Approaches to end-to-end ecosystem models

Journal of Marine Systems 81 (2010) 171–183

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Journal of Marine Systems j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j m a r s y s

Approaches to end-to-end ecosystem models Elizabeth A. Fulton ⁎ CSIRO Marine Research, GPO Box 1538, Hobart, Tasmania 7001, Australia

a r t i c l e

i n f o

Article history: Received 4 November 2008 Received in revised form 30 March 2009 Accepted 22 May 2009 Available online 4 January 2010 Keywords: End-to-end models Ecosystem models Marine models

a b s t r a c t Ever growing understanding of general ecological, biogeochemical and climatic processes is allowing for the construction of a growing list of end-to-end models. While many of these are taking the form of generic modelling frameworks, no one approach defines end-to-end ecosystem modelling. There is a wide range of scales, resolutions, forcings, components and represented processes. Examples drawn from existing models can be used to give guidance on best practice approaches for creating end-to-end models. In particular, it is clear that defaulting to the finest resolution and greatest complexity in all the dimensions (e.g. spatial, temporal, taxonomic, process detail) is not beneficial. There is also a lot of value, during model development and implementation, in trying different model types, assumptions and formulations; there is no one “best” model. Maintaining a diversity of approaches is important given that end-to-end models are most effective when used as strategic tools, to address questions that are at scales where there is still a lot of uncertainty about how systems function. There are still many challenges facing the end-to-end modelling field, particularly when long simulation periods are called for, but perhaps the greatest ones are: non-stationarity introduced by shifting climate, biodiversity and evolution; representing human responses; and handling uncertainty. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Over the last 60 years, particularly over the last few decades, the understanding of marine systems has risen substantially, as has computing power. Consequently, there is now a proliferation of endto-end models, also known as whole-of-system models. End-to-end ecosystem modelling approaches differ from earlier models by attempting to represent the entire ecological system (including human components) and the associated abiotic environment (extending through to climate impacts); integrating physical and biological processes at different scales; and allowing for dynamic two-way coupling (or interactions) between ecosystem components (Travers et al., 2007). Examples of these kinds of models include packages such as Ecopath with Ecosim (EwE; Christensen and Walters, 2004), OSMOSE (Shin and Cury, 2001a, 2004) and Atlantis (Fulton et al., 2005a). End-to-end models are taking many forms, each with its own focus, resolution, strengths and weaknesses. This diversity is not unhealthy, as they span a much broader set of applications than any one modelling approach could successfully tackle. Nevertheless the variety can be daunting and guidance regarding best practice approaches for use and development of such models can be quite useful. In particular, such guidance can guard against the natural human tendency to search for some single “best” solution by adding increasing levels of detail to

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their modelling platform of choice. Within the field of end-to-end modelling, experience over the last 10–30 years has shown that such a response is particularly inappropriate (Botkin, 1977; Costanza and Sklar, 1985; Iwasa et al., 1987; Fulton et al., 2003a; Bruggeman and Kooijman 2007; Metcalf et al., 2008). By drawing on methods used in existing modelling frameworks this paper will highlight some of the end-to-end modelling pitfalls and their solutions; warn of their weaknesses and the coming challenges; and draw attention to how common such modelling approaches have already become. Recent literature has discussed challenges to their development (Travers et al., 2007), but these models are already in widespread use and as such a broader audience should be aware of the benefits and traps associated with these whole-of-system models. 1.1. Ecosystems and end-to-end models The term ecosystem is now at least 70 years old and is considered one of the most important ecological concepts of the last century (Willis, 1997). Perhaps one of the most widely used definitions of an ecosystem is that by Lindeman (1942), which states that “an ecosystem is composed of physical–chemical–biological processes active within a space–time unit.” More recent usage of the term has expanded to also include anthropogenic components of the system. The flexibility of the term ecosystem, which can be applied at many scales, and its expansion through time is reflected in model development. Earlier ecosystem models typically included only physical and some ecological system components — for example

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within the marine realm they often only dealt with plankton groups (Menshutkin, 1979; Baretta and Ruardij, 1987; Tamsalu and Ennet, 1995; Gin et al., 1998; Allen et al., 2001; Fennel et al., 2001). While many of these kinds of models are still being developed (Vezina 2004; Blackford et al., 2004; Le Quere et al., 2005; Fasham et al., 2006; Zuenko, 2007; Werner et al., 2007; Baird and Suthers, 2007; Gregoire et al., 2008), over the last 20 years models have appeared that include a broader set of groups and their trophic connections (e.g. EwE). As the number of these expanded models has grown, and drawn in more system components, including anthropogenic ones, the term end-toend modelling has been adopted to distinguish it from the ecologically focused models (IMBER, 2005). End-to-end models attempt to include all major relevant processes in the system. Abiotically these include: catchments, riverine and atmospheric inputs; currents and other major water body features like eddies, upwelling, downwelling, turbulence and resuspension; wind; irradiance; precipitation and water column properties such as temperature, salinity, and resulting zones such as the mixed layer and photic zone. Ecologically they are expanding beyond just covering lower (or higher) trophic levels to incorporate: nutrients and biogeochemical cycling, benthos (both in and on the sediments), the microbial loop, different types of detritus, a range of pelagic and benthic primary producers, different forms of zooplankton and other invertebrate secondary consumers, gelatinous species, cephalopods, forage and other fish species, functional or morphological groups (that cover the entire trophic web, both demersal and pelagic often), as well as larger ‘charismatic’ groups such as sharks, rays, marine mammals, seabirds, and marine reptiles. Including the dominant processes that are needed to dynamically represent these groups is a challenge in itself and has been the focus of major research efforts for the last 40 years. Over 150 papers to date (based on a web-ofknowledge search) have discussed what processes to include in these kinds of models and how they should be formulated. Consequently, there is reason for continued on-going discussion, expansion and refinement. In general the models capture dominant processes, such as water column fluxes (i.e. advection, diffusion and dispersion), primary production, feeding, growth, reproduction and movement of ecological groups. Moreover, an increasing number of models are closing nutrient cycling and including long-term climate forcing or environmental variability; for example, OSMOSE (Shin and Cury, 2001a, 2004), Atlantis (Fulton et al., 2005a, 2007), InVitro (Gray et al., 2006), SEAPODYM (Lehodey et al., 2003; Lehodey, 2005), and APECOSM (Maury et al., 2007). The other major area of expansion in end-to-end modelling has been increasing sophistication of the representation of competing and cumulative impacts of human activities on marine systems, including: terrestrial run-off; coastal development, ports and shipping; fishing (recreational, artisanal and commercial); tourism and other recreational activities; oil and gas exploration and extraction (including pipelines and other infrastructure needs); and less obvious uses such as defence (e.g. bombing ranges). In many models the majority of these pressures are still represented as external drivers (e.g. EwE where fishing is explicit, but most other forces are not). However, through complex adaptive systems and management-oriented research these sectors are also beginning to be dynamically considered in end-to-end models (e.g. all of these sectors may be represented explicitly in InVitro). It is not surprising that models with such ambitious scope can span roughly 14 orders of magnitude in spatial scale, from micrometre bacterial scales to ocean basin scales or global scales on the order of tens of thousands of kilometres, and include processes that act on time frames from seconds to centuries or more. Considering systems in this way — identifying their critical processes, components and scales — is necessary for forming an integrated view of system-level issues and management options (Fulton et al., in review), but also pushes scientific understanding to the extreme. It simultaneously pushes the bounds of complication (in terms of the size of the models and the

number of associated parameters) and complexity (with regard to non-linearity of outputs, feedbacks and potential hysteresis). This can make these models uncertain and potentially difficult to work with. Generally, the patterns and relative distributions they produce are informative; the absolute values are far less reliable. This makes them inappropriate for use as tools for setting tactical management measures, like quotas or nutrient load caps, which is the role of more focused models like fisheries stock assessment or biogeochemical ‘ecosystem models.’ These targeted models are themselves complicated and complex and require thoughtful use. For example, the range of tuna assessment models can contain 100 s of parameters, as well as detailed age and spatial structure — see the comparative review by Sibert (2004). Cautionary guidance on using such complicated stock assessment models are significant sections of stock assessment manuals such as Hilborn and Walters (1992), Quinn and Deriso (1999) and Haddon (2001). Nevertheless, in comparison to these models end-to-end, models are in a league of their own and must be used in a different way. They are best used to consider system-level ‘what-if’ management or impact scenarios. End-to-end models are proving their worth as conceptual and strategic tools in support of adaptive resource management. For instance, insight into system function, impacts of human activities and the implications of combinations of management actions have been gained using end-to-end models within a management strategy evaluation framework (Fulton et al., 2005b, 2007; McDonald et al., 2006, 2008). Management Strategy Evaluation (MSE) — or Operational Management Procedures (OMPs) — is a simulation technique based on modelling each part of the adaptive management cycle (Fig. 1). This technique was originally developed more than two decades ago to consider implications of alternative management strategies applied to natural resources, like fish or whale stocks (IWC, 1992; Kirkwood, 1997; Punt and Smith, 1999; Butterworth and Rademeyer, 2005). The method is now widely accepted as a best practice approach for single stock (Butterworth, 2007) and ecosystem-level management questions (FAO, 2007) and has also been adopted for multiple use questions (McDonald et al., 2006, 2008; Fulton et al., 2008). It is used both by international bodies (e.g. the International Whaling Commission and CCAMLR) and national fisheries departments around the world; useful reviews of the approach can be found in Butterworth and Punt (1999), Sainsbury et al. (2000) and Plagányi et al. (2007). The strength of the approach is that instead of trying to find an optimal solution, it evaluates alternative hypotheses (typically management strategies) using multiple candidate models to represent the uncertainty about the function of, and relationships between, different steps of the adaptive management cycle. The approach is also consultative, with the potential for all interested parties to have input into the candidate models and management scenarios. The outputs highlight unanticipated consequences of management actions and system responses and tradeoffs between objectives held by different stakeholders. In this way, the approach effectively acts as a ‘flight simulator,’ giving interested people insight into the system dynamics. This is an important management aid, as without it managers may act on theoretically optimal solutions that are beyond what is actually feasibly achieved within the system's current state. As a result well intentioned management actions can have counter intuitive and counterproductive outcomes. The history of fisheries management is littered with examples of this kind of consequence. For example, the introduction of regulations and quotas in the Norwegian small-boat fisheries actually led to an increase in pressure on the cod rather than the intended decrease, due to a mismatch of management actions with socially driven fisher incentives and responses (Maurstad, 2000). 2. Model types The majority of multispecies and ecosystem models focus on either the biogeochemical components of a system and the lower trophic

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Fig. 1. Adaptive management cycle (showing major steps and components).

levels or target fish species (and potentially their immediate predators and prey). The former typically includes nutrients, phytoplankton and potentially zooplankton or filter feeding groups (e.g. Murray and Parslow, 1999; Kishi et al., 2007; Gregoire et al., 2008), while the latter includes one or more species that are targeted by fisheries and their immediate prey, predators or competitors (e.g. Magnusson, 1995; Punt and Butterworth, 1995; Hall et al., 2006; Xiao, 2007). The evolution of these models has been in two directions (i) increasing detail in the formulation of the focus elements of the models and (ii) some extension up (or down) the trophic web to cover those system components most closely tied to the subsystem of interest. For instance, plankton models have grown over time from a simple chain of nutrient, phytoplankton and possibly zooplankton boxes (e.g. Evans, 1978) to include multiple limiting nutrients and increasingly complex representations of a range of phytoplankton, zooplankton and detritus functional groups (e.g. Moore et al., 2004; Wiggert et al., 2006). The inclusion of benthic processes and filter feeding groups has also been a natural extension up the foodweb as plankton and water quality models have been applied in shallower systems, where cross connections between processes at different depths and in different media increase in importance, e.g., the Port Phillip Bay Integrated Model (Murray and Parslow, 1999) that added a microphytobenthos group and a benthic filter feeder group to a more traditional nutrient–phytoplankton–zooplankton NPZ model. The inclusion of environmental drivers or habitat in fish models is an example of how focused sub-web models are being extended to consider more of the system. Illustrative examples are the riparian restoration and salmon population models of Watanabe et al. (2005), or the models that incorporate environmental variability and fisheries reviewed by Keyl and Wolff (2008). While the number of end-to-end models has grown quite rapidly in the last decade, models that include the whole system are not new. Conceptual models that touched on action at this level can be found among writings of some of the earliest philosophers from many of the great ancient civilisations (e.g. China and Greece; Katz and Katz, 1995; Chen, 1996). The earliest quantitative models date back at least as far as the International Biological Program of the early 1970s and to seminal efforts such as that by Andersen and Ursin (1977). The latter has had a profound effect on the direction taken in multispecies fisheries modelling, such as the development of the multispecies virtual population analysis (MSVPA) approach by Magnusson (1995). The popularity of such models has grown significantly over the last

10–15 years as computing power has increased and tools like EwE and Ecospace (Christensen and Pauly, 1992; Walters et al., 1997, 1999, 2000; Christensen and Walters, 2004) have provided readily accessible scientific tools. The widespread use of EwE has seen the production of trophodynamic models that span considerable parts of the system become a commonplace tool in many ecology departments and research organisations worldwide. This level of use is symptomatic of, and driven by, the same pressures that have lead to the development of the majority of the end-to-end modelling platforms. Globally, public, scientific and political interests and concerns have grown from single sector or direct effects to multiple use and indirect or system-level effects. This is reflected in the content of national environmental policies and international documents such as the Johannesburg Declaration on Sustainable Development (United Nations, 2002). Given the complexity of the systems and questions end-to-end models must address, it is perhaps not surprising that a number of different approaches have been taken in their development. Some models take the minimum realistic approach, including the bare minimum as dynamic components and forcing any other relevant system components. This approach is taken in a suite of Antarctic models developed to consider options regarding the precautionary krill catch limit (Constable, 2006; Plagányi and Butterworth, 2006; Mori and Butterworth, 2006; Watters et al., 2006). These models include key processes such as transport, production, predation and harvesting, but do not fully specify the trophic web, concentrating instead on the krill and predatory species considered to be most important. This method is a valid one in its own right, but is also often used as a first step in the development of end-to-end models from other existing subsystem models, e.g., NEMURO.FISH which has added a fish model to the detailed NPZ model NEMURO (Megrey et al., 2007a). The three main approaches taken when developing a more inclusively dynamic end-to-end model are (i) intermediate complexity (when intricate process detail is sacrificed so a modestly complex representation is applied to all modelled system components; Moore et al., 2004); (ii) the rhomboid (or middle out) approach (when detailed models of the key or best understood parts of the system are linked to simpler representations of the rest of the system; deYoung et al., 2004); and (iii) when different types of models, which deal (often in some detail) with different components of the system, are coupled to create hybrid models (Lehodey et al., 2003). This last

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approach has really only become common with the advent of increased computing power in the last 5–10 years. Significant scalehandling issues still remain for hybrid models, but it is likely that they represent a method that will become increasingly common in the future. This is because they seem to be an effective means of capturing the broad range of scales and processes ecosystems span, without needing to artificially force everything into a common scale. In some cases this will see an increased reliance on parameterisations, where the coupling relationships need to be defined. However, in many cases the coupling will link existing well parameterised models and will remove unnecessary or artificial structures that were included to allow for all components to be represented on a universal scale. 2.1. Qualitative (and conceptual) models With the advent of large computing capacities the use of qualitative models has dwindled in the biophysical sciences. This is unfortunate, as they can provide quite substantial insights into system functioning (Levins, 1966). Qualitative methods can be rapidly deployed; a modelling exercise can take as little as an afternoon. They also readily allow incorporation of stakeholder advice and input, which ensures stakeholder requirements are addressed and can ultimately improve uptake, and can be very useful for identifying key system components and processes. For example, loop analysis uses the conventions of signed diagraphs (from network theory) to assign positive and negative signs to each connection or interaction in the conceptual model. Using these diagraphs and algebraic methods described by Dambacher et al. (2003a) significant insight can be gained into potential system-level evolution and responses to press perturbations. For instance, Dambacher et al. (in review) considered foodwebs in the central and south Pacific and the effects on these systems of climate change. It was found that not only did the systems have little commonality in the structure of the foodwebs, but also there was no consistent pattern in the effects of climate-based perturbations, often due to indirect effects overwhelming direct effects. The same methods are also a rigorous means of isolating relevant subsystems and essential processes for inclusion in any quantitative system model. Loop analysis can also be used to check for the potential magnitude of model structure uncertainty — by considering the result of perturbation experiments at differing degrees of resolution and with different conceptual models of system structure and checking for a divergence in results. This use is facilitated by the rapidity and flexibility of the qualitative modelling approach, which allows for the rapid exploration of a large number of alternative model structures and configurations. There are some constraints however, as the complicated nature of the networks of connections in very large models means that the results of any loop analysis on such models can potentially become ambiguous. 2.2. Aggregate system (or network-based) models Aggregate system models are based on trophodynamic networks of the entire system. They include bioenergetics models like those by Yodzis (1998) and Koen-Alonso and Yodzis (2004) and mass balance network models like EcoNetwrk (Ulanowicz and Kay, 1991; Ulanowicz, 2004). The dominant ecosystem-level example of this kind of model is EwE and the spatially explicit form Ecospace (Walters et al., 1999). Ecopath is used to create mass-balanced snapshots of the network structure and magnitude of biomass pools and energy flows in an ecosystem. Ecosim, which uses Ecopath parameters as initial conditions, produces time dynamic simulations for fisheries policy exploration and increasingly incorporates the consideration of environmental drivers. Ecospace extends the Ecosim approach onto a 2D grid (with the addition of potential habitat dependency, migration and spatially explicit productivity and fisheries distributions) to allow for consideration of the effect of spatial management.

In combination the EwE software suite provide tools for addressing questions regarding environmental influences on ecosystems, ecological dynamics and ecosystem effects of fishing strategies and management policy options. Some of the assumptions included in the modelling framework, particularly the vulnerability based feeding functional response in Ecosim, have been questioned in the past (Plagányi and Butterworth, 2004) and there is still the perception that network models like EwE cannot address non-linear dynamics. Neither of these is a universal issue impacting the general utility of the approach. For instance, the formulation of Ecosim and Ecospace mean that they can capture a range of non-linear dynamics (e.g. nonlinear indirect trophic effects seen in Fulton and Smith, 2004) even if they are initialised from mass balance conditions. Instead, these aspects of EwE's formulation should be kept in mind when determining its utility for specific applications, just as attention to the validity of assumptions should be a core principle in any modelling application. The on-going evolution of the Ewe software is an illustrative example of the continually evolving nature of end-to-end models. The development of end-to-end models is a dynamic, highly active, field. The models are increasingly multidimensional, for example expanding their capacity for greater ontogenetic and spatial resolution. Many of the end-to-end modelling platforms are embracing this on-going expansion via the use of plug-in modularity (e.g. Christensen and Lai, 2007). While there may be the perception that the models are needlessly becoming increasingly complicated, this is not the case. Recognising the gains available from using existing “record keeping structures” many of the additional features are not added in the expectation of universal use, but as options for use only in specific circumstances.

2.3. Biogeochemically-based end-to-end models Over the last 20 years biogeochemically-based models have represented a significant proportion of the ecosystem and end-toend models. They track nutrient flows through the components of the ecosystem. Traditionally these grew from nutrients only to include lower trophic levels and then finally vertebrates and human activities. These models represent some of the earliest end-to-end marine models; ERSEM (Baretta et al., 1995) and ERSEM II (Baretta-Bekker and Baretta, 1997) are among the first examples of end-to-end models. However, while fish and seabirds were inclusions in the original models they have not been widely used — the majority of ERSEM applications to date have concentrated on the lower trophic levels (e.g. Allen et al., 2001; Petihakis et al., 2002; Wirtz and Wiltshire, 2005; Polimene et al., 2006, 2007; Allen and Clarke, 2007; Kohlmeier and Ebenhoeh, 2007; Siddorn et al., 2007). The method of development of biogeochemical end-to-end models often epitomises the evolution of end-to-end models from inclusion of forced external pressures to explicit one-way coupled models to bidirectional dynamically-coupled model components. The evolution of NEMURO is a prime example. The core NEMURO model (Kishi et al., 2007) couples a plankton model to a basin scale, reasonably resolved, ocean hydrodynamic model. From there a fish production model was forced by the production from the plankton model and water column properties from the hydrodynamic model (Megrey and Kishi, 2002). This was used to consider the implications of climate change for the location of fronts and fish biomass. The most recent expansions of the NEMURO framework have introduced the capability for dynamic fish models to further insights into fisheries implications of changing climate conditions (Megrey et al., 2007b; Rose et al., 2007). Another good example of a model that couples a detailed fish model with the lower trophic levels is the bi-directionally coupled model of Oguz et al. (2008), which includes both a lower trophic foodweb sub-model and a bioenergetic-based anchovy population dynamics sub-model.

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This model has been used to investigate the long-term anchovy and gelatinous biomass changes in the Black Sea. Some of the largest end-to-end modelling platforms, such as Atlantis (Fulton et al., 2005a, 2007), have been focused from their beginning on two-way coupling of the many parts of marine systems. At the biological end of the spectrum this has involved the explicit inclusion of physical and biogeochemical system components right through to higher trophic levels; at the other extreme it incorporates the potential to consider human dynamics in some detail. This modelling framework includes process libraries for each part of the adaptive management cycle — biophysical, industry, monitoring, assessment, management, and socioeconomic (Fig. 1). Atlantis grew from other ecosystem models developed to consider the impacts of model complexity on performance (Fulton et al., 2003a) and consequently it is flexible in its construction, providing a wide range of resolutions and assumptions in each library. This flexibility has allowed it to concentrate on questions spanning all parts of the adaptive management cycle (from biophysical impacts to the evaluation of alternative monitoring and management options). Atlantis is intended for use in a MSE context. This is important given the role of end-to-end models for strategic management and science questions rather than tactical questions. Use of biogeochemical “ecosystem models” (nutrient–plankton production models) are often aimed at forecasts and tactical (e.g. water quality) management questions, but end-to-end models are not suitable for such questions and should only be used for asking larger scale overarching questions regarding robust forms of management for marine natural resources. 2.4. Coupled and hybrid model platforms With increasing computational power and the maturation of many process-based model types there is an increasing number of end-toend modelling platforms that couple different kinds of models together. While some model types, such as EwE and Atlantis, have an increasing capacity to couple to other models, other end-to-end modelling frameworks (e.g. those discussed below) are specifically, and often fundamentally, formed from coupling or combining models of different types. Many of these coupled models include a component that is, or can be, size-based. The simplest examples are where size spectra models have been coupled to environmental drivers. Size spectra models represent the ecosystem (or part of it) as a continuum of biomass per body-size bin, with biological rates (particularly growth and reproduction) and predatory interactions dictated by size ratios (Duplisea and Kerr, 1995; Zhou and Huntley, 1997; Duplisea et al., 2002; Benoît and Rochet, 2004; Jennings et al., 2008). This approach avoids the need to detail diets, metabolic or ontogenetic processes (Travers et al., 2007) and makes these models a convenient means of representing key linking ecosystem components and processes in end-to-end models; as the hardest links to define with certainty are the connections between the higher trophic levels and zooplankton or detritus. The size-based approach has been picked up in a number of end-to-end models including OSMOSE, which uses the approach to represent feeding interactions, and APECOSM, which uses size spectra to represent forage layers in models focusing on top predators (Maury et al., 2007). The nature of size spectra models also makes them relatively simple to link to environmental forcing (e.g. Maury et al., 2007) or fishing pressure models (Benoît and Rochet, 2004; Pope et al., 2006). A complex example of the coupled approach is SEAPODYM (Lehodey et al., 2003; Lehodey, 2005), which consists of: a biogeochemical model, which acts as a forcing field, providing hydrodynamic flows and low trophic level states; a box-model of forage components, representing vertically structured mesopelagic fish, cephalopods and crustacean groups; and an age-structured fish population model that can also include fishing pressure and multiple

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fleets. Predation dynamically links the forage and top predator model, but the physical properties (e.g. water movements, oxygen, temperature and primary production) supplied by the biogeochemical model do contribute to the handling of feeding, recruitment and movement dynamics. Some of the newest and promising forms of end-to-end models are agent-based models. These take the principle of individual-based models, which use decision algorithms to ‘play-out’ behaviour (e.g. Strand et al., 2002), but expand it so that different agents can actually be realised using different model types — including classical IBMs, but also meta-population and aggregate difference or differential equation models. In this way the most effective means of representing different parts of the system can be brought together to produce an effective model of the whole system. OSMOSE and InVitro are examples of these kinds of agent-based models. They include (or dynamically couple): IBM-based age-structured fish or predator population and trophic interaction models; biogeochemical plankton production models; hydrodynamic and environmental models; habitat models; and representations of human activities (and potentially their social and economic drivers). OSMOSE is currently primarily focused on ecological and fisheries questions (Shin and Cury, 2001b; Shin et al., 2004; Travers et al., 2006), while InVitro is focused on addressing multiple use management questions and includes dynamic representation of a broad range of human activities — from commercial, charter and recreational fishing, tourism, shipping, oil and gas extraction, to dumping and effluent release, coastal development, conservation, mining, defence, ports, local and regional economies, and infrastructure (Little et al., 2006; McDonald et al., 2006; McDonald et al., 2008; Fulton et al., 2008). While some of the other modelling approaches (e.g. Atlantis), include options for density and forage dependent fish movements and plastic growth (Fulton et al., 2005a), agent-based models more than any other type are allowing for fluid representation of processes like movement, growth, phenotypic expression and genetic heritability and evolution. This makes them a good tool for considering a range of questions from fine scale interactions (Rose et al., 1999) up to the implications of the non-stationary nature of a world influenced by climate change (Moss et al., 2001). 2.5. Model dimensions The complex and complicated nature of end-to-end models means that a lot of consideration has been given to the way they are structured. These dedicated efforts (e.g. Fulton et al., 2003a,b, 2004a,b, c; Pinnegar et al., 2005; Metcalf et al., 2008), and general conclusions drawn from modelling experiences, have shown that there are strong tradeoffs between the currency used; the degree of spatial, temporal and taxonomic resolution used; the kind of components included (e.g. only biophysical or the inclusion of extra components such as human industries); the physical, chemical, ecological and anthropogenic detail included in process representations; and the form and extent of boundary conditions and forcing. As mentioned above there are many approaches that can be taken when dealing with model complexity (e.g. the rhomboid approach or intermediate complexity), all of which have strengths and weaknesses — there is no “best way” of constructing end-to-end models. Nevertheless it is clear from experience across many groups that extreme resolution in all aspects is not an effective approach. Qualitative methods, such as those described above, can be useful tools for this model refinement process. Without taking the time to explicitly do this kind of model structural consideration there is considerable risk of adopting a model that is inappropriately complex and inapt for addressing the questions of interest. Research into model complexity shows that there is a domed relationship between model performance and complexity (Costanza and Sklar, 1985; Håkanson, 1995; Håkanson, 1997; Fulton et al., 2003a). Very simplistic models fail to capture critical interactions and system

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components and so are unhelpful. Nevertheless extremely complicated models are not necessarily useful either, as they are particularly impacted by uncertainty and there is a danger for large models to be prescriptive rather than predictive. Moreover there are considerable computation issues with using very large models. Thus, for computational cost, uncertainty and performance reasons inclusion of details beyond those required to address the specific issue of interest is ill advised. Models are suitably complex if all critical processes, drivers and components under scrutiny are captured (Nihoul, 1998; Nihoul and Djenidi, 1998; Fulton et al., 2003a). One useful approach to doing this is to employ sub-grid scale process implementations to represent the influence of smaller scale processes without defaulting to that resolution universally. For example, Atlantis uses statistical distributions and coefficients of variation to capture the patchiness and influence of features like eddies or habitat, avoiding the need to use a fine scale spatial resolution to explicitly represent them (Fulton et al., 2007). 3. Best practice model development Careful consideration of model form and complexity is key to appropriate and best practice use of end-to-end modelling. As pointed out by Rudolph Marcus, the best approach is to “attack problems at appropriate scales, with appropriate theories and methods. A universal scale is not useful.” This is the principle behind the FAO (2007) recommendations on best practice use of multispecies, ecosystem and end-to-end models for addressing fisheries management questions. The same principles would also hold true for other natural resource questions. The FAO (2007) best practice guidelines provide recommendations for each aspect of model construction and contents. They emphasise the need to only include components needed for capturing critical dynamics and the importance of explicitly including feedbacks. The guidelines also highlight the importance of addressing uncertainty, not simply parameterisation but structural uncertainty, and the associated requirements to try multiple options (e.g. using different options and candidate models within a MSE). A summary of the general principles for specific model dimensions will be given below, but readers interested in details are encouraged to go directly to FAO (2007) and other complexity related literature (e.g. Fulton et al., 2003a, 2004a,c; Walters and Martell, 2004; Pinnegar et al., 2005; Metcalf et al., 2008). Perhaps the strongest points to be made however are that: (i) across all the dimensions of model construction it is important not to default to the finest scales, as it is often inappropriate and unnecessary; and (ii) multiple model forms should be considered as there is no one “right” model, which means that at the level of the modelling community multiple approaches should be pursued and maintained and that the assumption that a single “consensus” model should be supported can be counterproductive and dangerous for both the breadth of system understanding and the appreciation of uncertainty. 3.1. Spatial and temporal resolution After conceptual thought has been given to what system components need to be included in a model, one of the initial considerations of model construction should be what defines the core domain of the model, based on the scale of action of the primary components of interest. Some thought should also be given to what proportion of the system influences and stressors, seasonal and ontogenetic shifts of components extend beyond this domain. In some instances (where those influences or life stages are tractable and form critical forces, bottleneck or feedback components) it may then be

apposite to explicitly extend the model domain to more inclusively cover these influences and life stages. In other cases, where key processes and dynamics are confined to the domain, the smaller domain should be maintained and external drivers and remote forcing treated in other ways. Once the boundary is defined, decisions are needed on the internal vertical and horizontal spatial resolution. Ultimately, the resolution used should be dictated by the ecological, environmental and anthropogenic (including jurisdictional) length scales. It is important for the spatial resolution of a model to capture the major characteristics of the system — e.g. major oceanographic features and structuring geomorphologies like shelf breaks, biological distributions and location of major human activities. Explicit spatial structure is not always required, but if it is not included then implicit spatial structuring should be taken into account when defining biological and other components — e.g. division of shelf, slope and pelagic fish groups in Bulman et al. (2006). Without this kind of structuring, erroneous dynamics, such as trophic self-simplification of foodwebs (Fulton et al., 2003a) will arise, which are artefacts of inappropriate contact of groups and processes that are in reality separate or because space itself is an important system resource (e.g. for benthos). When explicit spatial handling is considered essential for a model, as it often is in end-to-end models, the strengths and weaknesses of homogeneous grids versus heterogeneous networks of nodes or polygons should be evaluated before progressing this aspect of model development. It is also possible to have different model components using alternative spatial representations. For instance, in hybrid models bathymetry may be on a regular grid, while other features (e.g. habitat) may be more effectively represented as polygons (as this focuses on “hot spots” of activity and available data). An example of such approach is the application of InVitro in the Exmouth-Ningaloo Reef area of Western Australia. This model uses a grid for bathymetry, sediments, nutrients, some habitat types and benthic biomass pools; patches for other kinds of coastal habitats (e.g. mangroves); polygonal plumes for contaminants; regional subpopulations for many mid-trophic groups; school-sized aggregations for commercial invertebrates; individual or small groups of largebodied or high trophic level vertebrates (e.g. sharks or whale sharks); and nodes for roads, ports and accommodation networks (for tourist use). Many of the same considerations are required for the handling of time. An appropriate temporal resolution (e.g. tidal, daily, weekly, monthly, seasonal, or annual) for the system components must be selected, with the possibility for groups to be handled on differing time scales. For example, it is often necessary for lower trophic levels, which have faster rates of turnover, to be treated with finer time scales (Christensen and Walters, 2004; Walters and Martell, 2004). There is also a variety of ways in which the progression of time can be represented, each of which has its own computational and numerical implications. Synchronous (when all components share a common time step size) and adaptive time steps (where the rate of instantaneous change of biological groups dictates the size of substeps, which are cumulatively iterated until a full time step is completed) are the most common way of handling time. Adaptive time steps are typically used for lower trophic levels in biogeochemically-based models (e.g. Atlantis). Many of the hybrid models handle time more innovatively — allowing different groups to use different time steps, just as they use different spatial scales. One of the most innovative forms of this is seen in InVitro, which uses an asynchronous approach to handling time, where the time step shifts for each component depending on what actions they are taking, so attention can focus on critical events, and there is no requirement for all components to be using the same time step at any one time. While each of these approaches to handling time has its advantages and disadvantages, the common imperative is that no process bias or artefacts are introduced by execution order.

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3.2. Taxonomic resolution When defining the taxonomic resolution of an end-to-end model the first rule to follow is to avoid extremes. The subsystems relevant to addressing the questions of interest will dictate the magnitude of the ecological components of the model, but omission or aggregation of species will be inevitable. How this is done can be important not only for computational and data requirements, but also for maintenance, and performance. Again the domed relationship between model complexity and performance means that more is not guaranteed to be better when constructing the trophodynamic structure of end-to-end models. While the inclusion of all of a system's ecological components is not necessary, as evidenced by the strong performance of the minimum realistic modelling approach (e.g. Punt and Butterworth, 1995), consideration of the implications of different trophodynamic and ecological model structures should be considered so that model uncertainty related to potential taxonomic skew can be evaluated. It has been shown that model structures that emphasise particular parts of the foodweb can exhibit markedly different system-level dynamics to models that have a more even taxonomic resolution across the trophic levels (Fulton, 2001; Pinnegar et al., 2005). In particular, models in which lower trophic levels are heavily aggregated can overstate how resilient the system is to disturbance. To avoid this behaviour, it is typically better to omit some groups that have little influence on system dynamics than to inappropriately aggregate groups (e.g. predators and prey) (Fulton, 2001). Nevertheless, when omitting groups it is important in statements of uncertainty to be clear that such omissions do leave the door open to unexpected system behaviours (that are not captured by the model) due to the omitted groups (that may have a negligible role in the current system, but could change non-linearly to have a much larger role under an alternative system state). A range of approaches can be taken when defining a model's ecological structure. In the same way that space and time can be dealt with in a heterogeneous fashion, the way in which ecological groups

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are defined can be a mix of size, turnover rates, ontogeny, habitat and other non-trophic uses, predators and prey, role, movement patterns and distributions. The majority of ecological components of many end-to-end models (e.g. Atlantis, ERSEM, EwE and InVitro) are functional groups defined in this way, mixed with some components resolved to a species or even stock level (due to commercial or conservation interests). However, models such as SEAPODYM, APECOSM and OSMOSE use a more innovative mix of ecological group types, using completely size structured representations (i.e. biomass size spectra representations) for parts of the trophic web, e.g. forage layers in SEAPODYM. This is an excellent example of where thoughtful use of different modelling approaches has effectively captured the system components without resolving everything equally, while also avoiding issues of over aggregation. Regardless of how the ecological system is represented, it is important in end-toend models that these structures do not prevent models from having alternative stable states, as these are potentially key for understanding system behaviour under different environmental conditions and stressor levels. This will in part be dependent on the ecological substructure (e.g. age, stage or size structure) included in the model. Typically end-to-end models need to include the capacity for ontogenetic shifts and delays in the system (e.g. due to long habitat patch recovery times). The selective use of a combination of approaches (e.g. individual-based, age-structured, subpopulationlevel and biomass pool representations) can again be an effective means of doing this while not succumbing to computation and datarelated constraints (see Fig. 2 for an example). This is probably why many of the end-to-end modelling platforms (EwE, Atlantis, OSMOSE, SEAPODYM, APECOSM, InVitro) are evolving to include this mix of representations. 3.3. Process resolution and external forcing The spatial, temporal and taxonomic resolutions will direct appropriate levels of process detail (and to some extent vice versa).

Fig. 2. Hybrid model example — structure and model types used in the InVitro model of the Ningaloo Reef, Australia. Only major flows or connections are shown.

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For some influences on a system (e.g. environmental forcing of a local or regional system) the best (or only) means of representing them is to include them as an external forcing function. The decision to make such an inclusion is predicated on them being a defining feature of the system's primary driving forces. The impacts of anthropogenic activities (such as inputs and pollution, tourism, clearing and coastal development, shipping, ports and dredging, and economic markets) can also be included in this way, though these are increasingly being represented explicitly and dynamically in end-to-end models. Forcing components that are more closely connected to the core system components of interest can be successful in some instances — e.g. primary production (Bulman et al., 2006; Lehodey, 2005) or predation (Thomson et al., 2000; Mori and Butterworth, 2006; Plagányi and Butterworth, 2006). However, such forcing has typically only a developmental step during the formulation and implementation of end-to-end models — e.g. see the evolution of NEMURO (Kishi et al., 2007; Megrey et al., 2007a; Megrey et al., 2007b; Rose et al., 2007) and OSMOSE. This is because the need for feedbacks and system delays to be explicit in end-to-end models means that dynamic twoway coupling of the majority of system components is imperative. Nevertheless, as for every other dimension of model construction, simply defaulting to the most finely resolved process representation is inappropriate. Elaboration of process detail should only occur if it has a major impact on system dynamics, i.e. the omission causes significant departure of model predictions from observed dynamics. For instance, for many system-level resource extraction questions detailed physiological representations are not required and simpler growth and waste production representations will suffice (Fulton et al., 2004c). However, nutrient, light, oxygen and space limitation of growth does prove essential for correctly representing basal groups. This is another area where model structural sensitivity needs to be given in-depth consideration however, and alternative formulations should be trialled as much as possible. The use of sub-grid scale representations is also a very effective means of representing the impacts of a process without finely resolving the mechanisms involved — e.g. using distributions to represent patchiness without using fine scale activity tracking (Ellis and Pantus, 2001), or using coefficients of variation to represent the influence of eddies on production without requiring an eddy resolving model (Fulton et al., 2007). Linking different types of models is another effective means of doing this. Hybrid models explicitly do this. For example, InVitro uses meta-population representations for more numerous groups, but explicitly plays out the detailed feeding and movement behaviour of rarer or more vulnerable species. Also, EwE now has the potential for age-structured stanzas and individual-based larval dispersal to be played out against a gridded biomass pool-based background (Walters et al., in review). Other model types can also make good use of this approach. For example, a statistical model or empirical curve could be used to represent the impacts or gross form of a key process even if the fine scale mechanics cannot be represented explicitly. This approach is taken in Atlantis (Fulton et al., 2005a) to represent nutrient cycling processes in the sediments. 3.4. Anthropogenic components Anthropogenic components are typically the most lightly treated aspects of ecosystem and end-to-end models. Dedicated behavioural models have been developed in targeted literature — e.g. fleet dynamics models (Sampson, 1994; Laloe et al., 1998; Dreyfus-Leon, 1999; Xiao, 2004; Hutton et al., 2004; Soulie and Thebaud, 2006) and for quantitative bioeconomic and social models (Ward and Sutinen, 1994; Holland 2000; Little and McDonald, 2007; Merino et al., 2007; Scheffran and Hannon, 2007; Pollnac and Poggie, 2008). Typically however, these socioeconomic models were not dynamically coupled to equally detailed biophysical models until the last decade. Even now the attention given to anthropogenic components of end-to-end

models has generally not been to the same degree as for biophysical components. Notable exceptions are the inclusion of explicit economic and social parameterisations, product chain tracking and fleet behaviours in EwE (V. Christensen pers. com., University British Columbia); and options allowing the use of detailed (socially and economically driven) behavioural models in Atlantis (Fulton et al., 2007) and InVitro. This uneven treatment is unfortunate. Experience is showing that behavioural uncertainty, in the form of unanticipated responses to changing resources and management decisions, is key to determining long-term system dynamics in harvested and impacted systems. Moreover, capturing the dynamics of the human components of the system is proving to be as difficult (if not more so) than representing biophysical components. This is in part due to the relatively immature state of this kind of dynamic modelling, but is also a result of semantic and philosophical divides between the biophysical and social sciences (which are slowing collaborations). There is an extensive bioeconomic modelling literature (reviewed in Eggert, 1998; White, 2000; Knowler, 2002; Pelletier and Mahevas, 2005) and a growing body of behavioural models in the complex adaptive systems area (Berkes, 2006; Plummer and Armitage, 2007; Gaichas, 2008; Mahon et al., 2008), but these either have a different underlying philosophy (e.g. optimality and equilibrium states) or have not been designed with resource use questions in mind. These are not insurmountable scientific obstacles and it is only a matter of time before anthropogenic facets of end-to-end models are routinely handled with the same degree of sophistication as the biophysical components. In the interim, trialling alternative scenarios of possible behaviours or patterns and levels of anthropogenic activities are an acceptable approach. If explicit, dynamic representation of human sectors is included in an end-to-end model then the same approaches to deciding on appropriate resolution and process detail as used for other aspects of the model should be used. As with other aspects of end-to-end modelling, using different representations for different human sectors or components is a valid approach. For example, social and economic detail maybe given to some fishing fleets, while other fleets are represented more simply and other sectors, like coastal development trajectories, are forced — see Fulton et al. (2007) for such an application. 4. Handling uncertainty 4.1. Problems with classical methods of handling of parametric uncertainty The size and complicated nature of end-to-end models makes handling uncertainty an essential but challenging undertaking. Classical sensitivity analysis approaches (where parameters are systematically varied, like the methods discussed in Saltelli et al., 2004) are impractical when the number of parameters in end-to-end models is considered. This situation is compounded by feedbacks within these kinds of models, which mean that (i) the results of sensitivity analyses are dependent on the time frame being considered and (ii) that there is a combinatoric possibility for model sensitivity to parameter interactions or sets (Pantus, 2007). This sees the curse of dimensionality writ large, meaning that alternatives to classical sensitivity analyses must be found for end-to-end models. Simultaneously fitting or validating models against multiple datasets (e.g. pattern-oriented modelling, Kramer-Schadt et al., 2007) does constrain feasible parameter sets, but even this cannot alleviate the need for new ways of addressing uncertainty for these large models. The feedbacks in end-to-end models demand new approaches or a shift in focus in the handling of uncertainty. Moreover, the biophysical and stock assessment-based background of many model practitioners may have led to a misplaced focus on precise numerical outputs rather than more broadly considering overall patterns and connections

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captured by the models. Explicit focus of more of these latter components is likely to be necessary for checking the uncertainty of system-level dynamics in end-to-end models. Methods that can be adapted to this task may well exist already in other fields. While new approaches to handling parametric uncertainty in large feedback models are being discovered, some pragmatic approaches can be used in the interim. The first of these are functionality filters, which can be used to identify the most sensitive parameter sub-sets or system components and then these can be considered using more traditional methods (Pantus, 2007). This approach has some drawbacks regarding rigorous coverage, but in combination with Bayesian hierarchical modelling methods (Press, 2002) can provide a means of getting the most out of existing well-understood analysis methods. Two existing methods that are already readily used with end-toend models with some success are perturbation analysis and bounded parameterisations. Perturbation analysis is when different components of the system are intentionally perturbed (depleted, increased or systematically change in some way) and the flow on consequences to all other system components mapped. This form of analysis gives good information on model sensitivity, but can also give insight into potential system functions and pathways (Pantus, 2007). Bounded parameterisations also give insight into the span of possible system dynamics and represent a very simple (but tractable) means of handling uncertainty. In this approach a range or bounding set of parameterisations are used such that in each major dimension of the system (e.g. productivity and vulnerability, external forcing, level of human impacts etc) the most pessimistic, middle-of-the-road, and optimistic, but still feasible, versions are considered. This approach has been used with success in Australian models, e.g. an application of InVitro in northwestern tropical waters (Little et al., 2006), and Atlantis in south-eastern Australia (Fulton et al., 2007), to consider potential management outcomes under a range of system states, management combinations and levels of human activity. The assumptions underlying this approach are (i) that the combination of specifications and scenarios tested really do span the bounding set of feasible alternatives and (ii) the output of the bounding combinations of parameters and scenarios is also bounding (i.e. no parameter combination that lies within the range of explicitly trialled parameter combinations produces outputs that sit outside the explicitly produced results). The non-linear nature of end-to-end models can make these assumptions strong ones, but to date it has been an effective and practicable approach.

4.2. Structural uncertainty While parametric uncertainty is a significant issue in end-to-end models, structural uncertainty is typically even more of a concern. This is uncertainty about which processes, scales and system components to include in a model. One effective approach to this problem is to use loop analysis (Puccia and Levins, 1985). The same qualitative methods that can be used to give insight into system structure can also (once combined with clustering methods) provide useful information on potential structural sensitivity (e.g. due to levels of trophic or process aggregation). The body of work by Dambacher et al. (1999, 2002, 2003a,b) and Metcalf et al. (2008) presents a good example of this. For example, Metcalf et al. (2008) considered the form and degree of aggregation error introduced into trophic models that have been simplified using Euclidean distance, Bray–Curtis similarity, or regular equivalence. All three methods generated some error, but regular equivalence produced a simplified model most aligned with diet data, preserving more of the critical foodweb details, and with the least aggregation error (more than 86% of the predictions from this simplified model agreed with the original detailed model; the other aggregation methods leading to only a 65– 73% agreement in predictions).

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The issue of structural sensitivity is not divorced from parametric uncertainty and there are some methods common to both types of uncertainty. In particular, the robust performance of the bounded parameterisation approach is in large part due to the fact that it is used in combination with careful considerations of structural uncertainty. It has been shown that structural uncertainty (what and how a model includes components) is a critical determinant of model performance in any one situation (Fulton, 2001; Pinnegar et al., 2005; Hill et al., 2007; Metcalf et al., 2008) and that existing knowledge is not at a sufficient level to constrain most models (Yearsley and Lettenmaier, 1987; Keyl and Wolff, 2008). In combination, these findings not only mean that modellers must give careful thought about how complexity (and complication) is dealt with in models, but that multiple models should be developed, maintained and employed. It is important to re-emphasise in this context that there is no one single “right” model. By definition a model is a simplification of reality and will therefore have some associated idealisation. Consequently, it is best to use a range of models or alternative formulations that can address the question in different ways. Just as with climate questions, the uncertainty associated with whole-of-system-level questions means the greatest leverage is gained by considering ensembles of models (Fulton and Smith, 2004; Hill et al., 2007). The idea of bringing “the best and brightest” together to develop the “best” model sounds quite attractive, particularly to funding bodies. The principle being that it brings together peak experience, knowledge and understanding under a common framework, which in turn increases the ease of re-use and comparison between sites. Unfortunately, such an approach misses the fundamental strength of comparing different models to check the robustness of results across the outputs of multiple models. A single model is also a single vision of the world and is not suited to the broad range of questions facing resource managers. 5. Weaknesses and remaining challenges When using a tool like end-to-end modelling it is essential to be aware of the weaknesses not just the strengths of the approach. Many of the weaknesses of end-to-end models are related to their large, complicated and complex nature. The large data demands can be hard to fill in most cases so data pedigrees of the form standardised in the EwE modelling framework are key to tracking model quality and uncertainty. Documentation of such large models is also daunting, but essential because there is the danger of creating a ‘house of cards’ if a majority of the model is based on data from distant locations or taxonomic groups. Such an approach is not wholly inappropriate for very theoretical exercises, but is dangerous when a model is supposed to represent a specific ecosystem. The complexity of end-to-end models can also mean that they are challenging to use and that a good deal of experience, training or guidance is necessary to use them well, from their initial implementation through to interpreting their output. Not so long ago it was often argued (and still is in some quarters) that understanding and using large models effectively would be very difficult if not impossible (Lee, 1973; Grimm, 1994; Scheffer and Beets, 1994; Grimm, 1999; Raick et al., 2006). A decade of experience with these models has shown that with care, rigour and a good deal of effort it is possible to avoid these anticipated drawbacks. Access to such experience will grow with increasing use of these kinds of models, but it should still be kept as a cautionary note for practitioners new to the field. Experience with these models has not removed all the challenges facing their users, but it has broadened the kind of questions that are being asked with these tools. Perhaps the greatest issue confronting users of end-to-end models today is non-stationarity. This is an issue for many models, but is particularly an issue for system-level end-toend models. It has been recognised that ecosystems are not equilibrium or static systems and that they are characterised by

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change, whether due to changing genetic structures and evolution, shifts in biodiversity, environmental shifts (e.g. changing climates, but also other environmental cycles and variability) or changing pressures on the system due to shifting human behavioural responses. Determining how best to address change of this kind and the implications for management conclusions drawn from these models is likely be a focus of research in end-to-end modelling development and applications over the next decade or more. Fortunately, the already dynamic and interconnected nature of the components within most end-to-end models means they are better placed than many other kinds of models for explicitly addressing these challenges. 6. Application of end-to-end models Some have questioned whether the use of end-to-end models is feasible. At best, end-to-end models are (perhaps correctly) considered to be in their infancy. While the term end-to-end is relatively new, as is the size of the scope of some of the more recent models (e.g. Travers et al. (2006) and Fulton et al. (2007) cover large regions, Lehodey et al. (2003) and Maury et al. (2007) are basin-scale, and Christensen et al. (in review) is global), their incremental growth from earlier forms of model means that there is already an impressive number of applications. End-to-end models are in use in a significant proportion of the globe (Fig. 3). Even if static network models are omitted there is still a sizeable coverage. While it is admittedly early days for these modelling approaches they are now moving beyond proof of concept and are being used to consider topics as diverse as resource use impacts and management questions; e.g. identifying effective monitoring schemes and helping define the form of effective ecosystem management (Mackinson et al., 1997; Zeller and Reinert, 2004; Cheung and Pitcher, 2005; Travers et al., 2006; Fulton et al., 2007; Velasco et al., 2007; Coll et al., 2008); modelling and complexity theory (Fulton et al., 2003a; Pinnegar et al., 2005; Metcalf et al., 2008); and functional system understanding (Pinnegar and Polunin, 2004; Zetina-Rejon et al., 2008). The size of the models and the uncertainty and application challenges (e.g. non-stationarity) are non-trivial, addressing them requires both significant computing resources and intellectual input. Nevertheless, they should not be used as an excuse to back away from end-to-end models. These kinds of models have a key role to play, by (i) expanding thinking about whole of systems (rather than simply sub-sections), (ii) highlighting non-linearities in

system dynamics, and (iii) allowing for the identification of new forms of adaptive management that are appropriate for a changing system state. 7. In summary End-to-end modelling is a natural product of increasing scales of understanding and resource management questions (especially in the context of increasing computational power). There is still much to be learnt in the field, but a few key points are already clear: • End-to-end models are not tactical tools; they are most effectively used strategically as ‘what-if’ worlds. MSE is a particularly useful approach for using models in that way. • The value of thought and simple tinkering — trying different kinds of models, assumptions and formulations — cannot be overstated. Time spent doing this during developmental and implementation of a model can save significant difficulties with model usefulness and performance. • A flexible approach to model implementation is perhaps the greatest asset to have when applying end-to-end models. While there are general guidelines on best practices for model use and development, there is no single “best model.” The assumption that extra detail is beneficial appears to be flawed when applied at the scale and number of dimensions of end-to-end models. Instead modellers should flexibly draw from a range of approaches to capture the feedbacks and delays and multi-scale interactions that drive the dynamics of ecosystems. Acknowledgements This review is based on experience and discussion with many model developers, in particular thanks are due to Jerry Blackford, John Parslow, Randall Gray, Villy Christensen, Carl Walters, Kenny Rose, Yunne Shin, Olivier Maury, Patrick Lehodey, Eva Plagányi, Andre Punt, Andrew Constable and George Watters. Thanks are also due to the organisers of AMEMR II (Advances in Marine Ecosystem Modelling Research, Plymouth 23–26 June 2008) who originally invited the paper. Finally many thanks are due to Penny Johnson, Miriana Sporcic, Cisco Werner and Temel Oguz who commented on earlier forms of this paper.

Fig. 3. Map of end-to-end models implemented to date (many more have been proposed or are in early development).

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