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The Value of Larval Connectivity Information in the Static Optimization of Marine Reserve Design



Marine reserve design often involves a tradeoff between meeting conservation goals (persistence of fished populations) and minimizing economic costs (lost fishing grounds). Optimization tools such as Marxan navigate that tradeoff by finding reserve configurations that minimize economic costs while protecting some minimum fraction of fish habitat. However, typical Marxan implementations do not account for patterns of larval connectivity among reserves, a factor known to be the key to population dynamics. We show how connectivity information (self-recruitment and network centrality) can be incorporated into the optimization. We then used a spatially explicit population model to compare the performance of reserves designed using habitat information alone or including connectivity. Incorporating connectivity information improved reserve performance for some species but not others. We conclude that including connectivity information can improve reserve design algorithms, but it is essential to evaluate species’ population dynamics to determine which species will benefit from a given reserve network.


Marine reserves are increasingly used worldwide as a conservation and management tool (Wood et al. 2008). Although reserves generally increase biomass of target species (Claudet et al. 2008; Lester et al. 2009; Babcock et al. 2010), theoretical models predict that individual species’ responses should depend on differences in levels of exploitation, the spatial scale of dispersal, and other demographic factors, and empirical assessments generally confirm those predictions (White et al. 2011). Indeed, not all reserves exhibit increases in fish abundance (Lester et al. 2009) which could reflect either poor enforcement (Guidetti et al. 2008) or a design process that did not adequately account for key ecological factors (Lester et al. 2009; White et al. 2011). Here we focus on the latter problem.

Reserve design must strike a balance between meeting conservation goals (e.g., preserving sustainable fish populations; Botsford et al. 2009) and minimizing economic costs (e.g., lost fishing grounds; Klein et al. 2008b; Fox et al. 2013). These competing demands of reserve goals are addressed by two different modeling approaches that have been used to guide reserve design: dynamic models and static optimization. By dynamic models we refer to spatially explicit population models that use information on habitat distribution, larval connectivity, and other ecological factors to project how fished populations will respond to reserve establishment (e.g., Kaplan et al. 2009; White et al. 2010b; a; reviewed by White et al. 2011). Due to uncertainty about initial conditions for these models, analysis typically centers on long-term equilibria (White et al. 2011). This reveals how alternative reserve configurations could improve population persistence or fishery yield, but does not necessarily reflect short-term economic costs due to fishing ground closures (Sanchirico & Wilen 2001; White et al. 2013a; but see Moffitt et al. 2013; White et al. 2013b).

The second modeling approach, static optimization, focuses on minimizing the costs of lost fishing grounds, while protecting a target amount of key habitats assumed to be sufficient to ensure population persistence for species within the reserves (Klein et al. 2008b). This approach has grown in popularity because of the availability of the software Marxan (Ball & Possingham 2000). Marxan uses a simulated annealing algorithm to find reserve configurations that minimize reductions in resource use (i.e., fishing grounds) while meeting conservation goals (Klein et al. 2008a,b). Marxan was used to inform the rezoning of the Great Barrier Reef (Fernandes et al. 2005) and Sala et al. (2002) used it to suggest reserve configurations for the Gulf of California.

Two advantages of Marxan are ease of use (Marxan is well documented with user guides and a support community) and its ability to incorporate socioeconomic data from stakeholders, which can help mitigate short-term economic losses. A potentially key weakness in common applications of this tool, however, is that the biological data included in the optimization are typically limited to habitat distributions (e.g., Klein et al. 2008a), and do not include information on other factors important to marine population dynamics, particularly demographic connectivity among habitat patches by larval dispersal. Understanding larval connectivity is key to determining whether particular reserve configurations support persistent populations (Botsford et al. 2001, 2009; Gaines et al. 2003; White et al. 2010a; Watson et al. 2011). Without accounting for connectivity, it is possible that static optimization tools like Marxan could produce solutions that minimize short-term costs but do not adequately support fishery populations over the long term.

Here we propose an approach to link static and dynamic reserve design approaches by including larval connectivity information in the Marxan optimization framework. We illustrate our approach using a case study from California, though we draw general lessons from this example. Our work goes beyond similar efforts to account for connectivity (Beger et al. 2010) in that we also quantify the value of including connectivity information by comparing the performance of different Marxan-designed reserve configurations using a spatially explicit population dynamics model. We found that including information on larval connectivity can result in higher biomass and fishery yield for particular species while closing less overall reserve area to fishing.


Our analysis centers on a case study from the coast of northern California (Fig. 1), where a reserve design process was recently completed during the implementation of California's Marine Life Protection Act (MLPA; Kirlin et al. 2013). During that process, White et al. (2010b, 2013a) developed a spatially explicit dynamic bioeconomic model to project long-term equilibrium distributions of the biomass and fishery yield of each of five species. These model species have life histories representative of the range of species found in rocky reef habitats in this region (Table 1; Leet et al. 2001; Love et al. 2002). This model (along with other assessments) was used to compare alternative protected area designs proposed by stakeholders and choose the final proposal (White et al. 2013a). Klein et al. (2008a) have argued that the MLPA design process could have been improved by incorporating protected area configurations designed using Marxan.

Figure 1.

Maps showing location of study region in northern California, USA (inset; red outline); and distribution of hard-bottom habitat in the study region (blue: 0–30 m depth; red: 30–200 m depth).

Table 1. Species used in the model. Documentation for biological information provided in White et al. (2013a)
     Fishing mortality rate (y−1)
Species nameHabitat preferenceSpawning seasonPelagic larval duration (d)Adult home home range width (km)Low (FLEP = 0.3)High (FLEP = 0.2)Very high (FLEP = 0)


  1. Mortality rates for red abalone are extremely high because individuals do not become available to the fishery until quite late in life.

Red abalone (Haliotis rufescens, Haliotoidea)Hard bottom, 0-30 m depthApr-July50.11.4813.611163.70
Red sea urchin (Strongylocentrotus franciscanus, Strongylocentrotidae)Hard bottom, 0-100 m depthDec-Mar840.010.583.1691.02
Cabezon (Scorpaenichthys marmorata, Cottidae)Hard bottom, 0-30 m depthNov-Mar1050.060.420.718.68
Black rockfish (Sebastes melanops, Scorpaenidae)Hard bottom, 0-100 m depthJan-May150130.130.191.40
Brown rockfish (Sebastes auriculatus, Scorpaenidae)Hard bottom, 0-100 m depthDec-Jun4520.150.211.70

In our analysis, we used biological data generated during the MLPA design process to compare the performance of Marxan optimization with and without the inclusion of static information on larval connectivity. We generated Marxan solutions using habitat data only (as a standard Marxan implementation would do) or using a static estimate of the importance of each habitat patch to larval connectivity. We then compared the performance of each set of reserve configurations generated in Marxan in terms of coast-wide equilibrium biomass (both inside and outside reserves) and fishery yield using the White et al. (2013a) population model. Note that this approach focuses on two common goals of marine reserves: preserving sustainable populations and enhancing fisheries (Gaines et al. 2010); it does not address other potential goals such as protecting unexploited species.

Though we focused our analysis on a particular study location where both habitat and larval connectivity information are available, the goal of our investigation was broader. Given a particular spatial distribution of habitat and connectivity, is reserve design improved by accounting for that connectivity information? In answering this general question we essentially assume that habitat, connectivity, model parameters, etc. are known with certainty; that is, alternative reserve designs are compared to a fixed population dynamics benchmark. We do not attempt to produce actual recommendations for reserve design in California, which would require careful consideration of potential uncertainties in our biological information.

Population model

White et al. (2013a) provide a full description of the model, but in brief it is a spatially explicit age-structured model with 1 km2 spatial resolution and an annual time-step. It is a single species model but can be run in parallel for multiple species. Fish grow according to the von Bertalanffy relationship and fecundity of fish above the age of maturity is proportional to biomass. Larvae spawned in each patch disperse to other patches according to the probabilities defined by a species-specific connectivity matrix (see below); at settlement larvae experience Beverton–Holt density-dependent mortality with a maximum settler density proportional to the abundance of suitable habitat in that model cell. Each model cell may be designated as inside a no-take reserve or in a fished zone; adult fish move within home ranges, so fish that settle within a reserve as larvae may be exposed to fishing depending on the proportion of their home range that lies outside the reserve. We simulated population dynamics of five different species that differ in their life histories, habitat requirements, larval dispersal characteristics, and scales of adult home range movement (Table 1).

In the model, fishing effort is set as a coast-wide level of effort that is distributed spatially following an ideal free distribution so that catch per unit effort is equal in all fished cells (White et a. 2013a). For each species, the initial slope of the density-dependent Beverton–Holt function (the survival rate at low densities) determines the level of fishing that causes the population to collapse (White 2010). We set that parameter so that each species collapsed when fishing reduced lifetime egg production to 25% of its unfished maximum. We then specified fishing effort for each species as the fishing mortality rate that would reduce lifetime egg production to 20% of its maximum in a nonspatial model (Table 1); thus all species experienced a dynamically equivalent level of fishing (White et al. 2010a) and none persisted in the absence of reserves. This represents a worst-case scenario designed to test the effectiveness of reserve designs (cf. Botsford et al. 2001). For comparison we performed additional simulations in which fishing reduced lifetime egg production to 0% (extreme overharvesting) and to 30% (fishing near the maximum sustainable yield).

Habitat maps

Habitat data for the study region were developed during the MLPA design process; benthic habitat was classified by type (hard, soft) and depth range (0–30 m, 30–100 m), and each model cell was classified by the proportion of each habitat type it contained (White et al. 2013a), although the model species in this analysis only used hard habitats.

Larval connectivity matrices

Larval dispersal among model cells was described by connectivity matrices comprised of the probabilities pji of a larva spawned in cell i dispersing to cell j. The pji were estimated using Lagrangian drifter simulations run offline in numerical ocean circulation models implemented for the study region (Drake et al. 2011; Appendix S1). For each species, millions of Lagrangian particles were released into the three-dimensional model circulation field every other model day for 7 model years (2000–2006). Particles were released from and allowed to settle into 70 connectivity nodes along the California and Oregon coasts, each node spanning 40 km in the alongshore direction (Figure 2). Connectivity probabilities were then downsampled to provide probabilities to and from each 1 km2 cell in the population model (White et al. 2013a). For each model species, particle behavior was defined by the spawning season and larval duration (Table 1; Drake et al. 2011; White et al. 2013a).

Figure 2.

Larval connectivity predictions. (A) Map showing the connectivity nodes to and from which larvae disperse in Lagrangian simulations. Those simulations are used to calculate dispersal matrices giving the probability of dispersal from each node to every other node. Matrices are shown for (B) Sebastes melanops (black rockfish), (C) Haliotis rufescens (red abalone), (D) Sebastes auriculatus (brown rockfish), (E) Scorpaenichthys marmorata (cabezon), and (F) Strongylocentrotus franciscanus (red sea urchin). The full model has 70 nodes along the coast; only those in the north coast study region are shown here.

The larval connectivity probabilities produced by the Drake et al. (2011) model are the best and highest resolution estimates currently available for the study region. As with any such model there are some limitations to accuracy at particular scales, including coarse resolution of larval behaviors and processes in the inner shelf where some of the model species spawn (improving these features is an active topic of research; Drake et al. 2013). Nonetheless, for the purposes of this study it is sufficient to assume that the modeled connectivity information is correct, and then to gauge the relative performance of reserve design efforts that either do or do not use that information.

Larval connectivity metrics

To include connectivity information in Marxan optimizations, we used two different summary statistics to characterize the importance of each habitat patch to connectivity for a particular species. The first metric was the diagonal elements of the connectivity matrix, pii, which give the probability of larval self-retention for each patch i. Higher values of this quantity make it more likely that a patch can be self-persistent (Burgess et al. 2014). The second quantity was a patch-importance metric termed centrality (Bonacich 1972). The centrality of patch i is the ith element of the dominant left eigenvector of the connectivity matrix. This value gives the contribution of patch i to the growth rate of a linear metapopulation model (Jacobi & Jonnson 2011; Watson et al. 2011).

Because connectivity depends on both larval transport and larval production in each patch (Botsford et al. 2009), prior to calculating self-retention or centrality we multiplied each column of each species’ connectivity matrix by the proportion of that species’ habitat in the corresponding model cell. The proportion of habitat sets the maximum density in each cell, so this essentially scaled connectivity by the potential maximum reproductive output of each cell. The spatial distributions of habitat, self-retention, and centrality for each species are shown in Figure S1.

Marine spatially explicit annealing (Marxan)

We used Marxan v. 2.43 (Ball et al. 2009) to obtain optimized reserve configurations. After preliminary optimizations (following Game & Grantham 2008) we used 1,000 algorithm runs for each optimization and chose a value of 1.0 for the boundary length modifier (BLM). This produced reserves 10–20 km wide, similar to size recommendations in the MLPA process (Saarman et al. 2013), although preliminary runs indicated that the BLM value did not affect the overall results so long as it was constant across patches.

We conducted Marxan optimizations to produce reserve configurations corresponding to each of the biological criteria: habitat, self-retention, and centrality. When operating Marxan, one specifies a target level of protection for a particular habitat type (e.g., 10% of rocky reef habitat). We treated both habitat and centrality as “habitat types” and varied the target level of protection between 0.25% and 50%, with increments of 0.25%. In the case of habitat, this has the straightforward interpretation of requiring the specified proportion of habitat be protected in the optimal solution. For self-retention and centrality, the interpretation of the target (the proportion of self-retention or centrality in reserves) is less intuitive, but nonetheless functional. We did not include socioeconomic costs in this analysis, so each habitat patch was assigned the same cost of inclusion in a reserve.

We performed optimizations for all species simultaneously, so each optimization had the same target percentage for all five species. We conducted 10 replicate optimizations for each target percentage of each criterion (600 total Marxan optimizations). For each replicate optimization we saved the outcome (of the 1,000 algorithm runs) that best satisfied the optimization objective function as the final optimization result. We then simulated the population dynamics of each species in each of the 600 optimized reserve configurations. We compared the performance of reserve configurations by calculating the total equilibrium biomass and fishery yield of each species in the entire model array. We scaled the biomass of each species by the equilibrium biomass in a simulation without fishing and scaled the yield by the maximum sustainable yield in a simulation without reserves; this allowed us to compare relative biomass and yield values across species.

For comparison, we also implemented the connectivity optimization procedure described by Beger et al. (2010) and used the population model to evaluate those designs as well (Appendix S2).


As the conservation target (optimization weighting) was increased for each optimization criterion, the proportion of habitat in reserves also increased. For the habitat criterion, this proceeded as expected: a target of 20% habitat produced reserve networks with approximately 20% coverage for each species. For the self-retention and centrality criteria, a given percentage target generally produced a network covering somewhat less than that percentage of habitat (e.g., a 37.5% centrality target produced networks with approximately 20% habitat coverage). Consequently, the maximum self-retention and centrality targets had ≤20% and ≤35% habitat coverage, respectively. More importantly, the three criteria produced distinctly different reserve configurations. For example, in three representative reserve networks with ∼20% habitat coverage, habitat optimization yielded a large reserve centered on a large northerly habitat patch, while centrality optimization avoided that patch but placed reserves in the center and southern edge of the domain (Figure 3), both locations where some species have high rates of larval import and export (see nodes 48 and 54 in Figures 2B, E, and F) and thus high centrality (Figure S1). Self-retention optimization placed reserves in locations similar to centrality in the southern region, but avoided the center of the domain where self-retention is low (Figure S1) and also protected several small, high-retention patches in the north (see node 58 in Figure 2; Figure S1) distinct from the nearby large patch protected by habitat optimization (Figure 3). Notably, reserve configurations, designed using habitat, were highly variable among Marxan solutions, but self-retention and centrality optimization produced extremely consistent configurations across Marxan runs (Figure S2).

Figure 3.

Representative MPA networks obtained by Marxan optimization using (A) habitat only, (B) self-retention, and (C) network centrality. All three networks contain approximately 20% of hard habitat in the study region.

In general, total biomass of all species increased with the amount of habitat in reserves, but the species differed in their relative performance in reserves designed using the three criteria (Figure 4). For red abalone and, to a lesser degree, cabezon and red sea urchin, performance was highly variable under habitat optimization (e.g., a >twofold difference in biomass between networks containing the same fraction of habitat in reserves, Figures 4A and C) but was much less variable and better with centrality optimization, and better still with self-retention optimization (Figures 4A, C, and E). For these species, reserve networks designed using self-retention or centrality achieved a particular level of biomass with a much lower fraction of the habitat in reserves (Figure 4). The pattern for the two rockfish species was different; black rockfish had essentially the same biomass in reserves designed using the three criteria (Figure 4B), and brown rockfish had lower biomass using centrality than in most networks designed using habitat, though self-retention optimization produced slightly higher biomass than habitat (Figure 4D). Extremely similar patterns held for both biomass and yield as a function of reserve area for all species across a range of fishing mortality rates (Figures S3–S7).

Figure 4.

Equilibrium total biomass in the study region as a function of the proportion of hard habitat in reserves for (A) red abalone, (B) black rockfish, (C) cabezon, (D) brown rockfish, and (E) red sea urchin. Each species was fished a rate that would reduce lifetime egg production to 20% of the unfished maximum in the absence of reserves. Each point corresponds to one optimized reserve configuration, designed using habitat (black circles), self-retention (blue triangles), or network centrality (red diamonds). Biomass is expressed relative to the biomass of that species in a simulation with no fishing.

To illustrate the source of the variation in reserve network performance, we compared the spatial distribution of biomass in the three representative reserve configurations shown in Figure 3 (Figures 5 and 6). In the self-retention and centrality optimized networks, biomass densities were higher inside reserves (compare the northernmost reserve in Figures 5A, D, and G to the southernmost reserve in Figures 5B, C, D, E, F, H, and I) and there was more spillover of biomass to areas outside of reserves than in the habitat-optimized network. The latter effect was particularly evident in the southern region of the domain for red abalone and cabezon (Figure 6).

Figure 5.

Comparison of the spatial distribution of biomass across the model domain at equilibrium for three representative reserve networks optimized using habitat (A, D, G), self-retention (B, E, H) or network centrality (C, F, I). Results are shown for red abalone (A, B, C), cabezon (D, E, F), and black rockfish (G, H, I). All three reserve networks had approximately 20% of hard habitat in reserves; reserve boundaries are shown in Fig. 3 and identified by arrows and gray background in this figure. Biomass (indicated by color) is expressed relative to the biomass of that species in a simulation with no fishing.

Figure 6.

Comparison of the spatial distribution of biomass in the southern portion of the model domain for two representative reserve networks optimized using habitat (A, D, G), self-retention (B, E, H) or network centrality (C, F, I). Results are shown for red abalone (A, B, C), cabezon (D, E, F), and black rockfish (G, H, I). All three reserve networks had approximately 20% of hard habitat in reserves; reserve boundaries are shown in Fig. 3 and identified by arrows and gray background in this figure. Biomass (indicated by color) is expressed relative to the biomass of that species in a simulation with no fishing. This figure shows the same data as Fig. 5 but is zoomed in to show finer detail near the southernmost reserves.

Marxan optimizations using the Beger et al. (2010) consisted of many smaller reserves scattered across the spatial domain (Figure S8), apparently as a consequence of the way the method repurposes the BLM parameter (Appendix S2). These reserve configurations produced biomass and yield results comparable to habitat-only optimization (Figures S9 and S10).


Including connectivity information (in the form of self-retention or network centrality) in the reserve design algorithm improved the performance of reserve networks for three of the five model species, and reduced the variation in reserve performance for all five species. We draw two key conclusions from these results. First, this reaffirms that connectivity patterns are crucial to reserve design (Crowder et al. 2000; Costello et al. 2009; Rassweiler et al. 2012). Reserve configurations optimized using habitat data alone varied widely in the amount of biomass they were predicted to support (in some cases greater than twofold differences despite protecting the same total amount of habitat). This illustrates the risk of reserve designs premised on the assumption that a successful reserve network need only encompass a particular fraction of available habitat (e.g., Klein et al. 2008a,b). For some species, not all habitat patches are equally valuable, and reserves may be placed in suboptimal locations, unable to accumulate sufficient larval settlers to greatly increase biomass, and unable to successfully export large numbers of larvae beyond the reserve boundaries.

Interestingly, optimizing for self-retention tended to produce better results than optimization for centrality, which is a measure of overall connectedness. This result puts a finer point on the widely accepted idea that reserves should be designed with “connectivity” in mind (Costello et al. 2009; Rassweiler et al. 2012). Not all connectivity metrics are created equal, and focusing on self-retention (and thus self-persistence) may be generally more advantageous.

The second key conclusion is that the importance of connectivity varies greatly among species. The three species that had higher performance with connectivity-based optimization either had extremely short-distance larval dispersal with a few key highly self-connected patches (red abalone, Figure 2B) or relatively structured connectivity patterns in which some patches had appreciably higher export or import probabilities than others (cabezon, red sea urchin; Figures 2E and F). For those three species, reserves could be tailored to those key patches. By contrast, the black rockfish had an extremely diffuse connectivity pattern, with few obvious high-value patches. For that species, all patches were approximately equivalent in terms of connectivity, and so adding additional reserve area anywhere in the metapopulation produced a similar improvement in biomass. Finally, the brown rockfish offers a cautionary result: that species had a connectivity pattern that differed from that of many of the other species, with greater self-retention in the northern area of the model domain. As a result, it tended to do worse in reserve networks that were designed using a suite of centrality values from multiple species than in networks designed using habitat information alone. However that species did well in self-retention-optimized reserves, likely because self-retention is more consistent across species than is directional transport (Figure 2).

These results suggest that it can be valuable to include connectivity information in reserve network optimization, but it is essential to independently determine whether a connectivity-based design is actually an improvement. For example, Beger et al. (2010) showed that their connectivity-based reserve design approach led to greater inclusion of high-centrality patches in the examples they tested, but they did not evaluate their method's performance in a multispecies population dynamics context as we did. In fact, we have shown that maximizing centrality can improve population dynamics for some but not all species, and our implementation of the Beger et al. (2010) method did not outperform optimization using habitat information alone. Of course, it is impossible to optimize reserve design for all species simultaneously, but our results reinforce the necessity to take care when choosing target species for the optimization process. Additionally, being able to predict the population dynamic response of the various species is essential when setting expectations for reserve performance and postimplementation adaptive management (White et al. 2011; 2013b).

Sala et al. (2002) required Marxan-designed reserve networks to satisfy a maximum spacing distance constraint in an effort to ensure strong larval connectivity. This is a simple but increasingly common approach to reserve design for connectivity in low-information settings (Anadón et al. 2013; Saarman et al. 2013). However, Moffitt et al. (2011) showed that such guidelines typically have little value from a population dynamics standpoint, and that when connectivity information is missing it is preferable to focus on maximizing reserve size and total reserve area rather than adjusting spacing criteria. Of course, circulation model simulations are not the only source of useful connectivity estimates, and in data-poor regions they would not be available. In such cases a variety of other empirical data could also be used in a reserve design setting (Botsford et al. 2009; Burgess et al. 2014).

Here we have illustrated an approach for using connectivity information to improve reserve design using an established optimization procedure. This analysis should not be interpreted as a call to reconfigure the California reserve network. After all, for the sake of simplicity we omitted socioeconomic costs, considered only no-take reserves, and focused only on species in a single habitat type. Nonetheless, our work shows how static and dynamic design approaches can be linked to improve reserve performance and set expectations for the adaptive management of reserves after implementation.


This work was supported by North Carolina Sea Grant (R/MG-1114) and the UNCW Center for the Support of Undergraduate Research and Fellowships. The authors are grateful to the Marxan development group at the University of Queensland for their efforts developing, documenting, and supporting free Marxan software, and to Matthew Bell and Maria Beger for suggestions on implementing the Beger et al. (2010) method. We thank four anonymous reviewers for helpful comments that improved the manuscript, particularly the idea for examining the diagonal elements of the connectivity matrix as an optimization target.