating the environmental carrying capacity for polyculture of scallops and oysters. Findings indicate that the model successfully reproduces some of the main features of the simulated system. Although requiring some further work to improve predictive capability in parts, predictions clearly indicate that Sungo Bay is being exploited close to the environmental carrying capacity for suspension-feeding shellfish. Comparison of different culture scenarios also indicates that any significant increase in yield will depend largely on a more optimal spatial distribution of the different cultivated species.

Assessment and comparison of the Marennes-Oléron Bay (France) and Carlingford Lough (Ireland) carrying capacity with ecosystem models

Based on the individual growth, food limitation,population renewal through seeding, and individualmarketable size, a theoretical model of the culturedspecies population dynamics was used to assess thecarrying capacity of an ecosystem. It gave adome-shape curve relating the annual production andthe standing stock under the assumption of individual growth limited by the available food inan ecosystem. It also showed the influence ofmortality rate and marketable size on this curve andwas introduced as a means to explore the globalproperties resulting from the interactions betweenthe ecophysiology of the reared species and theenvironment at the ecosystem level.In a second step, an ecosystem model was built to assess the carryingcapacity of Marennes-Oléron bay, the mostimportant shellfish culture site in France, with astanding stock of Crassostrea gigas around 100000tonnes fresh weight (FW) and an annual production of30000 tonnes FW. The ecosystem model focused on theoyster growth rate and considered the interactionbetween food availability, residence time of thewater, oyster ecophysiology and number ofindividuals. It included a spatial discretization ofthe bay (box design) based on a hydrodynamic model,and the nitrogen or carbon cycling betweenphytoplankton, cultured oysters, and detritus. Fromsimulations of the oyster growth with differentseeding values, a curve relating the total annualproduction and the standing stock was obtained. Thiscurve exhibited a dome shape with a maximumproduction corresponding to an optimum standingstock. The model predicted a maximum annualproduction of 45000 tonnes FW for a standing stockaround 115000 tonnes FW. The prediction confirmedsome results obtained empirically in the case ofMarennes-Oléron bay and the results of thetheoretical model. Results were compared with thoseobtained in Carlingford Lough (Ireland) using asimilar ecosystem model. Carlingford Lough is asmall intertidal bay where the same species iscultured at a reduced scale, with current biomassless than 500 tonnes FW. The model showed that thestanding stock can be increased from 200 tonnes FWto approximately 1500 tonnes FW before any decreaseof the production.

A functional model of responsive suspension-feeding and growth in bivalve shellfish, configured and validated for the scallop Chlamys farreri during culture in China

A dynamic growth model is presented for the suspension-feeding scallop Chlamys farreri. The model is configured and validated for C. farreri cultured in Sungo Bay, China, using functional relations to simulate rapid and sensitive adjustments in feeding and metabolism as observed in response to the highly changeable environment there. Notable novel elements include resolving significant adjustments in the relative processing of living chlorophyll-rich phytoplankton organics, non-phytoplankton organics and the remaining inorganic matter during both differential retention on the gill and selective pre-ingestive rejection within pseudofaeces. We also include a facility to predict the energy content of non-phytoplankton organics. This is significant, for living phytoplankton contributed less than 20% towards suspended particulate organic matter within Sungo Bay. Further, the energy content of non-phytoplankton organics was very much more variable than for phytoplankton organics. Whether using that facility or assuming an average value for the energy content of non-phytoplankton organics, resolution of the relative processing of different particle types allows simulation of how the rates, organic compositions and energy contents of filtered, ingested and deposited matter change in response to differences in seawater temperature, seston availability and seston composition. Dependent relations predict rates of energy absorption, energy expenditure and excretion. By these means, our model replicates dynamic adjustments in feeding and metabolism across full ranges of relevant natural variability, and successfully simulates scallop growth from larvae or seed to harvestable size under different temporal and spatial scenarios of culture. This is an important advance compared with simpler models that do simulate responsive adjustments. Only by modelling the complex set of feedbacks, both positive and negative, whereby suspension feeding shellfish interact with ecosystem processes, can one realistically hope to assess environmental capacities for culture.

Trophic capacity of Carlingford Lough for oyster culture – analysis by ecological modelling

A one-dimensional ecosystem box model is presented forcarrying capacity assessment. The model includesphysical and biological processes. The physicalprocesses are the transport of nutrients, suspendedmatter and phytoplankton through the system boundariesand between model boxes. The biological processes areprimary production and oyster (Crassostreagigas) population dynamics and physiology. The modelwas implemented using an object-oriented approach. Themodel was employed to estimate the carrying capacityof Carlingford Lough (Ireland) for oyster culture. Inthe Lough, low water temperatures prevent the oystersfrom reproducing. Therefore, recruitment ishuman-dependent. Small oyster spat is seeded everyyear during spring and harvested after the summer ofthe next year. During this period oysters reachcommercially harvestable weight. The results obtainedindicate that the carrying capacity of this system isapproximately 0.45 g oysters (AFDW) m-3,determined more by the availability of particulatematter than by phytoplankton. It is suggested that afive-fold increase in oyster seeding may optimiseharvest yield.

Leads in Arctic pack ice enable early phytoplankton blooms below snow-covered sea ice

The Arctic icescape is rapidly transforming from a thicker multiyear ice cover to a thinner and largely seasonal first-year ice cover with significant consequences for Arctic primary production. One critical challenge is to understand how productivity will change within the next decades. Recent studies have reported extensive phytoplankton blooms beneath ponded sea ice during summer, indicating that satellite-based Arctic annual primary production estimates may be significantly underestimated. Here we present a unique time-series of a phytoplankton spring bloom observed beneath snow-covered Arctic pack ice. The bloom, dominated by the haptophyte algae Phaeocystis pouchetii, caused near depletion of the surface nitrate inventory and a decline in dissolved inorganic carbon by 16 ± 6 g C m−2. Ocean circulation characteristics in the area indicated that the bloom developed in situ despite the snow-covered sea ice. Leads in the dynamic ice cover provided added sunlight necessary to initiate and sustain the bloom. Phytoplankton blooms beneath snow-covered ice might become more common and widespread in the future Arctic Ocean with frequent lead formation due to thinner and more dynamic sea ice despite projected increases in high-Arctic snowfall. This could alter productivity, marine food webs and carbon sequestration in the Arctic Ocean.

The relationship between phytoplankton diversity and community function in a coastal lagoon

The decrease of biodiversity related to the phenomena of global climate change is stimulating the scientific community towards a better understanding of the relationships between biodiversity and ecosystem functioning. In ecosystems where marked biodiversity changes occur at seasonal time scales, it is easier to relate them with ecosystem functioning. The objective of this work is to analyse the relationship between phytoplankton diversity and primary production in St. Andre coastal lagoon — SW Portugal. This lagoon is artificially opened to the sea every year in early spring, exhibiting a shift from a marine dominated to a low salinity ecosystem in winter. Data on salinity, temperature, nutrients, phytoplankton species composition, chlorophyll a (Chl a) concentration and primary production were analysed over a year. Modelling studies based on production-irradiance curves were also conducted. A total of 19 taxa were identified among diatoms, dinoflagellates and euglenophyceans, the less abundant group. Lowest diversities (Shannon— Wiener index) were observed just before the opening to the sea. Results show a negative correlation (p 90% of cell abundance) and production was maximal (up to 234.8 mg C m−3 h−1). Maximal photosynthetic rates (Pmax) (2.0–22.5 mg C mg Chl a −1 h−1) were higher under lower Chl a concentrations. The results of this work suggest that decreases in diversity are associated with increases in biomass and production, whereas increases correspond to opposite trends. It is suggested that these trends, contrary to those observed in terrestrial and in some benthic ecosystems, may be a result of low habitat diversity in the water column and resulting competitive pressure. The occurrence of the highest photosynthetic rates when Chl a is low, under some of the highest diversities, suggests a more efficient use of irradiance under low biomass-high diversity conditions. Results suggest that this increased efficiency is not explained by potential reductions in nutrient limitation and intraspecific competition under lower biomasses and may be a result of niche complementarity.

Winter to summer oceanographic observations in the Arctic Ocean north of Svalbard

Oceanographic observations from the Eurasian Basin north of Svalbard collected between January and June 2015 from the N-ICE2015 drifting expedition are presented. The unique winter observations are a key contribution to existing climatologies of the Arctic Ocean, and show a ∼100m deep winter mixed layer likely due to high sea ice growth rates in local leads. Current observations for the upper ∼200m show mostly a barotropic flow, enhanced over the shallow Yermak Plateau. The two branches of inflowing Atlantic Water are partly captured, confirming that the outer Yermak Branch follows the perimeter of the plateau, and the inner Svalbard Branch the coast. Atlantic Water observed to be warmer and shallower than in the climatology, is found directly below the mixed layer down to 800m depth, and is warmest along the slope, while properties inside the basin are quite homogeneous. From late May onwards, the drift was continually close to the ice edge and a thinner surface mixed layer and shallower Atlantic Water coincided with significant sea ice melt being observed. This article is protected by copyright. All rights reserved.

Modelling growth of Ruppia cirrhosa

The main objectives of this work were to synthesise information on the autoecology of Ruppia cirrhosa Petagna (Grande) in a mathematical model and to use the model to simulate its growth, production and harvest. Model parameters were allowed to vary as a result of acclimation, following experimental data reported in the literature. Biomass data from Santo Andre lagoon (SW Portugal) were used to calibrate the model. Validation was carried out with independent data sets from Santo Andre lagoon and from Tancada lagoon (NE Spain). Model simulations show a reasonable agreement with observed data with a similar biomass temporal dynamics and peaks. Self-shading appears to be an important self-regulating mechanism of biomass growth and production. The results obtained predict an annual net primary production of 361 g DW m 2 well within the estimates based on harvesting techniques (295‐589 g DW m 2 ). Model results suggest that controlled harvesting of macrophyte biomass may be carried out without affecting macrophyte real net production, through the reduction of light limitation under the plant canopy.

Influence of river discharge patterns on the hydrodynamics and potential contaminant dispersion in the Douro estuary (Portugal).

Freshwater input to estuaries is a fundamental feature of these ecosystems, which may be profoundly altered by river damming as human needs for water consumption, irrigation or energy production increase. The Douro estuary is limited upstream by a dam since 1985, which reduced its length by ca. 60%. Freshwater inputs to the estuary are now irregular and greatly dependent on hydroelectric power demand; values ranging from zero to over 1000m(3)s(-1), in a matter of hours, especially in summer are common. In the present study, a three-dimensional hydrodynamic model was applied to the Douro estuary. The model was calibrated and validated against water elevation, current velocity, salinity and temperature data. Thereafter, it was used to analyse the effects of different flow regimes and magnitudes on estuarine hydrodynamics and contaminant dispersion. Results obtained suggest that the highly variable flow regimes, currently observed in the Douro, tend to reduce water column stratification and to enhance seawater intrusion, when compared with flow discharges of similar average magnitude, but lower variability. Stable flows seem to be the most effective in dispersing contaminants eventually introduced into the estuary through its small river tributaries. Overall results suggest that flow management may have important effects on estuarine hydrodynamics through non-linear interactions between flow magnitude and variability.

A model for the simulation of macroalgal population dynamics and productivity

Abstract A mathematical model to simulate the population dynamics and productivity of macroalgae is described. The model calculates the biomass variation of a population divided into size-classes. Biomass variation in each class is estimated from the mass balance of carbon fixation, carbon release and demographic processes such as mortality and frond breakage. The transitions between the different classes are calculated in biomass and density units as a function of algal growth. Growth is computed from biomass variations using an allometric relationship between weight and length. Gross and net primary productivity is calculated from biomass production and losses over the period of simulation. The model allows the simulation of different harvesting strategies of commercially important species. The cutting size and harvesting period may be changed in order to optimise the calculated yields. The model was used with the agarophyte Gelidium sesquipedale (Clem.) Born. et Thur. This species was chosen because of its economic importance as a the main raw material for the agar industry. Net primary productivity calculated with it and from biomass variations over a yearly period, gave similar results. The results obtained suggest that biomass dynamics and productivity are more sensitive to the light extinction coefficient than to the initial biomass conditions for the model. Model results also suggest that biomass losses due to respiration and exudation are comparable to those resulting from mortality and frond breakage. During winter, a significant part of the simulated population has a negative net productivity. The importance of considering different parameters in the productivity light relationships in order to account for their seasonal variability is demonstrated with the model results. The model was implemented following an object oriented programming approach. The programming methodology allows a fast adaptation of the model to other species without major software development.