When is a pattern a pattern?

This week I received my copy of 'Patterns of Land Degradation in Drylands: Understanding Self-Organised Ecogeomorphic Systems' which I contributed to after participating at a workshop in Potsdam, Germany. It's a well produced book and as I was flicking through it I came across one of the pieces I wrote. Rather than just leave it hidden away on pages 60 - 61 in the book I thought I'd reproduce it here. It's less than 500 words and to the point. Just right for a blog post.

"In science, patterns are observations of any non-random structure. In ecology for example, a pattern has long been understood as the “structure which results from the distributions of organisms in, or from, their interactions with their environments” (Hutchinson 1953, p.3, also see Watt 1947, Greig-Smith 1979). However, when identifying patterns in nature, scientists more precisely mean the identification of patterns in data about nature. Important considerations for identifying patterns, therefore, are the means by which data were collected, and most importantly the scales of measurement used to collect data. In particular, two components of scale – grain and extent – are important in determining whether a pattern is identified. Grain is the resolution of measurement (i.e. the smallest unit of measurement at which objects or states can be distinguished), whereas extent is the full scope of observation or total range over which measurements are made. As examples, different spatial patterns will be detectable in maps of vegetation configuration in semi-arid areas depending on the grain and extent of the maps (e.g. compare Figures 3 and 6 in Barbier et al. 2006), and different temporal patterns will be detectable in storm hydrographs depending on the resolution and duration of measurement (e.g. compare drainage for 10 minute intervals with full 80 minute duration, and observed drainage with simulated drainage, in Figure 5 of Mueller et al. 2007). In other circumstances, observed structures may be described as being ‘scale-free’. These structures lack a characteristic length scale and have the same properties across any grain and extent of measurement (e.g. power-law distributions of vegetation patch sizes; Kéfi et al. 2007). These scale-free structures can also be considered to be patterns.

Because patterns are non-random, they have the potential to provide information. In natural science this information is usually understood as being about the processes that caused the pattern. Thus, identifying patterns is useful because they can be used to investigate processes (Levin 1992). Processes are typically assumed to act at a different scale from the patterns they produce, with patterns either emerging from processes at smaller scales (‘bottom-up’ processes) or imposed by constraints at larger scales (‘top-down’ processes). It is also important to consider the reciprocal effects of patterns on processes (Turner 1989). For example, the field of landscape ecology has placed an emphasis on the quantification of spatial pattern using pattern metrics (e.g. McGarigal 2006) and shown how the history of previous ecological processes can increase the strength and extent of spatial pattern (Peterson 2002). The ‘pattern-oriented modelling’ (POM) approach has been developed to use models to help decode the information present in patterns to better understand processes (Wiegand et al. 2003, Grimm et al. 2005). The POM approach iteratively compares empirical and model-output patterns at multiple scales and levels of organization and for multiple models to identify most appropriate models. Approaches like POM, which place pattern at the centre of scientific investigation, are vital for improving understanding about physical processes."

References

• Barbier N, Couteron P, Lejoly J et al (2006) Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems. J of Ecol 94:537-547
  Greig-Smith P (1979) Pattern in vegetation. J of Ecol 67: 755-779
  
• Grimm V, Revilla E, Berger U et al. (2005) Pattern-oriented modeling of agent-based complex systems: Lessons from ecology. Science 310:987-991
  
• Hutchinson GE (1953) The concept of pattern in ecology. Proc of the Acad of Nat Sci of Philadelphia 105:1-12
  
• Kéfi S, Rietkerk M, Alados, CL et al (2007) Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449:213-217
  
• Levin SA (1992) The problem of pattern and scale in ecology: The Robert H. MacArthur award lecture. Ecology 73(6):1943-1967
  
• McGarigal K (2006) Landscape pattern metrics. In: El-Shaarawi AH and Piegorsch WW (eds) Encyclopedia of Environmetrics. Wiley: Chichester, UK
  
• Mueller EN, Wainright J, Parsons, AJ (2007) Impact of connectivity on the modeling of overland flow within semiarid shrubland environments. Water Res Res 43:W09412
  
• Peterson GD (2002) Contagious disturbance, ecological memory, and the emergence of landscape pattern. Ecosystems 5:329-338
  
• Turner MG (1989) Landscape ecology: The effect of pattern on process. Ann Rev of Ecol and Syst 20:171-197
  
• Watt, AS (1947) Pattern and process in the plant community. J of Ecol 35:1-22
  
• Wiegand T, Jeltsch F, Hanski I et al (2003) Using pattern-oriented modeling for revealing hidden information: A key for reconciling ecological theory and application. Oikos 100:209-222
  

Citation
Jeltsch, F., Millington, J.D.A., et al. (2014) Resilience, self-organization, complexity and pattern formation In: Mueller, E.N., Wainwright, J., Parsons, A.J. and Turnbull, L. (Eds.) Patterns of Land Degradation in Drylands. Springer, pp. 55-84.