Workshop 3: Sustainable Management of Living Natural Resources
I will give an overview of mathematical challenges that arise in developing management strategies for natural systems. The emphasis will be on issues that arise from the nature of the biological systems, including, but not limited to, limited data, nonlinearities, stochasticity, constraints that arise from biological issues, and time scales. I will illustrate the concepts by starting with some of the best studied examples, which come from fisheries, then discuss issues of invasive species, and finally move on to lesser studied and more poorly specified areas. The goal of the talk will be to set the stage for the workshop and initial discussions.
Conservation organizations often rely on incentive payments to private landowners to "buy" conservation benefits. In evaluating the efficiency of such programs, conservation biologists have often assumed contracts can be acquired at landowners' willingness-to-accept. Were this possible it would represent something of a best possible outcome for conservation from a negotiation with private landowners. Drawing on game theory, optimization methods and agent-based simulations, I will examine how conservation outcomes would be affected if landowners instead were to hold out for payments over and above their willingness-to-accept to gain some surplus from the transaction.
Biological invasions are spatial-dynamic processes â€” they unfold over space and time, driven by a combination of reproduction and dispersal. Consequently, their management requires weighing not only how much and when to invest in control to reduce their damages, but where controls should be applied. Furthermore, invasions unfold in landscapes comprising numerous, independently managed properties such that their spread depends on the control choices of many landowners. Here I present three bioeconomic studies that address these complexities of bioinvasion management. They examine 1) optimal surveillance design for early detection of invasions, 2) optimal spatial control strategies, and 3) individual and cooperative invasion management.
Disturbances are ubiquitous in nature, and are believed to be strong drivers of both ecological diversity and species invasion. The need to address the impacts of environmental disturbance is increasingly urgent in the face of anthropogenic alterations to existing disturbance regimes. I will discuss how an ecological niche-based theory of disturbance, encompassing five interacting aspects (frequency, intensity, duration, extent and timing), can be used to study a wide range of issues related to disturbance regimes and their effects on biological systems. This conceptual framework allows an integrated study of disturbance across levels of biological organization: from the individual through to the population, the community and entire ecosystems. Ongoing theoretical and empirical research not only informs us about when disturbances are likely to pose a problem, but also lets us assess how we can manipulate disturbances to achieve desired management outcomes. As disturbances of many types are increasingly used to manage ecosystems, this approach therefore can be applied to a wide range of management issues. Managers and policy makers need to be able to make reliable predictions â€” only if we can anticipate them, can we avoid or ameliorate the impacts of such disturbances.
In this talk I will focus on the role of vector dynamics and its ecological and economic implications for disease control. Genetic methods of controlling insects and agricultural pests have advanced in recent years but their economic benefits remain largely unexplored. By integrating epidemiological and economic approaches we can build sensible mathematical models for exploring the implications of vector control on levels of disease burden. In this talk I will illustrate the ways that we have approached this for understanding Dengue dynamics and some of the subtle ways that understanding human movement and flows are important for implementing disease invention strategies.
Management of stochastic renewable natural resources occurs in the presence of various forms of uncertainty (e.g., parametric, model, and state).While the implications of different types of uncertainty for management have been carefully analyzed individually, it is not clear when each different type of uncertainty is relatively more or less important for the resource manager.In this talk, I will attempt to define three different forms of uncertainty.I will then discuss some of the challenges of comparing the value of learning about these different uncertainties within the same resource management problem. I will then describe and simulate one candidate method for comparing two different types of uncertainty.