In an era of invasive species, climate change, and rapid habitat loss, ecological systems may never experience a “stable equilibrium”, according to Kim Cuddington, a professor in Waterloo’s Department of Biology. Instead, the system may be experiencing temporary behaviour, a transient, which differs markedly from what we predict in the long term.
“Transient behaviours are ubiquitous in ecology.” says Cuddington. “We see them in every observation of population size or ecosystem state.
She and her international colleagues have used dynamical systems theory to understand a number of questions in ecology, including population dynamics, ecosystem regime shifts and the role of environmental variation, over ecologically relevant timescales.
Previous researchers have often treated sudden changes to an ecological system as though they are driven by environmental change. The existence of long transients means, however, that an abrupt change can occur for a number of reasons, and even for no reason at all.
Cuddington and her colleagues have been able to classify observations of transient dynamics in ecology and link them to possible underlying causes. Their review and mathematical analysis of transient dynamics - a first for the field of ecology - appears this month in the journal Science.
Take for example population dynamics - whether it’s for coral reefs, fish, zooplankton or budworms - in a simple model we can find two types of behaviour: an asymptotic stable equilibrium, also known as the carrying capacity, and the temporary behaviour that lasts until the population reaches the equilibrium.
Where it gets tricky for ecologists is when transient phases become extremely long-lived: Either the population never reaches an equilibrium (even after thousands of years), or there is a disturbance, and the population returns to exhibiting transient behaviour.
“How do you know when you’re in a period of transient dynamics and how long will it last?” says Cuddington. “It’s easy under to think under certain circumstances the phenomenon you’re tracking is stable, when it’s actually not.”
The authors argue that by classifying transient dynamic patterns, and even viewing them over different timescales, it provides a framework that ecologists can use to analyze increasingly complex problems in the field, including extinction and biological invasion.
“Our goal is to be able to use this approach to start unraveling the forces behind the major drivers of ecological change,” Cuddington says. “Uncovering the existence of long transients can reveal that we were in mistaken about the forces we believed were having an impact
Authors on the paper include Alan Hastings (University of California, Davis), Karen Abbot (Case Western Reserve University, Cleveland, Ohio) , Tessa Francis (University of Washington, Tacoma), Gabriel Gellner (Colorado State University), Ying-Cheng Lai (Arizona State University), Andrew Morozov and Sergei Petroveskii (University of Leicester, UK), Katherine Seranton (University of California, Los Angeles) and Mary Lou Zeeman (Bowdoin College, Brunswick, Maine).