Mathematical Biology Seminar (cosponsored by MTBI)

F Sep 17, 3:40, PSA 104

Yang Kuang, Department of Mathematics and Statistics, Arizona State
University

TITLE:

A Stoichiometric Discrete Predator-Prey Model: Chaos and its Implications

Abstract:

In the last decade, several theoretical models based on stoichiometric
principles as well as field and laboratory experiments have shown that nutritional quality
of the prey can have dramatic and counterintuitive impact. For example, the predator can
become extinct while having plentiful prey in a completely deterministic system. Another
effect is the halt of oscillations that are ubiquitous to predator-prey systems, which happens
when bad prey quality drives the system through a saddle-node bifurcation. All the
existing models exhibiting these effects are continuous in time. However, in experiments, data are
collected on discrete time intervals and many producers in nature have non-overlapping
generations. Such scenarios call for discrete equation models. Hence we ask: can novel
stoichiometric effects arise in discrete systems? By comparing a continuous stoichiometric model to its
discrete analog, we show that stoichiometric impacts of prey quality persist in discrete
system. Moreover, not only bad prey quality can pull the system out of oscillations but
also it can halt chaotic dynamics that surfaces in the discrete system. Indeed, chaotic prey
population can lead to the extinction of the predator population.