Applied Math Seminar: Wildlife Habitat Management using Optimization
3:10 pm, Neill Hall 3W
ABSTRACT: Territorial dispersers are species whose offsprings disperse away from the parents and inhabit new areas. In the typical case of the Northern Spotted Owl (NSO), the offsprings can occupy a new habitat only if it is suitable ("green") and is unoccupied by other members of the species. Hence the survival of the species depends on the availability of green habitat areas within the range of search of the offsprings. Lamberson et al. have defined a measure of the suitability of a landscape (a collection of habitat areas) for the survival of NSO called the Habitat Connectivity Index (HCI). A higher value of HCI indicates that there are more of the green habitat areas that lie close to each other. Long-term occupancy rates in each habitat area of a landscape were estimated by simulating a dynamic model of the system. The key bone of contention in the management of the habitat for the NSO is to decide which areas of the landscape should be maintained green, and which ones could be cleared (or utilized for other activities such as logging). We develop optimization models where the decision to either clear out or maintain each of a candidate set of habitat areas is represented by binary variables. The goal is to pick a limited subset of the candidate habitats that maximizes the HCI, which is a highly non-linear function. We obtain linear approximations that are as close to the original function as we want. We can solve the optimization models of arbitrary landscapes made of 125 by 75 (square) habitat patches within minutes on a standard PC. This is joint work with Bala Krishnamoorthy and David Allen as part of an ongoing Undergraduate Math Biology (UBM) project.