  The theory of alternative stable states and tipping points has garnered a lot
of attention in the last decades. It predicts potential critical transitions
from one ecosystem state to a completely different state under increasing
environmental stress. However, typically ecosystem models that predict tipping
do not resolve space explicitly. As ecosystems are inherently spatial, it is
important to understand the effects of incorporating spatial processes in
models, and how those insights translate to the real world. Moreover, spatial
ecosystem structures, such as vegetation patterns, are important in the
prediction of ecosystem response in the face of environmental change. Models
and observations from real savanna ecosystems and drylands have suggested that
they may exhibit both tipping behavior as well as spatial pattern formation.
Hence, in this paper, we use mathematical models of humid savannas and drylands
to illustrate several pattern formation phenomena that may arise when
incorporating spatial dynamics in models that exhibit tipping without resolving
space. We argue that such mechanisms challenge the notion of large scale
critical transitions in response to global change and reveal a more resilient
nature of spatial ecosystems.
