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Moving toward an unstable equilibrium: saddle nodes in population systems
Article first published online: 5 JAN 2002
DOI: 10.1046/j.1365-2656.1998.00194.x
British Ecological Society
1365-2656/asset/cover.gif?v=1&s=e1c445961d632cd41e33852af907c4900097559b "Journal of Animal Ecology")
Additional Information
How to Cite
Cushing, Dennis, B., Desharnais and Costantino (1998), Moving toward an unstable equilibrium: saddle nodes in population systems. Journal of Animal Ecology, 67: 298–306. doi: 10.1046/j.1365-2656.1998.00194.x
Publication History
- Issue published online: 5 JAN 2002
- Article first published online: 5 JAN 2002
- Abstract
- Cited By
Keywords:
- non-linear demographic dynamics;
- transient behaviour;
- Tribolium
1. We identify an unstable equilibrium with a two-dimensional stable manifold and a one-dimensional unstable manifold in a three-state variable (larva, pupa, adult) insect population growth model.
2. The saddle node forecasts that the time series of some initial numbers of larvae, pupae and adults are drawn closely to the unstable equilibrium before approaching the asymptotic stable attractor (a two-cycle), while the time series of other initial points are not.
3. Using two quantitative indices, we examine time series from a Tribolium experiment for evidence of the predicted saddle node. We conclude that a saddle node accounts for the transient dynamics in these data and for the differences between the transient behaviour of different replicates of the same experiment.