Most ecosystems exist in a constantly changing environment. Yet, most

models for ecosystem dynamics are based on autonomous dynamical systems

and asymptotic analysis of their qualitative behaviour. While

seasonality (periodic variation) can still be cast in terms of

autonomous systems (by considering the period map), the same is not

true for directional variation, such as increasing mean temperatures or

increasing habitat destruction and fragmentation. The study of such

temporally forced systems is still very much in its infancy.

In this talk, I will present some simple population and community

models with a linear forcing in one parameter. I will describe the

phenomenon of "tracking unstable states", whereby a community can

remain near a state that would be unstable, in a temporally constant

environment. This phenomenon shows the usefulness and limitations of

bifurcation diagrams in the analysis of temporally forced systems.

The second focus of my talk will be on early warning signals and the

question of whether and how we can predict when a given community might

undergo a regime shift, i.e., a large change in state in response to a

small change in parameters.