DIMACS/MBI US - African BioMathematics Initiative: Advanced
Study Institute on Conservation Biology Part II
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Section I: ASI on Conservation Biology Section II: The Advanced Study Institute
In a broad sense, conservation biology is concerned with the problems of conserving genes, populations, and biological communities. As the subject has grown, so too have its links with epidemiology, economics, and the management sciences; all of which have strong mathematical underpinnings in dynamical systems, optimization, and stochastic process theory. The biological systems of concern to conservation biology are complex, and improved understanding has required increasingly quantitative approaches, leading to an urgent demand for better and more appropriate mathematical tools. At the heart of conservation biology is the problem of the optimal allocation under rigid economic and sociological constraints of scarce parcels of land, wetland, and marine environments needed to preserve extant biological communities and to provide areas for the restoration of ecosystems and reintroduction of locally extinct species.
Populations of endangered or threatened species tend to be small. Mathematical analysis of stochastic fluctuations in small populations carries some complex challenges. The idea of a "minimum viable population" (MVP) was an early idea in this direction. MVP is concerned with the probability that a population will survive for at least a certain number of years. A more general framework is "population viability analysis" (PVA), which requires methods of estimating expected time to extinction. To make PVA precise in mathematical terms, one needs to develop models of how the fate of a species depends on habitat and population structures by temporally varying, spatially explicit distributions of organisms and landscape features.
As a result of an explosive 4-fold increase in the human population over the past century, accompanied by an even larger increase in economic development, an extraordinary imperative now exists to preserve the last remnants of unique biological environments in a milieu of insufficient resources and competing uses for land. If this problem is to be addressed within a constrained optimization framework, we must first address the issue of valuation of biological diversity. Such considerations yield multiple optimization criteria, each reflecting differences in the views of the various stakeholders associated with the ecosystems under consideration. Although multicriteria decision making (MCD) is a well-developed field within operations research (OR) and related areas of economics, levels of uncertainty are often much higher in conservation problems than are standard within OR and economic modeling and new algorithms are needed that utilize stochastic optimization. Methods from mixed integer programming are relevant, as are methods of stochastic dynamic programming. But many of the problems arising here are very large and NP-hard, so that the development of appropriate and effective heuristics are needed.
To make the problem of choosing biodiversity reserves even more complicated, we need to distinguish between measures of biodiversity under "present conditions" and such measures under future conditions. Future biodiversity will depend on the management plan for a reserve. For example, we might want to institute restoration plans for a species in a reserve, to increase the values of certain important "surrogates." The problem becomes even more complex when we consider hundreds of species interacting in a given reserve, with varying surrogate values over time depending on these interactions. Clearly, reserve management then becomes an area that calls for mathematical modeling, combined with the need for computer simulation and powerful computational tools. Since biodiversity might be only one of the criteria by which we judge a land use plan, MCD seems particularly relevant to this topic.
Models for the design of ecological reserves must be developed in the context of assumptions about climate, disease, and other factors. These factors are sometimes interconnected, as for example the effect on disease of changing climatic conditions ? already noted in Africa, for example, with the presence of malaria in the highlands of Kenya where it was not present before. Design of a healthy ecological reserve will make it relatively invulnerable to the spread of disease. Models of reserve design that minimize vulnerabilities to diseases of both animals and plants ? and the interconnection between spread of those diseases and the overall biodiversity of the reserve ? need to be developed and will present significant modeling challenges to mathematical epidemiologists and ecologists.
Reserve design is just one of a suite of issues that must be dealt with in conservation biology. The dynamics of populations in structured environments, the overall effects of climate change and land use and economic development, the potential spread of disease between wild and domestic populations, the impact of invasive species, and even rapid evolutionary change brought about by the activities of humans are all subjects with rich mathematical literatures, and of profound importance for conservation biology. Issues of conservation genetics are also central, and include genetic models and notions of genetic diversity.
Applications Requested from Interested Graduate Students
The ASI is open to three types of participants:
The Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) and the Mathematical Biosciences Institute (MBI) are holding a one week Advanced Study Institute (ASI) that will bring together US and African graduate students and introduce them to basic theoretical concepts in population demography and genetics; stochastic dynamic modeling of small populations, focusing on invasion and extinction analyses using ideas from evolutionarily stable strategy theory and risk analysis; optimization and MCD methods of analysis; economic modeling; models of plant and animal disease spread and the impact of climate change on disease; and case studies from the African environment, including both terrestrial and marine examples.
The ASI will provide a basic introduction to mathematical modeling in conservation biology at a fast pace. This is designed to allow students who have never taken a course in the mathematics of conservation biology to acquire the necessary preparatory background they need. As time permits, more advanced material will be introducedl. Students with prior exposure to conservation biology are encouraged to apply as well, and we will provide more rapid introduction to advanced topics. Various modeling paradigms will be discussed, as well as introductory lectures on related topics. There will be a number of hands-on and computer exercises together with group projects to reinforce and extend the various concepts covered. Participants are expected to continue the research project they begin during the institute or begin work on a new project when they return to their home institution, under the supervision of a mentor.
A student who does not require funding or only partial funding should so indicate on their application. They will be accepted if there is space and they are qualified.
For returning students, the goal is to continue research on topics that arose at the SA ASI and workshop, and make progress toward a completed project and a paper writing it up. Send an email to Holly Gaff HGaff@odu.edu addressing the following:
The institute is open to graduate students from all areas of science (genetics, bioinformatics, computational biology/chemistry, etc.) and mathematics, statistics, computer science, operations research. Students will be selected based on their applications, letter of recommendation, and letter of commitment from a mentor to support the continuation of the research project begun during the institute or a new project begun afterward. (The mentor and recommender can be the same.) Students selected for the institute will primarily be from Kenya and neighboring countries, with a small number of slots for US students.
Additional Information: See the institute website http://dimacs.rutgers.edu/Workshops/ASICBII/ to:
Send additional questions to firstname.lastname@example.org, or telephone at (732) 445-5930.
This is part of the DIMACS/MBI US - African BioMathematics Initiative Project.