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Ecological Modelling 220 (2009) 2583–2593

Contents lists available at ScienceDirect

Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

patial optimization of protected area placement incorporating ecological,ocial and economical criteria

illy Christensen a,∗, Zach Ferdana b, Jeroen Steenbeek a,c

Fisheries Centre, University of British Columbia, 2202 Main Mall, Vancouver, BC, Canada V6T 1Z4Global Marine Initiative, The Nature Conservancy, 1917 1st Ave, Seattle, WA 98101, USAUNIGIS, Vrije Universiteit, Amsterdam, Netherlands

r t i c l e i n f o

rticle history:eceived 4 December 2008eceived in revised form 9 June 2009ccepted 12 June 2009vailable online 28 July 2009

eywords:copath with Ecosimcospace

a b s t r a c t

We describe two approaches for spatial optimization of protected area placement, both based on maxi-mizing an objective function that incorporates ecological, social, and economical criteria. Of these, a seedcell selection procedure works by evaluating potential cells for protection one by one, picking the onethat maximizes the objective function, adding seed cells. This continues to full protection of the projectarea. The other is a Monte Carlo approach, which uses a likelihood sampling procedure based on weightedimportance layers of conservation interest to evaluate alternative protected area sizing and placement.This is similar to the objective function of Marxan, a priority-selection decision-support tool based onoptimization algorithms using geographic information system data. The two approaches are alternative

cosystem modelarxanarine zoning

ritical fish habitat

options in a common spatial optimization module, which uses the time- and spatial-dynamic Ecospacemodel for the evaluations. The optimizations are implemented as components of the Ecopath with Ecosimapproach and software. In a case study, we find that there can be protected area zoning that will accom-modate economical and social factors, without causing ecological deterioration. We also find a tradeoffbetween including cells of special conservation interest, and the economic and social interests. While thisdoes not need to be a general feature, it emphasizes the need to use modeling techniques to evaluate the

tradeoff.

. Introduction

The Ecopath modeling approach has been under constant devel-pment over the last quarter of a century, with major milestonesepresented by the first model description and application in984 (Polovina, 1984); the Ecopath II model in the early 1990sChristensen and Pauly, 1992), the addition of the time-dynamiccosim model (Walters et al., 1997, 2000), and the spatial-dynamiccospace model (Walters et al., 1999). During this time the approachas grown to become the most widely applied ecosystem modelingechnique (Christensen and Walters, 2005), with more than 6000egistered users, and, to illustrate the level, 19 derived publicationsppearing in the key international journal, Ecological Modelling,uring the first 10 months of 2008. The Ecopath with Ecosim soft-are (EwE) implementing the approach is open-source and freely

ownloadable from www.ecopath.org.

Emphasis for using the approach has shifted over the 25 yearsrom initially being descriptive (Christensen and Pauly, 1993),oward a focus on ecosystem network analysis, notably aimed

∗ Corresponding author. Tel.: +1 604 822 5751; fax: +1 604 822 8934.E-mail address: v.christensen@fisheries.ubc.ca (V. Christensen).

304-3800/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2009.06.029

© 2009 Elsevier B.V. All rights reserved.

at comparative studies of properties such as ecosystem maturity(Christensen, 1995). In the late-1990s, the development of thetime-dynamic Ecosim model opened up the option for applyingthe integrated approach, Ecopath with Ecosim (EwE), to fisheriesmanagement questions, notably aimed at evaluating how fish-eries impact ecosystem resources (Walters et al., 2005). In doingso, enhancing the capabilities of Ecosim to address environmentalimpact on ecosystem productivity has been a key concern (Waltersand Martell, 2004), and this has led to new ways of evaluatingboth relative impacts of various ecosystem drivers (Guénette et al.,2006), and tradeoff between ecological, economical and social con-cerns for managing at the ecosystem level (Christensen and Walters,2004).

While the time-dynamic simulations have leaped a light-yearover the last decade, spatial-dynamic model applications have beenslower moving making their mark. We attribute this to severalfactors, including that spatial-dynamic applications have receivedless attention in fisheries research than time-dynamic, and that

the modeling techniques generally are less developed. For theEcospace model two important obstacles have, however, recentlybeen removed.

First, Ecospace has not had the capability built into Ecosim forseveral years enabling modeling of multiple age cohorts within

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pecies, and related to this, equilibrium approximations in Ecospaceave largely precluded realistic time-dynamic simulations. Thesebstacles have, however, been removed through a recent restructur-

ng of the approach, so that it can now realistically model age- andime-dynamics (Walters et al., in press). Second, Ecosim simulationsave benefitted from tuning to time-series data, while capabilities

or tuning to time- and spatial-data have been lacking for Ecospace.e have, however, added such capabilities to the new version 6 of

he EwE approach (Christensen and Lai, 2007) as demonstrated infew applications (Christensen and Booth, 2006; Le Quesne et al.,008).

Overall, the Ecospace approach has now grown to a level wheret should be seriously considered as a decision-support tool forse in ecosystem-based management, or multiple-objective marinepatial planning. Here, interest in using models for design and eval-ation of protected area design is of increasing interest, and suchse was indeed the main purpose for the original development ofcospace, the paper introducing it including “with emphasis on the

mpacts of marine protected areas” in the title (Walters et al., 1999).While Ecospace has been applied quite extensively in a gaming-

nd scenario-development mode, we have only seen very limitedffort applied to spatial optimization and zoning. A first attemptn this direction is represented though, by the ‘Ecoseed’ approach,eveloped for Ecospace some years ago as part of a thesis projectBeattie et al., 2002), but never fully implemented and released asart of the software.

We here describe how we have further developed this approacho incorporate a new objective function, bringing it to a level wheret is part of the released EwE6. Further, we describe a new spatialptimization module, which uses the same objective function ashe updated seed cell selection approach, but where the spatial cellelection process is influenced by geospatial information, hereineferred to as importance layers. With the inclusion of geographicnformation systems (GIS) data, we demonstrate how other man-gement objectives (i.e. biodiversity conservation) are representedn the selection process.

The most widely used selection tool for developing priorityreas with a conservation perspective is the Marxan and MarZonepproach and software (http://www.uq.edu.au/marxan/), devel-ped primarily by Hugh Possingham and colleagues at the Ecologyentre, University of Queensland. Marxan is a very flexible approachapable of incorporating large amounts of data and use categories.t is computationally efficient, and lends itself well to enablingtakeholder involvement in the site selection process (Ball andossingham, 2000).

We view the new importance layer sampling procedure as com-

lementary to the Marxan approach in that Ecospace’s strong side,hrough the underlying trophic modeling background is in eval-ating ecological processes, including spatial connectivity; topicshat are not fully developed in Marxan analysis. Similar to Marxan,

able 1bjectivity function employed for spatial optimization. Each objective is given aeighting factor, and the optimization seeks to optimize the summed, weighted

bjectives.

bjective Description

rofit Estimated by ‘fleet’, and summed over all suchobs Estimated from value of fisheries, and relative

number of jobs/valueandated rebuilding A minimum acceptable level, by group

cosystem structure Default values based on biomass/productivityratios expressing average longevity, weighted bygroup

iomass diversity Biomass evenness among groupsoundary weight Estimated as total boundary length over the

protected area size. Captures spatial connectivity

elling 220 (2009) 2583–2593

Ecospace is also both intuitive and flexible enough to be used aspart of a stakeholder consultation process. In the Ecospace anal-ysis, we, however, involve a rather complicated dynamic model,which, even with its user-friendliness, unavoidably has a cost.We therefore advocate that the two approaches, with their givenadvantages and limitations, be applied in conjunction—using twosources to throw light at a problem from different angles, beats one,any time. We have in order to facilitate such comparative studiesdeveloped a two-way bridge between Marxan and EwE, enablingexchange of spatial information and of optimization resultsbetween the two approaches. We describe only briefly aspects ofthis below, as we will apply the bridge elsewhere for a formalcomparison.

2. Methodology

2.1. The spatial-dynamic modeling approach

The methodologies for spatial optimization described here relyon the Ecospace model, implemented within the Ecopath withEcosim approach and software. The Ecospace model is describedin a number of publications, notably by Walters et al. (1999, inpress). The Ecospace model builds on an underlying Ecopath trophicmodel, which can have any number of functional groups or age-and species-specific groups as appropriate for the questions to beaddressed. The Ecospace run picks up levels of fishing effort overtime from the associated Ecosim run, including mediation factorsand most other factors that do not have a potentially important spa-tial dimension. As an example, Ecospace does not inherit Ecosimtime varying productivity functions (‘forcing functions’), as there isno information about how to distribute the time varying produc-tivity spatially.

Ecospace, in essence, employs the time-dynamic Ecosim modelin each cell in a grid, while accounting for cell connectivity andfish movements explicitly. Fishing effort is distributed over spaceaccording to a gravity model, optimizing the gain obtained fromfishing. Fish migration and advection can be modeled explicitly, andthe base map can be populated from spatial layers such as benthichabitat types.

In addition, Ecospace, can work with any number of designatedprotected cell types. For each of these, fishing may be banned forone or all fleets, and for all or part of the year. While Ecospace canhandle multiple types of protected cells, it needs to be specifiedfor the optimization routines, which type of protected cells theyare to work with; we can only consider one type within a givenoptimization run.

2.2. Objectivity function

We employ an objective function for the optimizations, whichcorresponds to the objective function used in the policy optimiza-tion module of EwE. This module, which has been applied to anumber of case studies (e.g., Christensen and Walters, 2004; Araújoet al., 2008; Arreguin-Sanchez et al., 2008) uses a non-linear searchroutine to find a combination of effort by fishing fleets that willmaximize the objective function. The objective function in turnincludes ecological, economical and social indicators, even legalconstraints if pertinent, through considering profit, number of jobs,stock rebuilding, and two ecological measures. For the spatial opti-mizations we add a further indicator in form of a boundary weight

factor (Table 1).

The profit objective is calculated by summing revenue acrossall fleets, and subtracting the cost for operating. Cost is considereda linear function of effort with a fixed cost added. The followingcalculation is performed for each time step (t) to estimate the profit

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ith Ffi being the fishing mortality for group i caused by fleet f, Bis the biomass of i, and Vfi is the ex-vessel value per unit weight ofcaught by f. Ef is the relative effort, Cv,f the variable cost per unitffort, and Cp,f is the fixed cost, all for fleet f.

The calculations in Eq. (1) are, as indicated, performed for eachime step, with benefit summed over time. We, however, discountuture values based on either a traditional discount rate, or an inter-enerational discount rate (Sumaila and Walters, 2005), based onser preference.

As a social indicator, we use the number of jobs over time (Jt)reated in the ecosystem, and we estimate this for each time stept) from the landed value of the exploited group times the relativeumber of jobs per unit value (Ni), or

t =∑

f

Ffi · Bi · Vfi · Ni

Similar to the profit objective, we discount the number of jobsver time.

We estimate the mandated rebuilding objective (Mt) for eachime step (t) from

t =∑

i

Bi′

Bi∗

here Bi∗ is baseline Ecopath biomass for group (i), and Bi′ equalshe group biomass Bi if Bi is lower than the mandated biomass, Bm,ior the group, and Bm,i if it is not.

The mandated rebuilding objective can be used to set ‘minimumiological acceptable levels’ (or MBAL as commonly used). By set-ing high mandated biomasses (Bm,i) for a group it can also be usedo capture ‘existence values,’ e.g., of marine mammals of interestor a whale watching industry. We do not discount the mandatedebuilding structure over time.

The ecosystem structure objective is meant to capture thatature (K-type) ecosystems tend to be dominated by long-lived

pecies and individuals (Odum, 1969). We seek to capture this char-cteristic through the inverse production/biomass ratio, estimatingor each time step (t)

t =∑

i

Bi · Si

here St is the overall ecosystem structure measure, and Si thecosystem structure factor for (i). We provide default values for Sin form of the inverse Pi/Bi ratios (unit year), supplied as part ofhe basic parameterization of the Ecopath model. To avoid unduenfluence by very short-lived species we have (arbitrarily) set Si tofor groups with an average lifespan of less than a year (i.e. groupshose Pi/Bi is higher than 1 year−1).

The ecosystem structure objective is not discounted over time;aving long-lived species in the future being deemed as importants having them now.

As a measure of biomass diversity, we used a modified ver-ion of Kempton’s Q75 index, which originally was developed toescribe species diversity (Kempton, 2002). We here used a biomassiversity indicator following Ainsworth and Pitcher (2006), albeit

lightly modified. We estimate the biomass diversity index (Q75)rom

75 = S

2 log(N0.25−S/N0.75−S)

elling 220 (2009) 2583–2593 2585

here S is the number of functional groups, and Ni−S is the biomassof the (i·S)th most common group, using a weighted average of thetwo closest groups if (i·S) is not an integer. The biomass diversityindex describes the slope of a cumulative group abundance curve.As a sample with high diversity (evenness) will have a low slope,we reverse the index and express it relative to index value from theEcopath base run (Q ∗

75)

Q ′75 = 2 − Q75

Q ∗75

We truncate the index in the extreme and unlikely case thatQ75 would more than double from the base run. We only includehigher trophic level groups (TL > 3) in the calculation of the biomassdiversity index—should this, for models with only few functionalgroups, lead to less than 10 groups being included in the calcula-tions, we, however, base the calculations on all living groups. Asfor the other ecological indicators we do not discount future indexvalues.

The final element in the objective function represents spatialconnectivity, expressed through the boundary weight factor, L

L =∑

cAc∑bIb

where the total protected area size (Ac, km2) is summed over spatialcells (c), and the boundary length is estimated by summing over allprotected cell (b) the side lengths (Ib, km) that do not border anotherprotected cell or land.

With the elements of the objective function being defined, wecan now obtain the overall objective function measure (O) from

O = wR · R + wJ · J + wM · M + wS · S + wQ · Q ′75 + wL · L (2)

where each of the objective weighting factors (w), can assume anyvalue, including zero, which is used for measures that are ignoredin a given optimization. We use the objective function measure forboth of the optimization methods described below.

2.3. Seed cell selection procedure

This optimization method is based on a previous study (Beattie,2001; Beattie et al., 2002), in which a very simple optimizationscheme was used to evaluate tradeoff between proportion of areaprotected and the ecosystem-level objective function. We havemodified the previous approach by securing a better program flow,and notably by changing the objective function from consideringonly profit from fishing and existence value of biomass groups tothe more detailed function described above (Eq. (2)).

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 consid-ered as potential protected cells in the next program iteration. Theprocedure will then run the Ecospace model repeatedly betweentwo time steps, closing one of the seeds cells in each run, whilestoring the ecosystem objective function value. The seed cell thatresults in the highest objective function is then closed for fishing,and its four neighboring cells (above, below, and to either side) arethen turned into seed cells, unless they are so already, or alreadyare protected, or are land cells. This procedure will continue untilall cells are protected.

Another question is how to select the initial seed cells, and howthe selection impacts the final result. Time permitting one has the

option of declaring all cells as seed cells and let Ecospace search allpossible starting points. For the case study used here, this involvesa total of 4371 Ecospace runs, which with a runtime just shy ofa second per run, takes about an hour on a newer dual-processornotebook computer.

2586 V. Christensen et al. / Ecological Mod

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ig. 1. Logic of the importance layer sampling procedure. For each run a given per-entage of all cells are protected based on weighted likelihood in importance layers.he evaluation of each run is done independently based on a defined objectiveunction.

The time over which the selection procedure is run is chosenependent on the application. Typically, an ecosystem model is

nitially developed and tuned using time-series data to cover a cer-ain time period, e.g., from 1950 to 2005. Subsequently, the models used in a scenario-development mode to evaluate for instancerotected area placement covering the period 2006–2020.

The major result from the seed cell selection procedure is anvaluation of the tradeoff between size of protected area, and eachf the objectives in Eq. (2). This can, for instance, be used to decidehat proportion of the total area to close in subsequent, more

etailed analysis based on importance layer sampling.

.4. Importance layer sampling procedure

An advantage of the seed cell modeling approach describedbove is that it allows a comprehensive overview of the tradeoffetween the proportion of area closed to fishing, and the eco-

ogical, social, and economical benefit and costs of the closures.his is done, based on the information already included in thewE modeling approach, with no new information being needed.hile this may be an advantage from one perspective, it does

ot allow use of other forms of information, notably in form ofeospatial data, such as, for instance, critical fish habitat layers fromIS.

To address this shortcoming, we have developed an alternativeptimization routine for the Ecospace model, which uses spatial

ayers that represent a conservation objective (‘importance layers’)o set likelihoods for spatial cells being considered for protec-ion. The optimizations are performed using a Monte Carlo (MC)pproach where the importance layers are used for the initial cellelection in each MC realization. The Ecospace model is then run,he objective function (Eq. (2)) is evaluated, and the results, includ-ng which cells were protected, are stored for each run (see Fig. 1).

The importance layers are defined as cell-based layers, withimensions similar to the base map layers in the underlying

cospace model, i.e. they are rectangular cells in a grid with a certainumber of rows and columns. Each cell in a given layer has a certain

importance’ for conservation, expressed, e.g., as the probability ofccurrence for an endangered species. For each importance layerl), we initially scale the importance layer values to sum to unity,

elling 220 (2009) 2583–2593

and then calculate an overall cell weighting (wc) for each cell (c)from

wc =∑

l

wl · Cc,l (3)

where wl are the importance layer weightings, and Cc,l the cell-specific, scaled importance layer values.

In order to evaluate how well the importance layers are repre-sented in each optimization run, we estimate

w′l =

∑c′ wl · Cc′,l∑c∗ wl · Cc∗,l

(4)

where c’ indicates cells selected in a given run, and c* the cell withthe highest weightings for the given layer. The layer-specific indi-cator (w′

l) can obtain values in the range between 0 and 1.

For each optimization search, one has to select the proportionof water cells to protect in the runs, as well as how many times torepeat the Monte Carlo runs. It is possible to set the search routineup 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 developand tune the model to an initial time period, and then use thesampling procedure to evaluate scenarios for protected areas fora subsequent time period.

We have developed a capability for Ecospace to read files withgeospatial information such as importance layers or other Ecospacebase map layers. The reading is possible from comma separatedtext files (.csv), ESRI ASCII files (.asc), and ESRI shapefiles (.shp).The files need to have layers or columns with row and columnnumbers matching the Ecospace model. This capability is designedto allow straightforward exchange between the Ecospace model-ing and Marxan analysis, with the constraint that all informationrepresented in the layers be contained within the same grid orcell environment (i.e. information within the cells containing thesame identification system across all layers). With this capabilitydirect comparisons of Ecospace importance sampling and Marxanoptimization can be conducted. The reading of the spatial files isdescribed in more detail in the draft EwE6 User’s Guide, availablefrom the Ecopath website.

2.5. The ecosystem model application

We illustrate the use of the spatial optimization through a simplemodel of a marine ecosystem (Pauly and Christensen, 1993). Themodel is the ‘Ocean South China Sea’ model distributed with theEcopath software, and often used for testing and teaching purposes.We use a 10 × 10 cell base map in Ecospace with an island and threehabitat types, coastal, shelf, and open ocean (Fig. 2). The cell lengthis 50 km, and we use a dispersal rate of 30 km year−1 for all fishbut tuna, where we use either 30 or 300 km year−1. With the lowerdispersal rate, the spillover to neighboring cells, especially fromprotected to unprotected cells, will be much slower than with thehigher dispersal rate, allowing more build-up of biomass within theprotected areas.

We assume that adult tuna only occur on the shelf and offshoreareas, their juveniles not in the open ocean part, mesopelagics notat the coast, and other groups in all habitats. The tuna is the onlyexploited group, and fishing is not allowed in protected areas, i.e.such are strictly no-take zones.

We also assume that there has been an initial increase in fishing

effort over the first 15 years of the simulations, so that the exploitedspecies are below their carrying capacity when we start the spatialoptimizations in year 16. We let the effort increase 60% by year 3,and keep it at the level for the rest of the simulation time period. Thisresults in the tuna biomass being reduced to 36% of initial biomass

V. Christensen et al. / Ecological Modelling 220 (2009) 2583–2593 2587

F ersali by circp r cells

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ig. 2. Progress of seed cell selection procedure from a run with target species dispndicates shelf area, and darkest the deeper open ocean. (A) Three cells, indicatedicked the ‘best’, made it a protected area (hatched background), turned its neighbo

n the base run, while the catch show a 40% decline from the initialatch. We continue for an additional 10 years from the introductionf protected areas in year 16, keeping the effort constant at 1.6 timeshe starting effort. We further assume that the cost of fishing was0% of the revenue in the base year (15), i.e. at the start of the spatialptimizations.

To illustrate the use of importance layers we have, after years ofntense field research, been able to describe three layers that repre-ent a conservation objective (Fig. 3). The first (A) is the proportionf each spatial cell where the bottom is hard bottom, which may

avor reef species, provide shelter for planktivores in between for-ging trips, and in general be favorable for biodiversity. The secondayer (B) represents breeding assemblages of right whales in theoastal areas east of the island, and the third (C) occurrence of anndangered species of conservation concern.

ig. 3. Illustrative importance layers for the spatial optimizations, each with values indiabitat that is hard bottom. (B) Relative probability for encountering breeding right whal

rate of 300 km year−1. Dark area is land, surrounded by coastal cells, lightest colorles have been chosen as ‘seed cells’, i.e. potential protected areas. (B) The routineinto seed cells. (C) and (D) show progression steps toward full protection.

All of the importance layers have cell-specific values that rep-resent the probability of occurrence for the features. We use thelayer with layer-specific weightings to obtain overall cell weight-ings; here quite arbitrarily by assigning the right whale layer (B)twice the weight of the two other layers, once again favoring charis-matic mega-fauna over cryptic species. However, we recommend amore thorough examination of layer-specific weightings be con-ducted in decision making processes to ensure that biodiversityacross tropic levels is adequately represented.

It is worth noting that none of the three layers directly relate

to any of the functional groupings in the model. The endangeredspecies may be included in the benthic fish, but may also havebeen ignored in the Ecopath model due to its low biomass (endan-gered!) Right whales could have been included as a group in theEcopath model, but given that they do not feed while in their

cated by numbers and shading (light = low; dark = high). (A) Indicate proportion ofes. (C) The abundance density for a rare species.

2588 V. Christensen et al. / Ecological Mod

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ig. 4. Seed cell selection after 85% of cells protected in a run with target speciesispersal rate of 30 km year−1. The optimization keeps cells open throughout thease map in order to have spillover to the fished area.

reeding areas, there is little incentive to add them to a trophicodel.

This above is meant to illustrate, however, that it is feasible todd any kind of conservation features as importance layers for thepatial optimizations. Criteria for selecting conservation featuresave been defined elsewhere (Beck, 2003) and can be consultedhen designing a conservation objective within the EwE model. The

efinition of the underlying Ecopath model does not pose limits;ata, knowledge, and common sense do.

For the simulations reported on here, we in all cases optimizedor net economic value, obtained as revenue of the fishery less theost of the fishing. We assumed that in the base year (15) the fish-ries were operating with the cost at 80% of revenue (25% profit).he net economic values are expressed in the results relative to thisaseline. For discounting of net economic value and value of fish-ries, we use a traditional discounting approach with the defaultarameter value of 0.04 year−1. The other objectives (employment,cosystem structure, and biomass diversity) are also expressed rel-tive to their value in the base year.

We ran the importance layer sampling 20,000 times in a Montearlo approach, all with 30% of the water cells being selected forrotection. This level of protection was selected based on the results

rom the seed cell selection procedure, which was run before themportance layer sampling.

The ecosystem model used here, along with the spatial layersor the optimizations can be downloaded from www.ecopath.org,y searching for the title of this paper or the authors in the modelection.

. Results

.1. Seed cell selection

We initially ran two series of optimizations differing by the dis-ersal rate for the target species, tuna. The first assumed a dispersalate of 300 km year−1, or five times the cell length, and the second aispersal rate of 30 km year−1. Ecospace simulations are very sensi-ive to the dispersal rates, which correspond to the residual annual

elling 220 (2009) 2583–2593

movement, and we therefore chose to illustrate how sensitive theresults are to this parameter.

In both runs, the optimization was started off with three seedcells; one in each of the three habitat types. In the higher dispersalrate run, the optimization started off protecting the offshore area,followed by cells in the two other habitats (Fig. 2). When 70–80% ofthe area was protected (Fig. 2D), there were still cells throughoutthe map open to fisheries, clearly indicating that the optimizationwere indeed designed to optimize economic profit. This was alsothe case, and to an even larger degree, in the lower dispersal raterun as indicated in Fig. 4. None of the cells that are open to fishingat this stage, where 85% of the area has been closed to fishing, hasa neighbor that is open to fishing.

The optimizations here are run with a constant, but high fish-ing intensity, and the biomass of the target species is reduced belowthe maximum sustainable level, with catches being reduced as well.Traditional advice in such cases is to reduce fishing effort. We can,however, use the spatial optimizations to evaluate other options.For the higher dispersal rate optimization, we see in Fig. 5A that asthe protected area is increased, the net economic value increasessome 30% when a third of the area is protected. The profit from fish-ing then gradually decreases, but only when three quarters of thetotal area is protected, does the net economical benefit go beyondthe baseline where all areas were open to fishing. Only when morethan three quarter of the area is closed to fishing, will the fisheriesbecome less profitable than in the baseline situation.

The social indicator, here expressed through employment, andquantified based on the value of the fisheries landings shows asimilar trend as the net economic value, only with less relativeincrease. The maximum increase is thus only 8%, but it is impor-tant that this represents an 8% increase in catch value—even withtotal fishing pressure being both high and constant. The model indi-cates that introduction of protected areas does not have to lead toreduced catch opportunities, at least not when the optimizationsare designed to maximize economic returns rather than conserva-tion measures.

The two ecological indicators show less dramatic change thanthe economical and social. Only as fishing really starts to declinedo we see a marked change in the biomass diversity indicator. We,do, however note that the trend in both indicators is as expected;pointing to the indicators being suitable choices for the purposethey serve.

We can compare this simulation to the corresponding one withlower dispersal rates. The results are somewhat more dramatic(Fig. 5B), with a marked increase in net economic value, even whenonly a smaller part of the area is protected. We obtain higher poten-tial increase, up toward 50% increase in profit, and 15% in catchlevels at levels of 15–40% of the total area being protected. The ben-efits, however, level off sharply when the 40% level is protected, andboth indicators move below the baseline (with no protection) when45% of the area is protected.

The results with regards to the objective function and systemindicators differs surprisingly little whether few or all cells are setas initial seed cells (compare Fig. 5 A and C). At levels up to 25%protected area coverage, there is next to no difference (<2%) in thenet economic return, while the optimization based on all cells beingseed cells, clearly obtains higher values for higher levels of protec-tion. This difference is somewhat surprising; one should intuitivelythink that the advantage for the ‘all seed cells’ approach would bebiggest initially, when the optimizations have free choice for whereto start.

3.2. Importance layer sampling

We ran the procedure 20,000 times, each time with 30% of thewater cells being drawn randomly for protection based on their

V. Christensen et al. / Ecological Modelling 220 (2009) 2583–2593 2589

F o fishi( (C).

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ig. 5. Objectivity function values (Y-axis, relative) against proportion of area closed tA and C), and 30 km year−1 (B). Initial number of seed cells is 3 (A and B) or all cells

eightings in the importance layers (Fig. 6). We optimized for netconomic value only, similar to the seed cell sampling run. We onlysed the higher dispersal rate for the target species (300 km year−1)

or this sampling procedure.

ig. 6. Basemap from importance layer sampling with 20,000 runs, selecting theun with the top 1% objective function values. Numbers and shading (light = low;ark = high) indicate how many times each cell was included in the best runs, withhe hatched cells being the 30% with highest count, that would be prime targets forrotection.

ng (X-axis) based on seed cell selection. Target species dispersal rate is 300 km year−1

The top 1% of the 20,000 runs yields gains in the net economicvalue in the range of 30–21% compared to the base line, with anaverage gain of 23.5%. The catches are estimated to increase with anaverage 6%, while the ecosystem structure measure and the biomassdiversity indicator show insignificant gains.

The results indicate that it is feasible to increase the net eco-nomic value while also obtaining higher employment, and that thiscan be done without compromising ecosystem structure or biomassdiversity. This is indeed a noteworthy result of spatial protection.It is not clear from the objective function, however, what impactthis will have on level of protection for the species of concern in theimportance layer. We could, as discussed elsewhere, have includedthe key species in the trophic model, but this is not always feasibleor practical. How do you, for instance, get stress-level of breed-ing right whales due to boat disturbance represented in a trophicmodel?

We can, however, estimate how well the conservation fea-tures represented by the importance layers are included in thesimulations with highest objective function values, i.e., here,with highest net economic return. For each of these ‘best’runs, we calculate the w′

las described in Eq. (4). This indi-

cator expresses for a given percentage of the area protected,how much of each weighted importance layer that is includedin the protected area, relative to how much at most could beincluded.

The results are shown in Fig. 7 for each importance layer, andexpressed with objective function values plotted against propor-tions of each layer that is protected. Included in the figure is the 1%

of the 20,000 runs that resulted in the highest objective function(net economic value). Several interesting results are clear from thefigure. One is, that there is a tradeoff between a conservation objec-tive and economical and social concern. The regression lines in Fig. 7all have a negative slope, indicating that if more of the importance

2590 V. Christensen et al. / Ecological Modelling 220 (2009) 2583–2593

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ig. 7. Representation of importance layers in top 1% of importance layer sampling rreeding area layer, and (C) endangered species distribution layer. Regression lines

ayers are included in the protected areas, the net economic returnill be lower.

. Discussion

We should initially mention that the results presented here forhe two optimization methods are not directly comparable. The cri-eria used for the initial cell selection for protection are different,nd it is hence difficult to directly compare the results. The approachncorporating the importance layers builds on additional informa-ion, and this naturally impacts how cells are selected using thepproach. One aspect of the results is, however, comparable. Theeed cell approach when optimizing for net economic value leadso a fragmented system where non-protected cells are dispersedver the map to maximize fishing benefit from fishes moving outf the closed areas. In contrast, the importance layer method tendso produce more contiguous protected areas, even if we have notncluded any penalty for area/border ratio in the optimizations.

.1. Dispersal rate

With the seed cell selection approach, we chose to comparewo simulations that differed only by the assumed dispersal fac-

he optimization was for net economic return. (A) Hard bottom layer, (B) right whaledicated.

tor (or residual annual movement) for the target species. We didso because Ecospace simulations are very sensitive to the disper-sal parameter, and the results illustrate this clearly. With the lowerdispersal rate, the net economic benefit is greatest with low pro-tection rates, peaking (at 49% higher profit) when 14% of the areais protected, while the peak is at 39% with the higher dispersal rate(yielding 28% higher profit).

The mechanism behind this relates to the buildup of targetspecies biomass, with lower dispersal more will build up withinthe closed area, and the optimum combination is obtained when asmaller proportion of the total area is protected. As protected areacoverage increases, the buildup becomes even more pronouncedwithin the protected area, but the spillover to the unprotected areasis lower. With higher dispersal rates the situation is similar, butthere is, of course, more spillover and the overall benefit of pro-jected areas is lower with such “leaking” MPAs, and occurs with alarger part of the area being protected.

Dispersal rates are of key concern for evaluating the potential

benefits of protected areas, notably with regard to the spillovereffect involving export of adult fishes and recruits. The key questionis: how can we choose suitable dispersal parameters? The pes-simistic answer for just about any marine population is that wedo not know a priori what rate to use for this parameter. We need

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arefully designed experimental closures, such as those of Russnd Alcala (1996, 1999) to evaluate the level of spillover, prefer-bly combined with tagging programs. From such, we can evaluatearameter settings for the ecosystem modeling in a more credible,ata-driven manner than currently possible. Meanwhile, we have toet by with what we have, this is not a showstopper. From a model-ng perspective the most meaningful approach, acknowledging thencertainty involved, is that we can use the models as tools to makeuantitative predictions of potential benefit and cost of introducingrotected areas, and we can evaluate how sensitive the predictionsre to the assumptions about dispersal rates.

Here, we conclude that intermediate levels of protection offermprovement in the economical and social indicators without com-romising the ecological, indicating that even if we do not know the

evel of dispersal, the trends are robust to different assumptionsbout this key parameter.

.2. SLOSS or openings?

A related debate has been ongoing since the 1980s focused onhe relative benefit of adopting a ‘Single Large Or Several Small’rotected areas (Boecklen, 1997; Possingham et al., 2000), and it

ikewise does not have a simple answer.When we started off the lower dispersal rate simulations, the

outine would initially close the offshore area, then continue withhe coastal area, and this was followed by a marked drop in netconomical value for the fisheries (Fig. 5B). The pattern from theimulations, showed areas open to fishing dispersed throughouthe spatial area, indicating that if concern for exploitation, social asell as economical, is to play a role for optimization, it is necessary

o have non-protected areas dispersed within the protected areatructure.

The lower dispersal rate simulation notably showed that when5% of the area was protected (Fig. 4) all of the remaining non-rotected cells were single cells distributed through the spatialap. This is in line with more general findings from Ecospaceodeling (Walters, 2000), which indicate that the consideration

f multiple objectives, social, economic, and ecological (notablyrophic), calls for protection of much larger areas than what maye obtained by focusing on direct spillover effects and the rolef protected areas as supplier of larvae from enlarged spawningopulations (Sala et al., 2002) only. Indeed, we may have to shifthinking from “regarding MPAs as exceptional areas to regardingshing areas as the exception” (Walters, 2000). This is especially

mportant for cases where the fishing power is strong enough tossentially eradicate stocks given the opportunity, and a realizationf this a hundred years ago is main reason that we still have thriv-

ng salmon fisheries in the Pacific Northwest, and more recently forhe rebuilding of herring stocks in the same area since the 1960sollapses.

.3. Weighting of importance layers

The results in Fig. 7 indicate that weightings of importance layersave to be carefully considered. On average, the weighted measuref concern for layers A, B, and C are represented by 50%, 58%, and6%, respectively in the top 1% of the simulations. Yet we have usedelative weighting factors for the three layers of 1, 2, and 1. It appearshat layer C is overrepresented? This is, however, not an error, but aimple function of how many cells that impact the selection processn each of the layers. In layer C, only six cells west of the island had

ositive values, and these six cells are therefore very likely to beelected given the cell selection process (Eq. (3)). We can see fromig. 7C that all top 1% simulations had at least 3 of the six cellsncluded in the protected area, and that the majority had at least 5f 6 cells protected. Overall, this shows that if there are small areas

elling 220 (2009) 2583–2593 2591

of special concern, the importance layer sampling procedure willensure that these are well represented in the area suggested forprotection.

4.4. Impact of cell selection criteria

If we examine the indicators in the spatial optimization objectivefunction, i.e. net economic value, employment, ecosystem struc-ture, biomass diversity, and boundary length (which is not includedin the plots, but which showed only the expected trends) we findsurprisingly little difference whether the optimizations were basedon the seed cell selection procedure or the influence layer sam-pling protocol. This enforces the finding from other studies thatany optimizations tend to be better than current, non-optimizedstates (Christensen and Walters, 2004).

While there thus is little difference in the outcome for the twooptimization rules, there is still one important difference. The seedcell selection procedure does not consider a conservation objec-tive as expressed here through the importance layers, but onlywhat may be covered through the ecosystem structure and biomassdiversity indicators. Where specific features are deemed importantfrom a conservation perspective they should of course be consid-ered if geospatial information is available, and this is a good reasonfor using the approach developed with this in mind, presented here.

Why then even consider using the seed cell approach? Thereare cases where we do not have importance layers considering fac-tors not captured by the trophic models. We could for instance haveincluded right whales in the trophic models, and used boat effort asa mediation factor that would negatively impact the productivity ofyoung right whales. Placing a high value on the right whale biomassin the ecosystem structure indicator, and including this (with a suit-ably high weight) in the objective function, would lead to similarresults as using an importance layer for the right whales. Still it isfrom a technical modeling perspective, a more demanding and timeconsuming approach, and, while it is straightforward to include alarge number of importance layers, 42 for instance, it would take alot of time and thinking to directly incorporate a similar number inthe trophic modeling approach.

Still, the seed cell approach offers a relatively quick way of eval-uating the tradeoff between area protected and tradeoff in theobjective function indicators, much quicker than performing MonteCarlo runs for all potential level of protection.

We recommend using the spatial optimizations for an initialseed cell search to get a relatively fast overview of the trade-off between proportion of area covered and ecological, social andeconomical consequences. Based on this, one can then perform amore in-depth analysis using importance layer sampling aimed atwidening the scope of conservation issues being considered, whileseeking alternative solutions for placement of the MPA cells.

4.5. When is enough, enough?

If we, in the seed cell optimizations with the very simple spatialgrid cell description used here, set all spatial cells as seed cells,we only need to run 4371 runs, which can be done in an hour ona dual-processor notebook, and much faster on a dual quad-coredesktop as Ecospace runs are threaded (Walters et al., in press). Thisis thus quite feasible, but it also assumes that an optimal solutioncan be obtained by a sequential cell selection. What if one doesnot start with the one cell that gives the biggest objective functionincrease (which actually is a very tiny increase), but just took any

one of the other cells as the starting point? Evaluating this fully, willincrease the run time by two orders of magnitude, i.e. it would notbe practical.

The importance layer sampling avoids the question of whetherthe order of selection matters through a large number of Monte

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arlo runs, each time selecting the cells for protection based on arobability distribution. But are 20,000 runs, as conducted here, ‘a

arge number?’If we wanted to evaluate all possible combinations for protected

rea placement, we would need to perform a large number (N) ofuns

= Ctot!Ctot−prot!

where Ctot is the number of potential cells, and Ctot−prot the num-er of cells that are not to be protected. In our simple case studyith 93 water cells of which 30 are to be protected, this would take

036 times the age of the universe; so not really an option.How do we tackle that dilemma? By using a smarter approach,

uch as represented by the likelihood-weighted sampling proce-ure, and while we cannot know how much improvement we couldbtain if we search 200 million times instead of 200 thousand,e can see from the first few hundred thousand runs that thereas only a small gain in the objective function as the number of

uns increased. This is in our case because there is little differenceetween individual habitat cells; it does not matter that much ifou pick a given cell or its twin sister.

With the few spatial cells we searched over, it was a feasibleask to search ‘a large number’ of times; it takes a few hours only.

ith more cells it will take longer to run the spatial model, and weaution that in such cases it is necessary to evaluate the tradeoffetween number of runs and objective function gain. One cannotnow a priori when enough is enough.

. Conclusion

We have presented two complementary approaches for spatialptimization, and we found from analysis of a simple spatial modelhat there were zoning combinations that could increase econom-cal and social factors without this having negative consequencesor the ecological aspects.

The optimizations showed though, that in the case study thereas a tradeoff between how much of the layers of conservation con-

ern that was included in the protected area, and the economicalnd social benefits. While there certainly is no explicit law statinghat there has to be tradeoff between conservation, and economicnd social concern in an exploited ecosystem, it is not a surprise thate found such a relationship. To evaluate this, our best chance is toodel the system, building on what we know, and let the results

peak. By developing the importance layer sampling procedure andllowing the user to set a range of protection levels we believeignificant enhancements have been made where Ecospace can besed as decision support in the consideration of both fisheries andonservation management objectives.

Another noteworthy aspect is that we have made it possibleo compare the most widely applied tool for ecosystem model-ng, EwE, with the most widely applied tool for spatial zoning,

arxan. For such comparisons to be meaningful there has to beommonalities between the approaches, a common language. Thiss provided through the common use of spatial layers of conserva-ion interest, what we call importance layers, and whose propertiesnd potential use of we have described formally. We have devel-ped a bridge between the Ecospace and Marxan approaches, whichllows two-way analysis of potential protected layer properties.

more thorough treatment of these approaches and the utilityf this interoperability will be conducted in subsequent analy-es. This indeed will take us a good step further to establishingultiple-objective marine spatial planning, a tenet of ecosystem-

ased management.

elling 220 (2009) 2583–2593

Acknowledgements

We thank Carl Walters for focusing the development of thecell sampling approach on a procedure for random, importance-weighted spatial selection, as well as for developing the Ecospacemodel. We also thank Alasdair Beattie and Daniel Pauly for coop-eration on the initial version of the seed cell selection approach.Joe Buszowski and Sherman Lai worked with us on program-ming and implementation, Robyn Forrest on documentation, andChiara Piroddi and Carie Hoover on program testing. An anonymousreviewer provided numerous suggestions from which this contri-bution benefitted. The overall development of EwE6, on which thisstudy relies, was made possible by the Lenfest Ocean Program, andthe Sea Around Us Project, initiated and funded by the Pew Char-itable Trusts of Philadelphia. VC also acknowledges the NaturalSciences and Engineering Research Council of Canada. The presentactivity was supported by funds from Duke University under anaward from The David and Lucile Packard Foundation. The findings,opinions and recommendations are those of the authors, and notnecessarily those of Duke University or the Packard Foundation.

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