History-dependent patterns of whole ecosystems

Spatial patterns at the landscape scale have been documented in a wide variety of ecosystems across many parts of the world. Mathematical models have played an important role in understanding the causes of these patterns, and their implications for ecosystem change as environmental parameters vary. Preliminary results from simulation studies suggest the possibility of hysteresis, meaning that the wavelength and other properties of the pattern will vary in a history-dependent manner. This paper presents a detailed study of this phenomenon for two established models of landscape-scale patterns: the model of Klausmeier (Science 284 (1999) 1826–1828) for banded vegetation in semi-arid environments, and the model of van de Koppel et al. (American Naturalist 165 (2005) E66–E77) for patterning in young mussel beds. In both cases, the author demonstrates history-dependent patterns. Moreover, he shows how a knowledge of pattern existence and stability enables a detailed understanding of this hysteresis.

► I present a detailed study of two established models of landscape-scale patterns. ► In both cases, I demonstrate history-dependent patterning. ► I show that a knowledge of pattern existence and stability enables a detailed understanding of the hysteresis.