Table 1 Key concepts used in this paper.

See (70, 71) for further elaboration of ideas from dynamical systems.

TermDefinition
Asymptotic dynamicsThe behavior that a system will eventually exhibit and then retain indefinitely if unperturbed (i.e., dynamics that are not
transient). Examples would include equilibria or limit cycles of predator-prey systems.
BifurcationA qualitative change in a system’s asymptotic dynamics as a parameter is varied, caused by gain, loss, or change in
stability of an invariant set. Examples are crises, Hopf bifurcations, and saddle-node bifurcations.
Regime shiftA qualitative change in a system’s dynamics after a long period of apparent stasis. Can occur at tipping points where a bifurcation
is crossed, or at a transition from transient dynamics to asymptotic dynamics (or from one transient to another).
Tipping pointThe conditions (or value of a changing parameter) at which a bifurcation occurs, producing qualitatively different asymptotic
behavior.
TransientNonasymptotic dynamics.
Long transientNonasymptotic dynamics that persist over ecologically relevant time scales of roughly dozens of generations (or longer).