HOT TOPICS IN SCIENCE AND TECHNOLOGY - Tipping in ecological systems under external forcing
Lecture by Prof. Syamal K. Dana
Centre for Mathematical Biology and Ecology,
Department of Mathematics, Jadavpur University,
Kolkata 700032, India
Tipping in ecological systems under external forcing
Abstract: In nature, a parameter of a system is time varying. When a parameter is assumed
varying with a rate, a system shows hard or slow transition from an existing stable state to a
qualitatively different stable state against the rate induced parameter change. This behaviour is
known as tipping. Such transitions may occur immediately at the bifurcation point, called as
hard transition. Alternatively, the transition may occur at a delayed time, called as slow
transition. If the rate of change of the parameter is larger than a critical value, such transitions
may occur even before reaching the bifurcation point. Noise can also induce such a transition
earlier than the bifurcation point. Examples of such tipping have been observed in many natural
systems, namely, Amazon rain forest, Atlantic meridional overturning circulation (AMOC),
green land ice cap, and Indian monsoon, due to global warming, to mention a few.
I introduce the different processes of tipping in model systems, first, then share our
experiences in ecological systems. First of all, I discuss about tipping in a Spruce budworm
population model. We address a question how the system changes from high population to a
desirable low population of insects when the carrying capacity of the ecological system is time
varying. Next, we deal with three bistable ecological models, equilibrium and nonequilibrium,
where partial tipping occurs against periodic environmental variability. In partial tipping, it
occurs only for a fraction or an ensemble of initial states of the systems, not for any arbitrary
choice of initial states of the basin of the system. Here, we determine the probability of tipping
against the rate parameter (environmental variability).