Extinction thresholds: insights from simple models

There are two types of deterministic extinction thresholds: demographic thresholds such as the Allee effect, and parametric thresholds such as a critical effective colonization rate or a minimum amount of available habitat for metapopulation persistence. I introduce briefly both types of thresholds. First, I discuss the Allee effect in the context of eradication strategies of alien species. Then, I consider an example of parametric threshold: the critical amount of suitable habitat below which a metapopulation goes deterministically extinct. I review how this spatial threshold changes in relation to the level of spatial detail and the complexity of the food web. Since classical metapopulation models assume an infinite number of patches, I proceed by considering how the extinction threshold is affected by environmental variability acting on a small number of patches. Finally, I consider recent work suggesting that if the network of connectivity among patches is not random but highly heterogeneous, the extinction threshold may disappear.