From robustness to resilience: A network Price identity approach

We model a closed-loop network of agents distributed among subnetworks and study the sustainability of network structures in presence of random perturbations. The model outcomes show that the stability of compartmentalized networks built on uniform operators depends on perturbations on between-subnetwork coupling, while the stability of networks built on mutation operators depends on their assimilation capacity. Through the study of eigenvalues of the Laplacian, we succeed in measuring the degree of network robustness and resilience. Our results also permit to situate the Price theorem, both in its standard and expanded forms, in the context of network evolutionary variational identity.     

Optimal harvesting of a logistic population in an environment with stochastic jumps

Dynamic programming is employed to examine the effects of large, sudden changes in population size on the optimal harvest strategy of an exploited resource population. These changes are either adverse or favorable and are assumed to occur at times of events of a Poisson process. The amplitude of these jumps is assumed to be density independent. In between the jumps the population is assumed to grow logistically. The Bellman equation for the optimal discounted present value is solved numerically and the optimal feedback control computed for the random jump model. The results are compared to the corresponding results for the quasi-deterministic approximation. In addition, the sensitivity of the results to the discount rate, the total jump rate and the quadratic cost factor is investigated. The optimal results are most strongly sensitive to the rate of stochastic jumps and to the quadratic cost factor to a lesser extent when the deterministic bioeconomic parameters are taken from aggregate antarctic pelagic whaling data.Research supported in part by the National Science Foundation under grants MCS 81-01698 and MCS 83-00562.     

Marine reserve effects on fishery profit

Some studies suggest that fishery yields can be higher with reserves than under conventional management. However, the economic performance of fisheries depends on economic profit, not fish yield. The predictions of higher yields with reserves rely on intensive fishing pressures between reserves; the exorbitant costs of harvesting low-density populations erode profits. We incorporated this effect into a bioeconomic model to evaluate the economic performance of reserve-based management. Our results indicate that reserves can still benefit fisheries, even those targeting species that are expensive to harvest. However, in contrast to studies focused on yield, only a moderate proportion of the coast in reserves (with moderate harvest pressures outside reserves) is required to maximize profit. Furthermore, reserve area and harvest intensity can be traded off with little impact on profits, allowing for management flexibility while still providing higher profit than attainable under conventional management.     

Optimal control of population recovery – the role of economic restoration threshold

A variety of ecological systems around the world have been damaged in recent years, either by natural factors such as invasive species, storms and global change or by direct human activities such as overfishing and water pollution. Restoration of these systems to provide ecosystem services entails significant economic benefits. Thus, choosing how and when to restore in an optimal fashion is important, but has not been well studied. Here we examine a general model where population growth can be induced or accelerated by investing in active restoration. We show that the most cost‐effective method to restore an ecosystem dictates investment until the population approaches an ‘economic restoration threshold’, a density above which the ecosystem should be left to recover naturally. Therefore, determining this threshold is a key general approach for guiding efficient restoration management, and we demonstrate how to calculate this threshold for both deterministic and stochastic ecosystems.     

Triple benefits from spatial resource management

Standard fishery management models suggest that regulations designed to produce maximum rent should reduce effort – and thus employment – from its open-access level. Using a simple diffusion model, we show that the opposite can be true when the spatial distribution of effort, as well as the total amount of effort, can be controlled. Under certain ecological and economic circumstances that we describe, optimal spatial management can produce “triple benefits” compared to open access: an increase in rent, an increase in standing stock, and an increase in employment. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Marine reserves and optimal harvesting

Advocates of no‐take marine reserves emphasize their conservation benefits. Critics counter that reserves would decrease fisheries yield. Analysis of a spatially explicit harvesting model, however, shows that no‐take marine reserves are always part of an optimal harvest designed to maximize yield. The optimal harvest generates a spatial source–sink structure with source populations placed in reserves. The sizes and locations of the optimal reserves depend on a dimensionless length parameter. For small values of this parameter, the maximum yield is obtained by placing a large reserve in the centre of the habitat. For large values of this parameter, the optimal harvesting strategy is a spatial ‘chattering control’ with infinite sequences of reserves alternating with areas of intense fishing. Such a chattering strategy would be impossible to actually implement, but in these cases an approximate yet practicable policy, utilizing a small number of reserves, can be constructed.