Robust and Optimal Control for Disturbed Population Dynamics
Lloyd, Stephanie Jane
Thesis or dissertation
University of Exeter
We use control theory to explore management of populations affected by disturbances and uncertainty. We consider five related topics. Chapter 2 uses linear programming to find optimal translocation strategies between wild and captive populations. To allow comparison of the solutions we classify the optimal strategy depending on which stage classes are kept in captivity. We find depending on species, that different stages are targeted when the resource available is limited. In Chapter 3 we use linear programming to create management strategies for an invading population affected by disturbance. For a sinusoidal disturbance, the final population with control is bounded between a transfer function approximation and a feedback control solution. Then we assume worst case disturbance, which creates a 2-player game. In this linear programming context then it is possible that minimax < maximin. Chapter 4 considers a 2-player linear-quadratic problem and introduces the use of disturbance attenuation into ecology. Disturbance attenuation shows how a disturbance is amplified or attenuated by the system. In Chapter 5 we consider an invading population, and we explore the effect that stochasticity has on the relationship between Allee effect and population inertia needed for successful invasion. We find that for small population densities, then demographic stochasticity dramatically reduces the likelihood of invasion and survival of the resident.
PhD in Mathematics