Feral Hogs (*Sus scrofa*) are an invasive species that have occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies on vegetation, mast, and harvest history were important for our work. Using these data, a model with discrete time and space was formulated to represent the feral hog dynamics in the Park. Management strategies and key characteristics of the population were investigated. The model uses observed mast variation to help govern population dynamics and results indicate that Park control efforts have limited the growth of the population.

Marine reserves are an increasingly used and potentially contentious tool in fisheries management. Depending upon the way that individuals move, no-take marine reserves can be necessary for maximizing equilibrium rent in some simple mathematical models. The implementation of no-take marine reserves often generates a redistribution of fishing effort in space. This redistribution of effort, in turn, produces sharp spatial gradients in mortality rates for the targeted stock. Using a two-patch model, we show that the existence of such gradients is a sufficient condition for the evolution of an evolutionarily stable conditional dispersal strategy. Thus, the dispersal strategy of the fish depends upon the harvesting strategy of the manager and vice versa. We find that an evolutionarily stable optimal harvesting strategy (ESOHS)—one which maximizes equilibrium rent given that fish disperse in an evolutionarily stable manner– - never includes a no-take marine reserve. This strategy is economically unstable in the short run because a manager can generate more rent by disregarding the possibility of dispersal evolution. Simulations of a stochastic evolutionary process suggest that such a short-run, myopic strategy performs poorly compared to the ESOHS over the long run, however, as it generates rent that is lower on average and higher in variability.

Renewable resource modeling is usually characterized by different time scales where some state variables such as biomass may evolve relatively faster than other state variables such as carrying capacity. A strong form of time scale separation (STSS) means that a slowly changing variable is treated as constant over time. Management rules that assume STSS do not account for a time scale externality and this may induce inefficiencies in resource management. In the current work, we study multispecies resource management under time scale separation by adopting the framework of singular perturbation reduction methods. By extending recent work by Vardas and Xepapadeas [] to interacting populations, we study regulation with full internalization of the time scale externality. We further study regulation and noncooperative outcomes under STSS and identify deviations in harvesting and biomass paths among these cases. Deviations indicate the inefficiencies associated with adopting STSS.

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no-take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.

The presence of sediments in a river is one of the major factors that characterize the river. The presence of sediment in any water resource is detrimental to its design purpose and it scratches any structure such as bridge foundations, conduit pipes, and turbine blades it comes into contact with while in motion and this leads to their eventual failure under load. The correct estimation of sediment yield transported by a river is indispensable in water resources engineering as sediment affects its hydraulic structure. The use of mathematical modeling algorithms such as genetic algorithms (GA) has proved to be very accurate in predicting sediment load in a river. The analogy behind GA is that genes in DNA functions are manipulated in specific ways through specific transcription operations. Therefore, applying the same logical operators to selected parameters relevant to sediment loads in rivers leads to mathematical prediction of the sediment load. This review article discusses the dynamic of sedimentation and analyses the use of GA as a hydrological model for accurately predicting sediment yield in a river, its potentials and shortcomings while recommending its modification.

We present a multispecies stochastic model that suggests optimal fishing policy for two species in a three-species predator–prey ecosystem in the Barents Sea. We employ stochastic dynamic programming to solve a three-dimensional model, in which the catch is optimized by using a multispecies feedback strategy. Applying the model to the cod, capelin, and herring ecosystem in the Barents Sea shows that the optimal catch for the stochastic interaction model is more conservative than that implied by the deterministic model. We also find that stochasticity has a stronger effect on the optimal exploitation policy for prey (capelin) than for predator (cod).

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two-patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.

Economic problems in the optimal management of strategic resource stockpiles can be rigorously studied and solved by formulating them as optimal control problems in continuous time. In these optimal control problems, the proper description of the control constraints and objective function are critical to reflecting a realistic economic model. Existing work in this area often ignores fundamental saturation effects in the economic systems under scrutiny, and the following paper introduces and compares several methods for correcting this common modeling simplification in both deterministic and stochastic contexts.

A theoretically based analytic model of plant growth in single species conifer communities based on the species fully occupying a site and fully using the site resources is introduced. Model derivations result in a single equation simultaneously describes changes over both, different site conditions (or resources available), and over time for each variable for each species. Leaf area or biomass, or a related plant community measurement, such as site class, can be used as an indicator of available site resources. Relationships over time (years) are determined by the interaction between a stable foliage biomass in balance with site resources, and by the increase in the total heterotrophic biomass of the stand with increasing tree size. This structurally based, analytic model describes the relationships between plant growth and each species’ functional depth for foliage, its mature crown size, and stand dynamics, including the self-thinning. Stand table data for seven conifer species are used for verification of the model. Results closely duplicate those data for each variable and species. Assumptions used provide a basis for interpreting variations within and between the species. Better understanding of the relationships between the MacArthur consumer resource model, the Chapman–Richards growth functions, the metabolic theory of ecology, and stand development resulted.

To integrate economic considerations into management decisions in ecosystem frameworks, we need to build models that capture observed system dynamics and incorporate existing knowledge of ecosystems, while at the same time accommodating economic analysis. The main constraint for models to serve in economic analysis is dimensionality. In addition, to apply in long-term management analysis, models should be stable in terms of adjustments to new observations. We use the ensemble Kalman filter to fit relatively simple models to ecosystem or foodweb data and estimate parameters that are stable over the observed variability in the data. The filter also provides a lower bound on the noise terms that a stochastic analysis requires. In this paper, we apply the filter to model the main interactions in the Barents Sea ecosystem. In a comparison, our method outperforms a regression-based approach.

The proliferation of double-crested cormorants (DCCOs; *Phalacrocorax auritus*) in North America has raised concerns over their potential negative impacts on game, cultured and forage fishes, island and terrestrial resources, and other colonial water birds, leading to increased public demands to reduce their abundance. By combining fish surplus production and bird functional feeding response models, we developed a deterministic predictive model representing bird–fish interactions to inform an adaptive management process for the control of DCCOs in multiple colonies in Michigan. Comparisons of model predictions with observations of changes in DCCO numbers under management measures implemented from 2004 to 2012 suggested that our relatively simple model was able to accurately reconstruct past DCCO population dynamics. These comparisons helped discriminate among alternative parameterizations of demographic processes that were poorly known, especially site fidelity. Using sensitivity analysis, we also identified remaining critical uncertainties (mainly in the spatial distributions of fish vs. DCCO feeding areas) that can be used to prioritize future research and monitoring needs. Model forecasts suggested that continuation of existing control efforts would be sufficient to achieve long-term DCCO control targets in Michigan and that DCCO control may be necessary to achieve management goals for some DCCO-impacted fisheries in the state. Finally, our model can be extended by accounting for parametric or ecological uncertainty and including more complex assumptions on DCCO–fish interactions as part of the adaptive management process.