Effects of stochasticity on the length and behaviour of ecological transients

Author:

Hastings Alan12ORCID,Abbott Karen C.3,Cuddington Kim4,Francis Tessa B.5,Lai Ying-Cheng6ORCID,Morozov Andrew78ORCID,Petrovskii Sergei79,Zeeman Mary Lou10

Affiliation:

1. Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA

2. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

3. Department of Biology, Case Western Reserve University, Cleveland, OH 44106, USA

4. Department of Biology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

5. Puget Sound Institute, University of Washington Tacoma, Tacoma, WA 98421, USA

6. School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA

7. School of Mathematics and Actuarial Science, University of Leicester, Leicester LE1 7RH, UK

8. Institute of Ecology and Evolution, Russian Academy of Sciences, Leninsky pr. 33, Moscow 117071, Russia

9. Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russia

10. Department of Mathematics, Bowdoin College, Brunswick, ME 04011, USA

Abstract

There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system’s transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.

Funder

National Science Foundation

Publisher

The Royal Society

Subject

Biomedical Engineering,Biochemistry,Biomaterials,Bioengineering,Biophysics,Biotechnology

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