Characterizing Ecological Transitions in Systems with Regularity

Humans depend on ecological systems in many ways, from their ability to provide water and food to their amenability for habitation. The response of an ecological system to environmental changes can shape the future of the goods and services associated with the ecosystem. Important examples include desertification and changes from high to low productivity regimes in fisheries, among others. Modeling the ecosystem state and predicting future shifts to other states requires the identification of measurable quantities that represent the state of the ecosystem. However, when the ecosystem shows spatial structure (for example, vegetation aggregates separated by bare soil, typical of semi-arid ecosystems), standard choices to represent the ecosystem state lead to erroneous predictions, unable to capture features shown by these systems across space and time. This project will combine concepts and techniques from mathematics and statistical physics to provide a novel theoretical framework able to describe reliably state shifts occurring in structured ecological systems. Such a framework will enable theoretical tools to diagnose ecosystem health and resilience as environmental conditions change and, therefore, facilitate preparedness, such as conservation strategies, against ecologically and economically costly shifts. Because aggregation occurs frequently in nature, the results of this project will be applicable to a wide variety of systems of socio-ecological importance (for instance, vegetation in ecosystems close to desertification). The project includes training through research involvement for junior researchers, to help develop the next generation of scientists.

Transitions between different states of a focal ecosystem often can be described with a single order parameter (observable representing the state of the system) and a single control parameter (factor whose change triggers the transition). For a given value of the latter, the order parameter enables the calculation of the stability landscape, a manifold that reveals key information such as potential ecological states, their basins of attraction, and the possibility of alternative stable states. When an ecosystem shows spatial regularity, however, standard approaches yield misleading results: a system-averaged order parameter neglects the underlying spatial patterns, and using the spatially-explicit population density as order parameter produces a stability landscape that erroneously detects the empty space between population aggregates as signs of extinction (and possibility of alternative stable states) even for healthy ecosystems. This project aims to offer the first framework able to represent reliably, for any dynamical system that shows spatial regularity and undergoes a phase transition, the key interactions between population dynamics, formation of non-trivial spatial aggregates, and changes in resilience occurring around the transition. The investigator will use existing theoretical models to identify an associated transition and the main features affected by it and aims to combine them in a single order parameter able to describe holistically the transition. The project involves innovative combination and development of concepts and tools associated with statistical physics and bifurcation theory (e.g. stability and perturbative analyses, numerical renormalization, Fourier transforms), typically used independently in the study of phase transitions or pattern detection. The results of this project will improve predictions and early warning signal tools for transitions in systems that show regularity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.