Examples (in addition to the LPA models and the chaos experiment) given by Henson et al. (2003b) show how temporal patterns from both mean (continuous state space) and mode (lattice state space) models are evident in realizations of a stochastic model.
Notice that from this point of view it is not so appropriate to inquire whether or not a specific time series of ecological data has a particular dynamic predicted by a deterministic model, and thus to identify the time series with some type of asymptotic attractor (equilibrium, limit cycle, chaos, etc.). Instead, one expects to observe intermittent episodes of various kinds of patterns, attractor and transient, from perhaps more than one deterministic skeleton. If one expects to see, and only looks for, deterministic attractor patterns, then the modeling exercise used to study the data might be judged a failure when in fact it is very much a success - a success because it can, using an expanded analysis as described above, successfully explain the observed temporal patterns.
For example, suppose one is looking for evidence of chaotic dynamics in time series data. How reliable are conclusions (pro or con) obtained from techniques and diagnostics (e. g., Lyapunov exponents) that are based on the assumption that the data is on an attractor (with some noise, of course), when, in fact, the dynamics might exhibit a stochastic "dance" of attractors, saddles, and transients (Dennis et al. 2003)? A chaotic attractor could be a role player - in this "dance" - and the fact be overlooked. If we found this to be so in the controlled environment and accurately censused populations cultured in our laboratory, then we would expect it to be so, perhaps even more prominently, in field situations.
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