Portfolio Decision Analysis Framework for Value-Focused Ecosystem Management

Management of natural resources in coastal ecosystems is a complex process that is made more challenging by the need for stakeholders to confront the prospect of sea level rise and a host of other environmental stressors. This situation is especially true for coastal military installations, where resource managers need to balance conflicting objectives of environmental conservation against military mission. The development of restoration plans will necessitate incorporating stakeholder preferences, and will, moreover, require compliance with applicable federal/state laws and regulations. To promote the efficient allocation of scarce resources in space and time, we develop a portfolio decision analytic (PDA) framework that integrates models yielding policy-dependent predictions for changes in land cover and species metapopulations in response to restoration plans, under different climate change scenarios. In a manner that is somewhat analogous to financial portfolios, infrastructure and natural resources are classified as human and natural assets requiring management. The predictions serve as inputs to a Multi Criteria Decision Analysis model (MCDA) that is used to measure the benefits of restoration plans, as well as to construct Pareto frontiers that represent optimal portfolio allocations of restoration actions and resources. Optimal plans allow managers to maintain or increase asset values by contrasting the overall degradation of the habitat and possible increased risk of species decline against the benefits of mission success. The optimal combination of restoration actions that emerge from the PDA framework allows decision-makers to achieve higher environmental benefits, with equal or lower costs, than those achievable by adopting the myopic prescriptions of the MCDA model. The analytic framework presented here is generalizable for the selection of optimal management plans in any ecosystem where human use of the environment conflicts with the needs of threatened and endangered species. The PDA approach demonstrates the advantages of integrated, top-down management, versus bottom-up management approaches.

The Snowy Plover, Piping Plover, and Red Knot are the threatened and endangered species (TERs) observed on beach and salt marsh habitats of Florida Gulf coast ecosystem (1)(2)(3)(4)(5)(6)(7)(8)(9). Figure S1 shows the occurrences of the abovementioned species for Santa Rosa Island (SRI). SRI is the barrier island, partially managed by EAFB (10)(11), that is considered in our study as location where species of concern and intense human use co-occur. The island that is about 30,000 m long and 500 m wide on average and is used for a variety of test and evaluation activities and training exercises by EAFB (10,11). A portion of the military beach area is open for public recreation and it constitutes a suitable habitat for multiple species including the shorebird considered (12). Thus, beach areas support both military activities and species needs. The portion of SRI managed by military is 12.5 km 2 and the portion within the military areas is 2.5 km 2 . Occurrences of these shorebirds for the period 2002-2012 are shown in Figure 1 and Figure S1. Data of the species considered are from the Florida Geographic Data Library (13), and from efforts of previous studies related to the effect of sea level rise on these shorebirds (1,14,15). The data of species from these sources is also integrated from information derived from (16). More information about species, habitat use, and suitability of species is contained in (2)(3)(4)(5)(6)(7)(8)(9). Data for the military installations and recreational use are from the Florida Geographic Data Library (13).
The local species richness (LSR), that is the number of unique species occurring in each pixel, is calculated in order to show how SRI is a hotspot of biodiversity and to make evident the importance of considering multiple species for a global conservation of the ecosystem. The pixel size is 120 m 2 that is the unit used in the biophysical modeling. LSR for the Panhandle-Big Bend-Peninsula region is shown in Figure 1. SRI is represented in the inset of Figure 1, and LSR for SRI is shown in Figure S1. The maximum local species richness for SRI is eight and for the whole Florida Gulf coast is ten. The global species richness, that is the total number of unique species in a region, of SRI is sixteen while for the whole Florida Gulf coast is forty-six.
For the human assets, we consider the military beach areas and infrastructure that falls into non-ocean pixels at each year of the analysis. These assets are shown in Figure S2 at the current state. Range operations rely on land-based radar and electro-optical timespace-position-information systems to monitor and transfer test data to the Central Control Facility on Eglin AFB (10)(11)(12). These instrumentation systems, located on Santa Rosa Island and other locations provide coverage for test and evaluation activities in the Gulf of Mexico (12). The use of SRI is evolving due to changes in threats to national security and the effects of hurricanes over the past decade. The SRI complex is used for Expanded Surf Zone Testing/Training, Mine Clearing Testing, Beach Obstacle Clearing and Neutralization, Small Boat Obscurant Testing, Live Fire, Expanded Special Operations Training, Amphibious Assaults, and other types of activities.

Management Area Scale
The extent of management areas is calculated by evaluating the tradeoff between the spatial needs for a correct representation of the assets (species and military areas) and a feasible scale for the implementation of restoration actions. The average home range of species, that is the average distance at which a species lives and disperses in the ecosystem, is a good indicator for the minimal dimension of the management area. The scale of infrastructure is in our case larger than the scale of the species considered. We consider the average home range of the Snowy Plover (120 m) that is the ``sentinel species'' of the beach habitat in the Florida Gulf coast (17), and the average shore length of the nourishment (7620 m) (9,18,19) that is the largest restoration action considered in this study. Thus, the average scale of a management area is 3750 m that is the average of the two abovementioned distances. For simplicity, the management area is assumed to be a square. Hence, each management area contains about 961 pixels used in the biophysical modeling. Values of spatially explicit criteria from biophysical models are averaged within each management area to obtain values of assets as a function of restoration actions at the appropriate scale for the portfolio decision model (PDM).

Biophysical Models and Restoration Actions
A land cover model (SLAMM) (19), a habitat suitability model (MaxEnt) (20-21), and a metapopulation model (RAMAS) (22) are used to reproduce the evolution of habitat area and quality, and the risk of assets as a function of sea level rise and restoration plans from 2013 to 2100 (1,(2)(3)(4)(5)(6)(7)(8)(9). Biophysical models are run at the resolution of 120 m 2 . A complete explanation of these models and their application to the scenario with no restoration action is included in (1) and (3). In this paper we rerun this set of models for the nourishment scenarios selected by the MCDA and the PDM. Models are run at the scale of the whole Gulf coast of Florida. However, MCDA and PDM consider only Santa Rosa Island that is managed by EAFB. Thus, the variability of restoration actions is considered only at the scale of Santa Rosa Island and no action is assumed elsewhere. Despite we focus only at the scale of installation management restoration plans chosen at SRI influence habitat and metapopulation dynamics outside SRI. The outputs of biophysical models are the inputs of the MCDA model (Tables S4 and S5) as explained in Materials and Methods.

Nourishment
In order to simulate the nourishment scenarios at SRI, we adopt the SLAMM model modified by (24). We consider the A1B sea level rise scenario rescaled to 2 m in 2100. The modified version of SLAMM takes into account time-specific changes in the land cover that are caused by the nourishment. These changes are simulated by adding another term to the equation that describes the evolution of the elevation z of pixels used in the biophysical modeling. The equation considers the natural accretion/sedimentation rate a in the time period Δt (where Δt=1 year) sea level rise SLR, and the increase in elevation Δz dictated by the nourishment, as follows .
[S1] By using Eq. S1, the modified SLAMM considers changes in elevation, slope and land cover classes at a specific year as a function of both natural and anthropogenic drivers. If beach nourishment is carried out in any management area SLAMM increases z(t) of beach cells of Δz = 1 m regardless of the location and the year considered. However, heterogeneous changes in space and time due to nourishment can be implemented. z(t) = z(t 1) + t a SLR(t) + z(t) Table S1. Restoration actions and their effectiveness for the Snowy Plover (SP). Each restoration action is characterized by an effectiveness factor that is proportional to the probability of success of each restoration action for each asset locally. The effectiveness factor is assessed after expert judgement and review of literature. The effectiveness is assumed equal to one when the effects of restoration actions are predicted by biophysical models. This is because the criteria values in the MCDA model consider already the effects of the simulated restoration action. In our case the baseline scenario (no restoration actions) is modeled in (1), and in (3). The nourishment is modeled as in (18) and in (24). Table S2. Restoration actions and their effectiveness for the Piping Plover (PP). The effectiveness is assumed equal to one when the effects of restoration actions are predicted by biophysical models. Table S3. Restoration actions and their effectiveness for the Red Knot (RK). The effectiveness is assumed equal to one when the effects of restoration actions are predicted by biophysical models.

Table S4. Restoration actions and their effectiveness for the Military Area (MA).
The effectiveness is assumed equal to one when the effects of restoration actions are predicted by biophysical models. Table S5. MCDA model for the Snowy Plover. Criteria at different order characterize each restoration action for the SP in all the management areas of SRI. Thus, criteria values of the MCDA model vary in each management area for the same action considered. The weights are assigned by expert judgement. In our case study we run the whole set of models (SLAMM, MaxEnt, and RAMAS) (20-23) for the no-action and the nourishment (1,24). We calculate the MCDA value of other restoration actions by multiplying the effectiveness factor of each restoration action to the MCDA value of the no-action (1). For the PP and the RK the subpopulation viability criteria are calculated using the statistical method of (3) rather than using RAMAS. The abundance of SP and RK is calibrated on abundance data in the suitable patches and rescaled to the predicted patches proportionally to their area for every year simulated. The weight of criteria for the PP and RK are the same of the weights for the SP.  Figure S2 within dotted and continuous lines (from A1 to A18). Training areas are the pink areas in Figure  S2 that are closed to all forms of public access. We assume that their training suitability is the same and equal to 1 in a range [0, 1]. In our case study we run the whole set of models (SLAMM, MaxEnt, and RAMAS) (20-23) for the no-action and the nourishment (1-24). Table S7. Input factors for the PDM for Santa Rosa Island. A number is assigned to each management area in which each asset occurs. Restoration actions are asset-specific or they benefit multiple assets at the same time in the same management area and in adjacent management areas. The value of each restoration action is the expected local value from the MCDA model and adjusted by the asset vulnerability that considers the whole restoration plan, and the effectiveness factor of each restoration action that considers the local effect of each action. The cost is the cost of each action at the management area scale. We considered costs derived from the literature available and from experts. Table S8. PDM restoration plan (Pareto set) in 2013 for Santa Rosa Island. The set is visualized in Figure 5b. Each Pareto set corresponds to a management plan with a global value V T (R) (Eq. 2) at the installation scale. The value in the table is the expected local value of each restoration intervention that is the restoration action selected by the Pareto optimization among all the possible actions that are part of possible restoration plans in the PDM. This value considers also the value of other assets that benefit from the same action selected for other assets. The restoration interventions in common to the MCDAbased plan are evidenced in red. The assets that benefit from the restoration intervention selected for other assets are shown in a lighter tone within parenthesis after the asset for which the intervention is selected.  Figure 5b. Each set corresponds to a management plan with a global value V T (R) (Eq. 2). The value in the table is the local value of each restoration intervention that is the restoration action with the maximum MCDA value among all the possible actions that are part of feasible restoration plans. This value considers also the value of other assets that benefit from the same action selected for other assets. The restoration interventions in common to the PDM-based plan are evidenced in red. The assets that benefit from the restoration intervention selected for other assets are shown in a lighter tone within parenthesis after the asset for which the intervention is selected. Figure S1. Local species richness for Santa Rosa Island and occurrences of the three threatened and endangered species considered in the case study. The occurrences of Snowy Plover, Piping Plover, and Red Knot, which are shown in red in the right plots (each pixel of 120 m 2 is marked in red if at least one species occurrence is detected), are the input of MaxEnt that is the habitat suitability model used in this study (7).