Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, November 1, 2021 - 12:00 to 12:50

Location:

Kidd 280 or contact Christine Escher for a link.

Guest Speaker:

Institution:

Hatfield Marine Science Center

Abstract:

Understanding and predicting critical transitions in ecological systems is of ever-increasing importance in the context of populations under stress due to human resource usage and a rapidly changing global climate. Understanding critical transitions in spatially explicit ecological systems adds further complication due to the high dimensionality of these systems and their complicated spatio-temporal dynamics. Here, we explore changes in population distribution patterns during a critical transition (an extinction event) using computational topology. Computational topology allows us to quantify changes in the population distribution patterns and reduce dimensionality by characterizing the patterns via two metrics, B0 and B1, the first and second Betti numbers. B0 and B1 count the number of ``connected components" and ``holes" in a two-dimensional population distribution pattern, respectively. Population distributions are created via a simple coupled patch model with Ricker map growth and nearest neighbors dispersal on a two-dimensional lattice. We find that the route to extinction critically depends on two factors; the dispersal rate d and the rate of parameter drift. Depending on d and drift rate, we witness two characteristic routes to extinction. These paths to extinction are easily topologically distinguishable, so categorization can be automated. We envision this work as a helpful addition to the critical transitions prediction toolbox, particularly because computational topology provides early warning signals for chaotic dynamical systems where traditional statistical early warning signals would fail.

Host: