The AquaDEB project (phase I): Analysing the physiological flexibility of aquatic species and connecting physiological diversity to ecological and evolutionary processes by using Dynamic Energy Budgets

The European Research Project AquaDEB (2007–2011, http://www.ifremer.fr/aquadeb/) is joining skills and expertise of some French and Dutch research institutes and universities to analyse the physiological flexibility of aquatic organisms and to link it to ecological and evolutionary processes within a common theoretical framework for quantitative bioenergetics [Kooijman, S.A.L.M., 2000. Dynamic energy and mass budgets in biological systems. Cambridge University Press, Cambridge]. The main scientific objectives in AquaDEB are i) to study and compare the sensitivity of aquatic species (mainly molluscs and fish) to environmental variability of natural or human origin, and ii) to evaluate the related consequences at different biological levels (individual, population, ecosystem) and temporal scales (life cycle, population dynamics, evolution). At mid-term life, the AquaDEB collaboration has already yielded interesting results by quantifying bio-energetic processes of various aquatic species (e.g. molluscs, fish, crustaceans, algae) with a single mathematical framework. It has also allowed to federate scientists with different backgrounds, e.g. mathematics, microbiology, ecology, chemistry, and working in different fields, e.g. aquaculture, fisheries, ecology, agronomy, ecotoxicology, climate change. For the two coming years, the focus of the AquaDEB collaboration will be in priority: (i) to compare energetic and physiological strategies among species through the DEB parameter values and to identify the factors responsible for any differences in bioenergetics and physiology; and to compare dynamic (DEB) versus static (SEB) energy models to study the physiological performance of aquatic species; (ii) to consider different scenarios of environmental disruption (excess of nutrients, diffuse or massive pollution, exploitation by man, climate change) to forecast effects on growth, reproduction and survival of key species; (iii) to scale up the models for a few species from the individual level up to the level of evolutionary processes.     

Differential reproductive strategies of two bivalves in the Dutch Wadden Sea

Cerastoderma edule and Mya arenaria are two common bivalve species in European waters. Longevity and maximum size are much greater in the latter species. Because comparison of species life-history strategies states that a long life span (i.e. high annual survival) generally goes with lower fecundity, we hypothesise that reproductive output would be lower in M. arenaria than in C. edule. In the present paper, we studied the reproductive strategies of these two species in an intertidal and a subtidal area of the western Dutch Wadden Sea, by following seasonal changes in absolute and relative weights of somatic and gonadal tissues in these bivalves. Starting of spawning was similar in the two species, around May, except for intertidal M. arenaria, which initiated spawning in August. Individual energy investment in reproduction was similar for the two species but, unlike M. arenaria, C. edule spawned completely, releasing all energy of gonadal mass in the form of gametes. Mya arenaria used the gonad not only for reproduction but also for storage. In the intertidal area, we found a trade-off between longevity and reproduction, i.e. maximum reproductive output (expressed as a proportion of body mass) was higher in C. edule than in M. arenaria. However, since body size is larger and life span longer in M. arenaria than in C. edule, mean lifetime reproductive output per individual must be higher in the first than in the latter. Based on the differences in reproductive strategies of these two species, we hypothesise that the negative effects of warming climate on bivalve population dynamics in the Wadden Sea will be stronger in C. edule than in M. arenaria.     

Spatial variability in growth and reproduction of the Pacific oyster Crassostrea gigas (Thunberg, 1793) along the west European coast

The Pacific oyster Crassostrea gigas was introduced in Europe for commercial purposes in the mid 1960s. It was initially thought that low winter temperatures would restrain this species' reproduction and settlement; however, its present distribution in areas where no introduction has taken place suggests that natural invasion and expansion has occurred. Along the European coast, wild populations of Pacific oysters are already found from northern Germany to southern Portugal. Whether C. gigas will continue to further expand through northern waters will depend on its physiological performance. In this study, the performance of wild oyster populations has been studied in terms of growth and reproduction at three stations: La Rochelle (France; 46°N), Yerseke (Oosterschelde estuary, The Netherlands, 51°N), and Texel (Wadden Sea estuary, The Netherlands, 53°N). The French population had the lowest somatic-shell mass ratio and an increase in maximum shell length, somatic and gonadal mass was observed from France to the Netherlands. In addition, mean oocyte diameter decreased significantly from south to north. The combination of increasing gonadal mass and decreasing oocyte volume suggests an increasing reproductive output in terms of egg numbers from France to The Netherlands. Differences in temperature between locations will at least be partly responsible for the observed patterns; however, other environmental factors (such as food availability, predation pressure, sediment type and/or seston concentration) cannot be excluded. Since smaller eggs (oocytes) are thought to have a longer development time, the environmental conditions along the Dutch coast may result in increased larval dispersal and possibly in further population expansion.     

Growth and reproduction of the bivalve Spisula subtruncata (da Costa) in Dutch coastal waters

The bivalve Spisula subtruncata is usually abundant in shallow coastal waters along the Dutch coast. However, its biomass has been decreasing since 1995. In order to assess whether reproductive failure may be the cause of the observed decline over the last decades, the energy investment in reproduction of a population of S. subtruncata from central Dutch coastal waters was studied. The population studied consisted of individuals of up to four years old. Shell length reached maximum values of around 32 mm and individual total body, somatic and gonadal ash-free dry mass reached maximum values of about 278 mg AFDM, 252 mg AFDM and 76 mg AFDM, respectively. A clear seasonal cycle in somatic and gonadal mass was observed. Somatic and gonadal mass indices increased in early spring and reached maximum values during summer, followed by a decrease to minimum values at the beginning of the following year. Spawning was in June–July and settlement of spat seems to have occurred in July–August. Mean oocyte diameter was 57.43 ± 0.03 μm, corresponding to a volume of 98972 μm³. These results suggested that reproductive failure was not the cause of the current population decline. Most likely, unsuccessful settlement of spat and/or severe predation during the first months of life were responsible for the observed patterns.     

Seasonal variability in somatic and reproductive investment of the bivalve Scrobicularia plana (da Costa, 1778) along a latitudinal gradient

Monthly investment in soma and gonads in the bivalve Scrobicularia plana is described for three populations along its distributional range: Minho estuary, Portugal; Westerschelde estuary, The Netherlands and Buvika estuary, Norway. Seasonal cycles in body mass (BMI), somatic mass (SMI) and gonadal mass (GMI) indices were observed for all populations. In Portugal, BMI and SMI peaked in mid-autumn, while in The Netherlands both indices were at their highest in mid-spring. Norway showed a different pattern with two distinct peaks: one in mid-autumn and a second peak in spring. GMI reached maximum values in July in Portugal and Netherlands and in June in Norway. Overall, mean BMI and SMI were lower in Portugal while mean GMI was lower in Norway. The spawning period lasted the whole summer in Portugal, but was shorter (only two months) in The Netherlands and Norway. The reproductive investment in The Netherlands was significantly higher than in Portugal and Norway, with the lowest values being observed in Norway. Differences in annual cycles between populations were attributed to environmental factors, namely temperature and food availability. Temperature seems important in shaping the reproductive pattern with more northern populations showing shorter reproductive periods starting later in the year, and a lower reproductive output. In addition, winter water temperatures can explain the lower mean body and somatic mass values observed in Portugal. Food availability influenced the physiological performance of the species with peaks in somatic mass coinciding with phytoplankton blooms. This relation between physiological performance and environmental factors influences S. plana distribution, densities and even survival, with natural consequences on its commercial importance.     

Modeling equilibrium bed profiles of short tidal embayments

In many tidal embayments, bottom patterns, such as the channel-shoal systems of the Wadden Sea, are observed. To gain understanding of the mechanisms that result in these bottom patterns, an idealized model is developed and analyzed for short tidal embayments. In this model, the water motion is described by the depth- and width-averaged shallow water equations and forced by a prescribed sea surface elevation at the entrance of the embayment. The bed evolves due to the divergence and convergence of suspended sediment fluxes. To model this suspended-load sediment transport, the three-dimensional advection–diffusion equation is integrated over depth and averaged over the width. One of the sediment fluxes in the resulting one-dimensional advection–diffusion equation is proportional to the gradient of the local water depth. In most models, this topographically induced flux is not present. Using standard continuation techniques, morphodynamic equilibria are obtained for different parameter values and forcing conditions. The bathymetry of the resulting equilibrium bed profiles and their dependency on parameters, such as the phase difference between the externally prescribed M₂ and M₄ tide and the sediment fall velocity, are explained physically. With this model, it is then shown that for embayments that are dominated by a net import of sediment, morphodynamic equilibria only exist up to a maximum embayment length. Furthermore, the sensitivity of the model to different morphological boundary conditions at the entrance of the embayment is investigated and it is demonstrated how this strongly influences the shape and number of possible equilibrium bottom profiles. This paper ends with a comparison between the developed model and field data for the Wadden Sea’s Ameland and Frisian inlets. When the model is forced with the observed M₂ and M₄ tidal constituents, morphodynamic equilibria can be found with embayment lengths similar to those observed in these inlets. However, this is only possible when the topographically induced suspended sediment flux is included. Without this flux, the maximum embayment length for which morphodynamic equilibria can be found is approximately a third of the observed length. The sensitivity of the model to the topographically induced sediment flux is discussed in detail.     

A fast direct solution method for nonlinear equations in an analytic element model

The analytic element method, like the boundary integral equation method, gives rise to a system of equations with a fully populated coefficient matrix. For simple problems, these systems of equations are linear, and a direct solution method, such as Gauss elimination, offers the most efficient solution strategy. However, more realistic models of regional ground water flow involve nonlinear equations, particularly when including surface water and ground water interactions. The problem may still be solved by use of Gauss elimination, but it requires an iterative procedure with a reconstruction and decomposition of the coefficient matrix at every iteration step. The nonlinearities manifest themselves as changes in individual matrix coefficients and the elimination (or reintroduction) of several equations between one iteration and the other. The repeated matrix reconstruction and decomposition is computationally intense and may be avoided by use of the Sherman-Morrison formula, which can be used to modify the original solution in accordance with (small) changes in the coefficient matrix. The computational efficiency of the Sherman-Morrison formula decreases with increasing numbers of equations to be modified. In view of this, the Sherman-Morrison formula is only used to remove equations from the original set of equations, while treating all other nonlinearities by use of an iterative refinement procedure.