Table 1.

Three categories of ecosystems where density-dependent aggregation of a conserved biotic or abiotic species can trigger the formation of spatial patterns

Ecosystem	Variables	Fluxes	Feedbacks
Grazing systems	$V$: Foraging herbivores $U$: Grazing herbivores	A: Herbivores switch to foraging B: Herbivores switch to grazing	1: Grazing herbivores reduce plant biomass. Less attractive high biomass causes herbivores to stop grazing and start foraging. 2: Grazing herbivores reduce plant biomass. More attractive low biomass causes herbivores to stop foraging and start grazing.
Biogeomorphic systems	$V$: Aeolian/suspended sand $U$: Deposited sand	A: Erosion B: Deposition	1: Elevated areas enhance productivity. Plants reduce erosion. 2: Elevated areas enhance productivity. Plants enhance deposition.
Oligotrophic ecosystems	$V$: Dissolved resource $U$: Sessile species	A: Release of resource through mortality B: Uptake, trapping, and demobilization of resource	1: $U\stackrel{-}{\to }A$ Reduced release of resource with increasing biomass of sessile species. 2: $U\stackrel{+}{\to }B$ Enhanced uptake, trapping, and demobilization of resource with increasing biomass of sessile species.

Variables, fluxes, and feedbacks refer to Fig. 2B. Variables $U$ and $V$ represent the less mobile and highly mobile state of the conserved species. $A$ and $B$ are the fluxes between $U$ and $V$. Feedbacks 1 and/or 2 depicted in Fig. 2B are established through the interaction between $U$ and a sessile species, as depicted in the right-hand column. In nutrient-poor ecosystems, $U$represents the ecosystem engineer, and the feedbacks result from facilitation (decreased mortality). Examples of the listed feedbacks are discussed in the main text.