Any behavior of any model, including transient behavior, reflects the values of the parameters. The effect of changes in those parameters (the perturbation problem) is important for many reasons, especially in conservation and management. Policy decisions must often be based on dynamics over short time scales, on which the relevance of asymptotic dynamics is uncertain. This makes the perturbation analysis of transient behavior an important problem.
Results/Conclusions
I will present a general solution to the perturbation problem for transient behavior. The solution is based on a dynamic model for the sensitivity or elasticity of a chosen index of population behavior. This dynamic model is written in terms of matrix calculus and is solved in parallel with the model for the population itself. Thus the same calculations that project the transient dynamics also project their sensitivity to parameter changes. I will show how to apply the approach to time-invariant or time-varying, deterministic or stochastic, linear or nonlinear models. Applications of these analyses have barely begun, but examples to be presented here demonstrate that transient behavior is as amenable as asymptotic behavior to a range of sensitivity and elasticity analyses.