Pareto frontiers after realization of the selected restoration plan.

<p>(a) Pareto optimization unconstrained to the available resources. Red points represent the suboptimal restoration plans for the frontier in 2013. Grey dashed lines represent the variability of the frontiers related to thirty Monte Carlo simulations generated considering a random white noise applied to the MCDA value. (b) Pareto frontiers constrained to the resources available for selected years of analysis; we assume that the total resources available are equal to 250 at the installation scale (Eglin AFB in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone-0065056-g001" target="_blank">Figure 1</a>). The frontiers show V_H and V_N (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone.0065056.e002" target="_blank">Eq. 2</a>) normalized to their maximum value. The blue and red dots represent unaffordable and affordable restoration plans (or portfolios) for 2100. All the possible values of V_H(<u>R</u>) and V_N(<u>R</u>) for selected years are shown along the Pareto frontiers. The choice of the Pareto set depends on relative stakeholder preferences for human and natural assets.</p

Portfolio Decision Analysis Framework for Value-Focused Ecosystem Management

<div><p>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.</p></div

Management scales and actions.

<p>An example is reported for three management areas in SRI. Assets in each management area are indicated by the number contained in each area (e.g., 1 is the SP, 2 is the PP and 4 is the military area). Thus, management area one has two types of assets, management area two has three types of assets, and management area three has one type of assets. At least one action for each asset is evaluated in each management area. The restoration actions are indicated as <i>R_i(j),m</i> (where, <i>i</i> is the action, <i>j</i> is the asset, and <i>m</i> is the management area). Same actions can be evaluated for different assets (e.g. nourishment) because different assets can benefit from the same actions. Only one action is selected by the PDM or by the MCDA model. The selected actions are called restoration interventions. The whole set of restoration interventions in a management area is called restoration alternative, and the set of restoration alternatives is defined as restoration plan.</p

Restoration plans for Santa Rosa Island for the MCDA and PDM.

<p>Restoration plans are shown for 2013 (a, b) and 2100 (b, d) after the MCDA and portfolio decision model (a, c, and b, d respectively). The size of each management area is 3750 m². The total cost of the selected restoration actions is 250 resource units that is the budget available.</p

Global value disentangled into expected human and natural value of optimal restoration plans for the MCDA and PDM.

<p>The expected natural and human values (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone.0065056.e002" target="_blank">Eq. 2</a>) are calculated by considering the vulnerability of human and natural assets given a restoration plan for the whole ecosystem and the effectiveness of each restoration intervention for each asset. The curves are shown for a budget of 250 units. We selected the Pareto set for which V_H(<u>R</u>) = 0.5 V_N(<u>R</u>). Grey dashed lines represent the variability of the patterns related to thirty Monte Carlo simulations generated by considering a random white noise in the MCDA value.</p

Region of the case study.

<p>The local species richness (LSR) and the occurrence of Snowy Plover (SP), Piping Plover (PP), and Red Knot (RK) are reported in the map. The Panhandle – Big Bend – Peninsula within the black line is the region considered in our biophysical modeling effort (land cover, habitat suitability, and metapopulation model). Considering the extent of each management area (3750 m²), 192 management areas in the whole Gulf of Mexico coastal ecosystem of Florida were considered. Eight management areas cover the portion of Santa Rosa Island managed by Eglin Air Force Base (EAFB) (a). (b) Tyndall Air Force Base that is the hotspot of SP, hosting about 60% of the whole SP population in Florida.</p

Diagram of the modeling framework.

<p>The Multi Criteria Decision Analysis model (MCDA) evaluates restoration actions for each human and natural asset at the management area scale. Outputs of biophysical models at 120 m resolution are averaged at the management area scale (3750 m). These models are run at the whole ecosystem scale that is the population scale (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone-0065056-g001" target="_blank">Figure 1</a>) if assets are species. These outputs are part of the criteria in the MCDA model. The risk model modifies the MCDA values by considering the vulnerability of the restoration plan for each asset at the ecosystem scale and the effectiveness of each action at the management area scale (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone.0065056.e002" target="_blank">Eq. 2</a>). The expected values of restoration actions are the inputs of a Pareto optimization model together with the cost of the restoration plan and the constraint of the budget at the installation scale. The Pareto optimization provides Pareto frontiers of optimal restoration plans at each year in the management horizon (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065056#pone-0065056-g004" target="_blank">Figure 4</a>).</p

Cumulative probability distribution map.

<p>Cumulative probability distribution map.</p

Correlation coefficient of conifer volume and RS factors.

<p>Correlation coefficient of conifer volume and RS factors.</p

Factors loading rotation matrix of varimax.

<p>Note: B1, B2 are visible bands, where B1 can detect absorption and reflectance of plant green hormone, and B2 belongs to the red light zone capable of distinguishing the color of different types of vegetation from the color difference; Where B3 is near-infrared bands, which can reflect the sensitivity of plants to chlorophyll by the correlation between some acquired strong information and factors like leaf area index and biomass; SWIR (short-wave (length) infrared (band)); NDVI (Normalized Difference Vegetation Index); SAVI (Soil-Adjusted Vegetation Index); MSAVI (Modified Soil-Adjusted Vegetation Index).</p