Oceanographic models, particularly computationally intensive hydrodynamic and biogeochemical models, have mostly been written in Fortran (e.g. hydrodynamic models: NEMO (Madec, 2008), ROMS (Shchepetkin and McWilliams, 2005), POM (Blumberg and Mellor, 1980), MITGCM (Adcroft et al., 2004), MOM (Stock et al., 2014); and biogeochemical models: ERSEM (Blackford et al., 2004), BFM (Vichi et al., 2015), ERGOM (Neumann, 2000)). In fact, Fortran was the first programming language specifically designed for solving engineering and scientific computing problems (Backus et al., 1957) and proved to be one of the most efficient for performing complicated mathematical tasks with its collection of predefined high-level mathematical functions. Over the years, frequent revision of the Fortran standard and the addition of new capabilities to the language to meet changing demands enabled it to remain the de facto standard for writing computationally intensive scientific and engineering applications.

Ecopath with Ecosim (hereinafter EwE) (Christensen and Walters, 2004; Christensen et al., 2005) is the most widely adopted tool for building models of marine and freshwater ecosystems, and possibly the first choice for analysis of food web dynamics. Freely available at www.ecopath.org, EwE has long been used for scientific studies related to fisheries, some aspects of aquaculture, marine ecology, climate and pollution. There are thousands of users of the software worldwide (last record in 2008, 5649 reported users; www.ecopath.org) and more than 400 scientific publications utilising EwE as a modelling tool have been issued only in the last 2 decades (a search on Web of Science on 29 September 2014 for “Ecopath with Ecosim”, “Ecospace” or “Ecopath” returned 469 items published between 1997 and 2014). Because many EwE models for a variety of aquatic ecosystems are available, it makes sense to capitalise on such experience when developing coupled/integrated modelling applications. This would require only minimal modifications in these models and remove the burden of starting from scratch. However, being written for the Microsoft .NET framework constrains EwE's ability to integrate with models written in Fortran, and the Fortran recoding of EwE presented in this paper will facilitate this.

EwE is designed for interoperability with other models, which is crucial considering that ecological modelling is facing an important challenge to set a basis for the comprehensive description of marine ecosystems through integrated modelling schemes that incorporate multiple models (e.g. hydrodynamic, biogeochemical, ecological and socioeconomic) interactively with one another (e.g. end-to-end (hereinafter E2E) models; Fulton, 2010). This interoperability leads to insightful linking of these models into EwE (e.g. Christensen et al., 2014), and EwE's flexibility already permits one to link physical/biogeochemical oceanographic models with EwE (e.g. Libralato and Solidoro, 2009). This one-way linking permits exchanges of information between models that are run separately and is valid, robust and usually faster to implement than a two-way coupling. In spite of the interesting results obtained, however, one-way linking lacks a complete representation of feedbacks that propagate two ways between the coupled models. These feedbacks were proven to be important and reveal important ecological mechanisms (Kearney et al., 2012) that need to be accounted explicitly for a full representation of ecosystem effects due to climatic changes, aquaculture, socioeconomic changes and other important drivers (Fulton, 2010). The scientific requirements for such modelling approaches, therefore, mandate two-way coupling with existing oceanographic models which are mostly written in Fortran. Because these models and EwE use different programming languages, the technical differences complicate the coupling task more than anticipated (e.g. Beecham et al., 2010). One possible solution is the offline coupling of EwE and Fortran-coded models via two-way data transfer between the models at predefined time intervals while pausing the other model (i.e. a turn-based run). Another solution could be to utilise inter-process communications such as pipes and/or sockets between EwE and the model to be coupled while simultaneously running the models. However, coupled model construction will benefit from a Fortran version of EwE that will permit direct integration of the EwE modelling approach with mainly, but not limited to, physical and biogeochemical models in Fortran, and will allow a straightforward and two-way propagating feedback between high trophic level (HTL) and low trophic level (LTL) models. Hence, the development of a Fortran version of EwE will be useful for integration of HTL food web models with potentially any other model written in Fortran which simulates, for example, socioeconomic, bioenergetic dynamics.

In this work, we present (Sect. ) the first version of EwE re-coded in the Fortran 95/2003 language standard (EwE-F, version 1.0). In Sect. , we provide evidence of the full reliability of the code by comparing EwE-F with standard EwE (version 6.5) utilising sample food web models. In Sect. , we present how EwE-F allows for easy coupling with other models, by providing an example of integration with a biogeochemical model of the Gulf of Trieste in the northern Adriatic Sea. Finally, in the same section, we discuss the possibilities opened up by the availability of EwE-F. We believe that EwE-F will appeal also to the scientific community previously sceptical of the EwE approach (usually more confident with Fortran programming) and provide the possibility of both easy modification of the EwE-F structure and parameterisation for specific cases and easy integration with other biogeochemical, population dynamics, individual-based and/or any type of ecological model written in Fortran.

EwE modelling software includes a suite of modules that enables the building and analysis of food web models. EwE includes three main modules: (i) Ecopath, the mass-balance representation; (ii) Ecosim, the time-dynamic simulation; and (iii) Ecospace, the 2-D spatial–temporal dynamics, plus other complementary routines: network analysis (Ulanowicz, 1986), Monte Carlo simulation and time series fitting. EwE-F comprises only Ecopath and Ecosim modules; thus, only these two are briefly summarised here.

The Ecopath module comprises a series of linear equations that defines a mass-balance stationary state of the food web. The functional groups are regulated by gains (consumption, production, and immigration) and losses (mortality and emigration), and are linked to each other by predatory relationships. Fisheries extract biomass from the targeted and by-catch groups. In Ecopath, a set of linear equations describes flows of mass into and out of discrete biomass pools of the form Bi×PBi-∑j=1nBj×QBj×DCji-Bi×PBi×1-EEi-Yi-Ei-BAi=0, where, for each functional group i, B stands for biomass, (P/B) stands for the production rate per unit of biomass, (Q/B) stands for the consumption rate per unit of biomass of predator j, DCji is the fraction of prey i in the average diet of predator j, Y is the fishery catches, E is the net emigration rate, and BA is the biomass accumulation rate (Christensen et al., 2005). EE is the ecotrophic efficiency representing the proportion of mortality of a group that is not attributable to predators or fishing activities. As can be seen, Eq. (1) is quite simple as a result of the fact that it represents the budget of biomass fluxes in a given time window within an ecosystem. Ecopath is also characterised by a top-down solution of the system of equations; i.e. consumption on a group is a function of predator biomass, which differs from bottom-up approaches used in other inverse modelling methods (Steele, 2009).

In the time-dynamic module of EwE (Ecosim), dynamics of a state variable are defined with a differential equation composed of sources and sink terms. Each state variable represents the biomass of a functional group representing species and/or groups of species or populations split into age–size categories (multi-stanza). The definition of such a differential equation in Ecosim is as follows: dBidt=γi×∑j=1nQji-∑j=1nQij+Ii-Mi+Fi+ei×Bi, where dBi/dt is the rate of change of biomass (B) of group i over time t, γ is the growth efficiency of group i, ∑Qji is the sum of the consumptions of group i over all of its preys, ∑Qij is the sum of the predation on group i by all of its predators, I is the immigration, M is the non-predation mortality, F is the fishery mortality and e is the emigration rate of group i (Walters et al., 1997). Qij is defined on the basis of biomasses of predator and prey in a form that represents a slightly modified version of the Holling type II functional response in order to consider only the part of the biomass of the prey i that is accessible to the predator j (foraging arena theory; Ahrens et al., 2012). For each trophic interaction, the accessible biomass is dynamically defined on the basis of a parameter called “vulnerability” (for details, refer to Walters et al., 1997, 2000; Ahrens et al., 2012). This system of differential equations is numerically integrated over time under the influence of forcing functions (typically fishing mortalities or efforts, changes in primary productivity) starting from the initial condition settings defined by the Ecopath module.

The EwE software was translated to Fortran 95/2003 language in its core architecture and kept limited to (i) the Ecopath mass-balance routine including multi-stanza calculations and (ii) the Ecosim time-dynamic simulation including multi-stanza calculations. Due to modularity considerations, EwE-F was implemented under two separate components: (i) Ecopath-F, the Ecopath mass-balance algorithm, and (ii) Ecosim-F, the Ecosim time-dynamic simulation algorithm. EwE-F v1.0 includes only core routines of Ecopath and Ecosim: complementary routines for calculation of indicators for network analysis, and routines for Monte Carlo simulation, time series fitting and Ecospace are not included. Also, the capability to define mediation functions is not yet implemented in EwE-F v1.0, although we plan to address it in future versions. A schematic view of the EwE-F components and the input/output (I/O) files necessary for information exchange are given in Fig. 1. In the following two sections ( and ), the structure and functioning of the components in Fig. 1 are described in detail.

The Fortran recoding of EwE creates great flexibility for customisation, modification or coupling to different models written in Fortran. An example, which illustrated the potential of such flexibility, came from the integration of EwE-F with a biogeochemical Fortran model. In fact, the direct integration of these two models required one to address and subsequently solve a number of problems. These included defining the links between the two models and modifying them accordingly, exchanging information between the two models, dealing with different model time steps, and accounting for different model currencies.

The HTL model is an updated version of the EwE model of the northern Adriatic Sea originally developed by Coll et al. (2007). The original model which is composed of 40 functional groups (FGs) has been updated by (i) removing discards and by-catch FGs; (ii) splitting phytoplankton and zooplankton into two FGs each to represent small and large taxa; (iii) adding bacteria to explicitly represent the microbial loop; and (iv) adjusting the diet of plankton feeders to split the diet into the new plankton FGs. The updated model has 44 FGs and parameters for the plankton groups were updated considering literature information (see Cossarini and Solidoro, 2008, and references therein). The model currency is wet weight. The time step of the model is 1 month, the default time step of the EwE software.

The biogeochemical model is a Fasham-like (Fasham et al., 1990) 0-D box model of the northern Adriatic Sea (Cossarini and Solidoro, 2008) and consists of phytoplankton, zooplankton, and heterotrophic bacteria groups, one pool of inorganic phosphorus (PO43-), one dissolved organic matter compartment in terms of phosphorus (DOP) and carbon (DOC), and one particulate organic matter compartment in terms of phosphorus (POP) and carbon (POC) (Fig. 4). The model is a multi-currency model calculating the biomasses of its particular state variables (sediment, dissolved organic matter, particulate organic matter) both in terms of carbon and phosphorus. The time step of the model is 1 h. A full description of the biogeochemical model is given in Cossarini and Solidoro (2008).

For the harmonisation of both models in an E2E coupled scheme, first, the state variables that were already present in the LTL model were removed from the HTL model as well as their links (grey-shaded area and links in Fig. 4). Then the linkages between the state variables of the HTL model and the state variables of the LTL model were set up in accordance with the removed state variables as shown in Fig. 4 (links in dashed and continuous black lines). In this way, a coupled model scheme that consisted of 44 functional groups was set up: 9 FGs represented the state variables of the biogeochemical model, i.e. plankton groups plus inorganic and organic nutrient forms (Fig. 4). For simplicity, the HTL and LTL groups are not given in detail in the figure; however, sources and sinks of the whole HTL compartment and the linkages between the HTL and LTL domains and state variables are shown.

The second step in the harmonisation of models consisted of accounting for the different currencies used. Considering the multiple currency utilisation of the biogeochemical model for some of its state variables and the fact that the application of a similar principle in the HTL model would require the modification of the various calculations in the state equation of the original EwE software, the state variables of the HTL model, which were in wet weight (tons), were converted to phosphorus (µmol P) weight utilising C : N : P ratios taken from the literature.

The third step in the harmonisation procedure was to reconcile the differences in the integration time step between the two models. Considering that the biogeochemical model consisted of state variables with faster dynamics compared to the HTL model, it was convenient to make the HTL model comply with the integration step of the biogeochemical model. For this purpose, the rates of the HTL model, which were “per year (yr-1)”, were converted to “per hour (h-1)” by simply dividing the rates by 8760 (365 d-1×24 h-1) so that the HTL variables could be integrated with the same time step of the biogeochemical model.

The final step in the harmonisation process would be to adjust the closure terms of the biogeochemical model (mortality rates of zooplankton and phytoplankton groups) so as to compensate for the additional losses through explicit predation of these groups by the HTL state variables. However, for our specific application, we decided to keep these values identical to the standalone biogeochemical model, as the coupled model produced similar seasonal cycles observed in the standalone biogeochemical model except the missing second cycle in mesozooplankton (Fig. 6) and as our aim was indeed to have plankton dynamics qualitatively comparable to the biogeochemical model.

The technical overview of the coupling scheme is given in Fig. 5. As shown in the figure, the coupled simulation was carried out in four consecutive stages. In the first stage, a static mass-balance model of the whole system, which comprised all the HTL and LTL state variables in the ecosystem, was set up utilising Ecopath-F. In this stage, the LTL state variables were ordered in advance of the HTL state variables so that the LTL state variables were numbered from 1 to 9 and the HTL state variables from 10 to 35 in the resulting scheme. Following this procedure, Ecopath-F was run to calculate the basic parameters and exchange rates between the state variables of the HTL and LTL compartments which were necessary to perform a dynamic simulation after completing all of the harmonisation steps. In the second stage, utilising the calculations from the previous stage, the HTL and LTL models were initialised by calculating initial conditions for each of their respective state variables utilising their specific internal routines. In the third stage, the sources and sinks of HTL and LTL state variables were computed by utilising their respective derivative functions during the whole simulation period. The selection of the derivative function to be used to calculate the differentials of the state variables depended on the rank of the state variables determined during the Ecopath-F set-up in the first stage. This stage continued iteratively until the end of the simulation and, at the end of each time step, the fourth stage was executed so that the results calculated at each time step were, if required, post-processed and then written to the results files. Post-processing of LTL results might not be necessary in all cases, but only if the LTL model is a multi-currency model and calculates its variables in more than one currency. In our example, because the LTL model represented some of its state variables both in carbon and phosphorus but the coupled HTL model only in phosphorus, a post-processing step was necessary to compute the corresponding phosphorus values of variables that were in carbon units while interchanging information between the HTL and LTL derivative functions as well as before writing the results into the output files. The coupled simulation was run for 10 years, two of which were for spin-off. In the simulations, we used default values for vulnerabilities (vij=2) that represent a mixed control (Christensen et al., 2005).

Comparison of uncoupled and coupled model results (Fig. 6) demonstrated that the coupling scheme worked successfully and highlighted the effects of integration of the LTL and HTL models. Because the aim of this exercise was only to demonstrate the capability of EwE-F to be used in integration with other models, the ecological interpretations of these results are not the focus of this work, and thus are only briefly discussed here. Comparing the seasonal dynamics of LTL state variables before and after coupling showed that explicit addition of HTL dynamics influenced the seasonality of the LTL state variables (grey-shaded plots in Fig. 6). It is worth noting that the presence of several detrital and predatory links between the HTL and LTL models (as shown in Fig. 4) resulted in clear top-down impacts on the LTL variables, particularly on non-living and bacteria. Furthermore, the comparison between the simulation results of the HTL model forced with primary productivity changes (green lines in Fig. 6) in stock EwE and the fully coupled HTL/LTL models (black lines) showed that changes in the biogeochemical dynamics, namely nutrient recycling, not only impacted the LTL groups, but also propagated up through the food web (bottom-up) to impact the biomasses of HTL organisms. While most of the bottom-associated state variables decreased by the incorporation of the biogeochemical model into the coupled scheme, pelagic-associated state variables increased due to the explicit representation of resuspension of detritus and remineralisation that favoured plankton. Thus, as shown in Fig. 6, the consequences of two-way coupling were not only one-directional. These proved that the proper exchange of information and the establishment of successful interaction between the two models were realised in the final coupled scheme.

It has been shown that a Fortran version of EwE software could open up various possibilities in terms of coupling and integration with other Fortran-coded biogeochemical and hydrodynamic models where an HTL compartment is required. In order to exemplify the applicability of the approach, a coupled biogeochemical–EwE-F E2E modelling example was demonstrated (Sect. ). However, this was done to demonstrate the feasibility of the approach, and it does not mean that EwE-F can be applied only in E2E modelling frameworks. As discussed in Sect. , many other uses of EwE-F are possible.

EwE-F is still in its infancy and future development efforts will focus on maturing the software and implementing missing useful features like times series fitting via vulnerability search, capability to define multiple fishing fleets and explicit spatial simulation. We believe that the development pace of EwE-F will accelerate with the adoption and utilisation of the software in the scientific community.

The source code of EwE-F version 1.0 detailed in the present work and the corresponding User's Manual can be obtained as a supplement to this article. In the User's Manual, detailed instructions to obtain the current and future versions of EwE-F along with building and running EwE-F on different platforms are described. Further versions of the EwE-F model and their respective documentations can be obtained at bitbucket.org (https://bitbucket.org/ewe-f). The system requirements, license and other basic information regarding EwE-F version 1.0 are given in Table 1.