## The Ecopath with Ecosim (EwE) approach

Ecopath with Ecosim (EwE) is an ecological modeling software suite for personal computers that has built and extended on for almost twenty years. The development is centered at the University of British Columbia’s Fishery Centre, while applications are widespread throughout the world. EwE is the first ecosystem level simulation model to be widely and freely accessible. As of October 2008 there were 5,649 registered users in 164 different countries (www.ecopath.org, 27th Oct 2008) and well over 300 publications making EwE an important modelling approach to explore ecosystem related questions in marine science. For all these reasons, Ecopath software was recently recognized as one of NOAA’s top ten scientific breakthroughs in the last 200 years.

EwE has three main components: **Ecopath** – a static, mass-balanced snapshot of the system; **Ecosim** – a time dynamic simulation module for policy exploration; and **Ecospace** – a spatial and temporal dynamic module primarily designed for exploring impact and placement of protected areas. The Ecopath software package can be used to

- Address ecological questions;
- Evaluate ecosystem effects of fishing;
- Explore management policy options;
- Evaluate impact and placement of marine protected areas;
- Evaluate effect of environmental changes.

Ecopath - mass-balanced snapshot

The foundation of the EwE suite is an Ecopath model ([1], [2]), which creates a static mass-balanced snapshot of the resources in an ecosystem and their interactions, represented by trophically linked biomass ‘pools’. The biomass pools consist of a single species, or species groups representing ecological guilds. Pools may be further split into ontogenetic linked groups called ‘multi-stanzas’: a group may, for example, be split in larvae, juvenile, age 1-2, and spawners (age 3+). Ecopath data requirements are relatively simple, and data is often already available from stock assessment, ecological studies, or literature: biomass estimates, total mortality estimates, consumption estimates, diet compositions, and fishery catches.

The parameterization of an Ecopath model is based on satisfying two ‘master’ equations. The first equation describes the how the production term for each group can be divided:

Production = catch + predation + net migration + biomass accumulation + other mortality

It is the aim with the Ecopath model to describe all mortality factors; hence the ‘other mortality’ should only include generally minor factors as mortality due to old age, diseases, etc. The second ‘master’ equation is based on the principle of conservation of matter within a group:

Consumption = production + respiration + unassimilated food

In general, an Ecopath model requires input of three of the following four parameters: biomass, production/biomass ratio (or total mortality), consumption/biomass ratio, and ecotrophic efficiency for each of the functional groups in a model. Here, the ecotrophic efficiency expresses the proportion of the production that is used in the system, (i.e. it incorporates all production terms apart from the ‘other mortality’). If all four basic parameters are available for a group the program can instead estimate either biomass accumulation or net migration. Ecopath sets up a series of linear equations to solve for unknown values establishing mass-balance in the same operation. The approach, its methods, capabilities and pitfalls are described in detail by Christensen and Walters [3].

The process of constructing an Ecopath model provides a valuable end product in itself through explicit synthesis of work from many researchers. The model construction process can bring together scientists, researchers and data from state and federal levels of government, international research organizations, universities, public interest groups and private contractors. Key results include the identification of data gaps as well as common goals between collaborating parties that previously were hidden or less obvious. We find the process especially important for enabling the interest groups to take ownership of the model that is derived; this is especially required when operating at the ecosystem level, where multi-faceted policy goals have to be discussed widely as part of the management process. This is facilitated by the policy exploration methods included in the Ecosim model discussed further below.

Ecosim - temporal dynamics

Ecosim provides a dynamic simulation capability at the ecosystem level, with key initial parameters inherited from the base Ecopath model. The key computational aspects are in summary form:

- Use of mass-balance results (from Ecopath) for parameter estimation;
- Variable speed splitting enables efficient modeling of the dynamics of both ‘fast’ (phytoplankton) and ‘slow’ groups (whales);
- Effects of micro-scale behaviours on macro-scale rates: top-down vs. bottom-up control incorporated explicitly.
- Includes biomass and size structure dynamics for key ecosystem groups, using a mix of differential and difference equations. As part of this EwE incorporates:
- Multi-stanza life stage structure by monthly cohorts, density- and risk-dependent growth;
- Adult numbers, biomass, mean size accounting via delay-difference equations;
- Stock-recruitment relationship as ‘emergent’ property of competition/predation interactions of juveniles.

Ecosim uses a system of differential equations that express biomass flux rates among pools as a function of time varying biomass and harvest rates, (for equations see Walters [4], [5]). Predator prey interactions are moderated by prey behavior to limit exposure to predation, such that biomass flux patterns can show either bottom-up or top down (trophic cascade) control ([5]). By doing repeated simulations Ecosim allows for the fitting of predicted biomasses to time series data.

Ecosim can thus incorporate (and indeed benefits from) time series data on:

- relative abundance indices, (e.g., survey data, catch per unit effort [CPUE] data);
- absolute abundance estimates;
- catches;
- fleet effort;
- fishing rates; and
- total mortality estimates.

For many of the groups to be incorporated in the model the time series data will be available from single species stock assessments. EwE thus builds on the more traditional stock assessment, using much of the information available from these, while integrating to the ecosystem level.

When an Ecosim model is loaded, you can load time series ‘reference’ data on relative and absolute biomasses of various pools over a particular historical period, along with estimates of changes in fishing impacts over that period. The fitting procedure uses either fishing effort or fishing mortality time series data as driving factors for the runs.

After such data have been loaded and applied, a statistical measure of goodness of fit to these data is generated each time Ecosim is run. This goodness of fit measure is a weighted sum of squared deviations (SS) of log biomasses from log predicted biomasses, scaled in the case of relative abundance data by the maximum likelihood estimate of the relative abundance scaling factor *q *in the equation *y = qB *(*y *= relative abundance, *B *=absolute abundance).

The model allows four types of analysis with the SS measure:

- determine sensitivity of SS to the critical Ecosim vulnerability parameters by changing each one slightly (1%) then rerunning the model to see how much SS is changed, (i.e., how sensitive the time series predictions ‘supported’ by data are to the vulnerabilities);
- search for vulnerability estimates that give better ‘fits’ of Ecosim to the time series data (lower SS), with vulnerabilities ‘blocked’ by the user into sets that are expected to be similar;
- search for time series values of annual relative primary productivity that may represent historical productivity ‘regime shifts’ impacting biomasses throughout the ecosystem;
- estimate a probability distribution for the null hypothesis that all of the deviations between model and predicted abundances are due to chance alone, i.e. under the hypothesis that there are no real productivity anomalies.

#### Using Ecosim for policy exploration

The inclusion of time series data in EwE facilitates its use for exploring policy options for ecosystem-based management of fisheries. An important preliminary conclusion from applications to various ecosystems is that the model is capable of producing a reasonable fit, (i.e. fits that can be compared to those obtained using single species models) for all available time series related to the ecological resources of an ecosystem in one go. This indicates a capability or at least a potential to replicate the known history of the ecosystems. In turn this lends some confidence to how the model can be used for policy exploration. It is also indicated that the fitting of time series in Ecosim may be used not just for identification of ecosystem effects of fishing but also to address questions of environmental impact at the ecosystem level (as well as for individual groups of course).

A central aim of fisheries management is to regulate fishing mortality rates over time so as to achieve economic, social and ecological sustainability objectives. An important dynamic modelling and assessment objective is thus to provide insight about how high these mortality rates should be, and how they should be varied over time (at least during development or recovery from past overfishing). We cannot expect models to provide very precise estimates of optimum fishing mortality rates, but we should at least be able to define reasonable and prudent ranges for the rates.

Ecosim provides two ways to explore impacts of alternative fishing policies:

- Fishing rates can be ‘sketched’ over time and results (catches, economic performance indicators, biomass changes) examined for each sketch. This is using Ecosim in a ‘gaming’ mode, where the aim is to encourage rapid exploration of options.
- Formal optimization methods can be used to search for fishing policies that would maximize a particular policy goal or ‘objective function’ for management.

These approaches can be used in combination, e.g. by doing a formal optimization search then ‘reshaping’ the fishing rate estimates from this search in order to meet other objectives besides those recognized during the search process. The first of these approaches has been implemented in Ecosim since its first version, and has been widely applied for exploring ecosystem effects of changes in fishing effort. The second is ‘open loop’ policy exploration simulation that acknowledges that policy may be defined as an approach towards reaching a broadly defined goal that fisheries policies are often implemented via TACs that are recalculated annually, and through regulation that affects fleet structure and deployment.

#### Policy objectives

Ecosim allows users to implement ‘open loop’ policy exploration simulations that acknowledge that policy may be defined as an approach towards reaching a broadly defined goal. The goal function for policy optimization is defined by the user in Ecosim, based on an evaluation of four weighted policy objectives:

- Maximize fisheries rent;
- Maximize social benefits;
- Maximize mandated rebuilding of species;
- Maximize ecosystem structure or ‘health’.

The first of these, maximizing profits, is based on calculating profits as the value of the catch (catch · price, by species) less the cost of fishing (fixed + variable costs). Giving a high weight to this objective often results in phasing out most fleets except the most profitable ones, and the wiping out of ecosystems groups competing with or preying on the more valuable target species. The second objective, maximizing social benefits, is expressed through the employment supported by each fleet. The benefits are calculated as number of jobs relative to the catch value, and are fleet specific. Therefore social benefits are largely proportional to fishing effort. Optimizing efforts often leads to even more extreme (with regards to overfishing) fishing scenarios than optimizing for profit.

The third objective, maximization of mandated rebuilding of species (or guilds), is incorporated to capture that external pressure (or legal decisions) may force policy makers to concentrate on preserving or rebuilding the population of a given species in a given area. In Ecosim this corresponds to setting a threshold biomass (relative to the biomass in Ecopath) for the species or group, and optimizing towards the fleet effort structure that will most effectively ensure this objective. The implications of this are case specific: we are finding that the optimization routine may rigorously hammer (through increased fishing) competitors and predators of the species in question; or at the other extreme that fisheries may be shut down without social or economic consideration (as is indeed often the case when legal considerations take over).

The last objective included, maximizing ecosystem structure (or ‘health’) is inspired by E.P. Odum’s description of ecosystem ‘maturity’, wherein mature ecosystems are dominated by large, long-lived organisms, (see Christensen, 1995). The default setting we have incorporated for ecosystem structure is therefore the group-specific biomass/production ratio as this measure is indicative of the longevity of the

groups. The ecosystem structure optimization often implies reduction of fishing effort for all fleets except those targeting species with low weighting factors. The fishing policy search routine estimates time series of relative fleet sizes that would maximize a multicriterion objective function.

Ecospace - spatial-temporal dynamics

Ecospace is the dynamic, spatial version of Ecopath that incorporates all the key elements of Ecosim (Walters et al. 1999). It dynamically allocates biomass across a grid map (sketched with a mouse by the user, and typically defined by 20 x 20 cells), while accounting for:

- Symmetrical movements from a cell to its four adjacent cells, of rate m, modified by whether a cell is defined as ‘preferred habitat’ or not;
- User-defined increased predation risk and reduced feeding rate in non-preferred habitat;
- A level of fishing effort that is proportional, in each cell, to the overall profitability of fishing in that cell, and whose distribution can also be made sensitive to costs (e.g., of sailing to certain areas).

Ecospace, in essence, employs the time-dynamic Ecosim model in each cell of the raster grid, while accounting for cell connectivity and fish movements explicitly. Fishing effort is distributed over space according to a gravity model, optimizing the gain obtained from fishing. Fish migration and advection can be modeled explicitly, and the base map can be populated from spatial layers.

Given its structure, Ecospace allows users to explore the potential role of Marine Protected Areas (MPAs) as a tool to mitigate, and perhaps reverse various ecosystem effects of fishing, notably the effects of ‘Fishing down marine food webs’. The results obtained so far (Walters 1999) suggest that, due to the effects of trophic cascades within MPA (as result of MPAs protecting predators, whose biomass will thus increase), and the net movements of predators toward food concentrations (i.e., out the MPA), the net effect of small MPAs may be to increase the catch of the fisheries that will invariably concentrate their operation near their perimeter. Only large MPAs, with short outer perimeter relative to their surface areas would be protected from this, as would MPAs in bays or gulfs, with limited adjacency to exploited areas.

#### Spatial optimization

Two approaches for spatial optimization of protected area placement have been implemented in Ecospace and both based on maximizing an objective function that incorporates ecological, social, and economical criteria. Of these, a seed cell selection procedure works by evaluating potential cells for protection one by one, picking the one that maximizes the objective function, add seed cells, and continue to full protection. The other is a Monte Carlo approach, which uses a likelihood sampling procedure based on weighted importance layers of conservation interest (similar to Marxan’s) to evaluate alternative protected area sizing and placement. The two approaches are alternative options in a common spatial optimization module, which uses the time- and spatial dynamic Ecospace model for the evaluations. The optimizations are implemented as components of the Ecopath with Ecosim approach and software. In a case study, we find that there can be protected area zoning that will increase economical and social factors, without causing ecological deterioration. We also find a trade-off between including cells of special conservation interest and the economical and social interest, and while this does not need to be a general feature, it emphasizes the need to use modeling techniques to evaluate the tradeoff (Christensen et al., MS).

#### Seed cell selection procedure

This optimization method is based on a previous study (Beattie 2001; Beattie et al. 2002), in which a very simple optimization scheme was used to evaluate trade-off between proportion of area protected and the ecosystem-level objective function. We have modified the previous approach by securing a better program flow, and notably by changing the objective function from considering only profit from fishing and existence value of biomass groups. The procedure takes as its starting point the designation of one, more, or all spatial cells as ‘seed cells’, i.e. cells that are to be considered as potential protected cells in the next program iteration. The procedure will then run the Ecospace model repeatedly between two time steps, closing one of the seeds cells in each run, while storing the ecosystem objective function value. The seed cell that results in the highest objective function is then closed for fishing, and its four neighbouring cells (above, below, and to either side) are then turned into seed cells, unless they are so already, or already are protected, or are land cells. This procedure will continue until all cells are protected. The time over which the selection procedure is run is chosen dependent on the application. Typically, an ecosystem model is initially developed and tuned using time series data to cover a certain time period, e.g., from 1950 to 2005. Subsequently, the model is used in a scenario development mode to evaluate for instance protected area placement covering the period 2006-2020. The major result from the seed cell selection procedure is an evaluation of the trade-off between size of protected area, and each of the objectives. This can, for instance, be used to consider what proportion of the total area to close in subsequent, more detailed analysis based on importance layer sampling.

#### Monte Carlo approach

An advantage of the seed cell modeling approach described above is that it allows a comprehensive overview of the trade-off between proportion of area closed to fishing, and the ecological, social, and economical benefit and costs of the closures. This is done, based on the information already included in the EwE modeling approach, with no new information being needed. While this may be an advantage from one perspective, it does not allow use of other form for information, notably in form of geospatial data, such as, for instance, critical fish habitat layers from GIS.

To address this shortcoming, we have developed an alternative optimization routine for the Ecospace model, which uses spatial layers of conservation interest (‘importance layers’) to set likelihoods for spatial cells being considered for protection. The optimizations are performed using a Monte Carlo (MC) approach where the importance layers are used for the initial cell selection in each MC realization. The importance layers are defined as raster layers, with dimensions similar to the base map layers in the underlying Ecospace model, i.e. they are rectangular cells in a grid with a certain number of rows and columns. Each cell in a given layer has a certain ‘importance’ for conservation, expressed, e.g., as the probability of occurrence for an endangered species. For each importance layer, we initially scale the importance layer values to sum to unity, and then calculate an overall cell weighting for each cell and then the cell with the highest weightings for the given layer. The layer-specific indicator can obtain values in the range between 0 and 1. For each optimization search, one has to select the proportion of water cells to protect in the runs, as well as how many times to repeat the Monte Carlo runs. It is possible to set the search routine up to iterate over a range of protection levels, e.g., from 10% to 100% protected in steps of 10%. Similar to the seed cell selection procedure, we typically develop and tune the model to an initial time period, and then use the sampling procedure to evaluate scenarios for protected areas for a subsequent time period.

References

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