A control theoretic approach to the conservation of migratory species

: (Alternative Format Thesis)

Abstract

More species are threatened with global extinction than ever before. It is often the case that migratory species are more at risk than sedentary species. Furthermore, migratory species are fundamental to many ecosystems as their movements link distant ecosystems, often providing large inputs of energy. Thus, the conservation of migratory species is not just crucial to their own survival but also the survival of the ecosystems that they interact with. To be effective, conservation management plans must consider the full annual cycle of migratory species. In this thesis we develop mathematical tools to aid the conservation of migratory species and aim to promote the use of control theoretic approaches in the field of ecology.

First, we detail how to construct a full annual cycle model using population projection matrices that specify the structure of the migratory network (i.e. habitats and pathways used) as well as the demographic variables that are both region- and season- specific (i.e. survival, reproduction and movement). We then develop a framework that quantifies how much different parts of the full annual cycle model contribute to the transient growth of the population, we call the resultant metrics pathway contribution metrics. Next, we provide two frameworks that may be used to evaluate how the pathway contribution metrics are impacted by perturbations to vital rates of the full annual cycle model. The pathway contribution metrics and perturbation frameworks may be used to inform the conservation of migratory species by highlighting which parts of the annual cycle are the most important to measure accurately or which parts will have the biggest impact on the growth of the population. Throughout the construction of these frameworks, we use positive difference equations, linear algebra as well as matrix calculus and ideas from control theory.

In the second part of the thesis, we develop a robust and adaptive control scheme that identifies a management strategy that ensures the persistence of a population, when there are several management strategies available, but their exact effect is uncertain. Robust and adaptive control techniques use feedback loops to determine how the control is applied and are designed to perform as intended in the presence of uncertainties and disturbances. Hence, a robust and adaptive control approach is beneficial in the setting of conserving populations as often management actions need to be implemented before models are fully parameterised. Existing adaptive control tools stabilise the zero equilibrium, which would correspond to extinction of the population in our setting. Thus, as our control scheme destabilises the zero equilibrium, it is novel in theory as well as application. We outline the key hypotheses that underpin our control scheme to allow the update laws, which use measured population data to inform the switching between strategies, to be tailored to suit the requirements of the user. Finally, we apply the control scheme to the full annual cycle model for migratory species and propose further adaptations to the update laws so that the switching process considers migratory species’ full annual cycles and their periodic nature. Numerical simulations show that, when applied to models for migratory species, the control scheme performs better when seasonal measurements are used and their periodic nature is considered in the update laws. Throughout the development of the control scheme, we use positive difference equations, linear algebra and developments from various areas of control theory, including: persistence theory, robust control and adaptive control.

Date of Award	24 Jun 2026
Original language	English
Awarding Institution	University of Bath
Supervisor	Ben Adams (Supervisor), Jane White (Supervisor) & Chris Guiver (Supervisor)