Tipping Points in Ecological Dynamics

Posted on July 13, 2012 by

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Potato_beetle_larvae

This post is from Dr John Bissell, a physicist researching tipping points in mathematical systems for the project.

In a conference that had largely focused on `tipping points’ in human society, especially those involving the spread of `buzzwords’, `innovation’ and `trends’, Prof Richard Law‘s talk on ecological dynamics (for those who might not have a clue as to what ecological dynamics means this rather humorous rap might help) acted as an important reminder of the role `tipping points’ might play in natural systems.

Perhaps the most classic–if not defining–example of a `tipping point’ is the fold bifurcation, and Law began his discussion here. Broadly speaking, fold bifurcations occur when changes in a system’s underlying parameters alter the number of its steady-states (solutions to the system that stay constant over time), for example, if the prevailing steady-state is destroyed, then the whole system may need to rapidly reconfigure to a new and often quite different equilibrium. These kinds of catastrophic transitions can be particularly important because they tend to exhibit what’s called hysteresis. Indeed, once `tipped’, large reverse changes to the governing parameters may be needed to return a system to its original steady-state. Law illustrated some transitions of this kind in terms of both desertification of scrubland following grazing by cattle, and the collapse of fish stocks due to over-fishing.

Another `tipping point’ mechanism in ecological systems is the onset of chaos, which Law described using an example taken from the population dynamics of the Colorado potato beetle. In this case, small modifications to the survival rate of beetle larvae can lead to otherwise stable numbers of adult beetles oscillating erratically between relatively small populations and sudden large outbreaks. This kind of chaotic dynamic is notoriously difficult to predict.

From Law’s discussion it seems that ecological systems can not only exhibit `tipping point’ dynamics, but that such behaviour may have significant implications for our understanding of the natural world. However, as Law pointed out in the conclusion to his talk, the evidence for `tipping-points’ is subject to ongoing debate, and warning signals of their onset are difficult to quantify. Nevertheless, areas of scientific uncertainty are often those which best lend themselves to further scrutiny, and I look forward to hearing of, and possibly participating in, future researches on the ecological `tipping-point’ theme.

Dr Richard Law’s slides from his presentation at the conference are available here.

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