Capturing chaos: a multidisciplinary approach to nonlinear population dynamics

Abstract

The hypothesis of chaotic population dynamics was proposed in ecology by Robert May in the mid-1970s. At that time the idea was controversial, and it remains a fascinating and unsettled issue today. We report the results of a 20-year laboratory research programme that continued in the tradition of the pioneering ecologist Thomas Park using the Tribolium flour beetle model. We present biological evidence of complex population dynamics – including bifurcations, chaos, saddle nodes, phase switching, resonance effects, and multiple attractors – by using a low-dimensional difference equation model for Tribolium together with carefully designed, conducted, and statistically analysed experiments. The model, parameterized with data, also explains the results of historical Tribolium experiments, such as the classical competition studies of Thomas Park and his colleagues. Our research programme has inspired other studies using the Tribolium mathematical and laboratory model. This work was conducted by a multidisciplinary team, which included Jim Cushing.

KEYWORDS:

• Nonlinear dynamics
• population ecology
• Tribolium
• chaos
• stochasticity

Acknowledgements

We congratulate Jim on the occasion of his 80^th birthday and for his outstanding career. He was a key member of the ‘Beetle Team,’ a multidisciplinary collaborative research group focused on the integration of nonlinear dynamics theory, statistics, and biological experimentation. The members of the Beetle Team were Jim Cushing, R. F. Costantino, Brian Dennis, Robert A. Desharnais, Shandelle M. Henson, Aaron A. King, and Jeffrey Edmunds. We are grateful to the U.S. National Science Foundation, and the American public who support NSF through their taxes, for the opportunity to pursue our passionate desire to strengthen the empirical ties among ecology, statistics, and mathematics.

Data availability statement

All of the data from beetle team research programme are publicly available at Dryad in the Beetle Team Tribolium Data Archive: https://doi.org/10.5061/dryad.qjq2bvqmp

 Google Scholar

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The Beetle Team research programme was supported by grants from the U.S. National Science Foundation [grant numbers DMS 9206678, DMS 9306271, DMS 9319073, DMS 9616205, DMS 9625576, DMS 9973126, DMS 9981374, DMS 9981423, DMS 9981458, DMS 0210474].