Anticipating Population Extinction in Ecological and Epidemiological Systems

Posted on: September 27, 2017

WAKE FOREST UNIVERSITY
DEPARTMENT OF MATHEMATICS

Presents

Suzanne M. O’Regan, PhD
Department of Mathematics
North Carolina A&T State University

 Thursday, October 5, 2017
Manchester Hall, Room 020 – 11:00am

“Anticipating Population Extinction in Ecological and Epidemiological Systems”

Many ecological systems exhibit critical transitions.  Bifurcations, small smooth changes in underlying drivers that induce sudden shifts in system behavior, are a mechanism for critical transitions that are of considerable interest. A bifurcation of a system may be anticipated because prior to reaching the dynamical threshold, the system gradually loses stability (‘critical slowing down’). Signatures of critical slowing down have been detected from temporal and spatial data from various ecological systems, such as lake ecosystems, and experimental microcosms. Anticipating collapse of vulnerable populations and documenting progress in infectious disease elimination are important applications for the theory of critical transitions. In this talk, I consider two case studies of population extinction from ecology and epidemiology: malaria elimination, and a metapopulation on the verge of collapse. What these case studies have in common is that both may be described by a trans critical bifurcation. I will consider stochastic models that are slowly forced through a trans critical bifurcation via gradually changing model parameters. I will discuss how I derived expressions for the behavior of candidate indicator statistics, including the autocorrelation coefficient, variance, and coefficient of variation.  I will additionally discuss the results of simulation studies to test the performance of each summary statistic as an early warning system of population extinction. The results suggest that extinction may be foreshadowed by characteristic temporal patterns in population.

Host: Jason Parsley, parslerj@wfu.edu