ABSTRACT
In order to apply the concepts and tools of pattern-formation theory to specific ecological contexts we need mathematical models for these contexts. As pointed out in Section 4.1.1 PDE models are more suitable for pattern-formation studies than individual-based models, because they are more amenable to mathematical analysis. The application of continuum PDE models to discrete small populations of life forms, however, requires some attention. This question is especially relevant to strongly water-limited vegetation, which often consists of sparse patches comprising a single or a few plant individuals. In Section 9.1.1 we will argue that despite the small size of plant populations in dryland vegetation, the above-ground biomass can justifiably be regarded as a continuous variable. The next question we address in this section is how detailed should continuous-biomass models be? The discussion of this question will lead us to the next section (9.1.2) in which we describe three biomass-water feedback mechanisms capable of forming vegetation patterns, and the ways by which they can be modeled.
