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.
Acknowledgements
We congratulate Jim on the occasion of his 80th 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
Disclosure statement
No potential conflict of interest was reported by the author(s).