[Coral-List] Fractal analysis and reef complexity

[Sam Purkis]

Dear Coral-List,

In response to Harry Goudge's recent posting concerning the application of 
fractal analysis to quantify habitat complexity, I have recently looked 
into the spatial complexity of reefs on Ikonos satellite imagery. Although 
at a much larger spatial scale to that relevant to fish communities, the 
methodology is likely to be transferable.

Fractal patterns have certainly been observed in the small-scale structures 
of coral (relevant papers would be Bradbury and Reichelt 1983; Basillais 
1997) and using Ikonos satellite imagery in the Arabian Gulf I observe 
behaviour in patches of different substrates types that scale with power 
laws within certain thresholds. The pattern is robust over three decades of 
magnitude both for the frequency-size distribution of patches and using the 
box-counting metric to quantify patch boundary 'wiggliness' (complexity).

To look at habitat complexity at scales relevant to reef fish, I'd start by 
recording the rugosity of the seabed through photography and then analyse 
the relief using box-counting. On the positive side, the fractal dimension 
is elegant in so far as it represents a single index of complexity. On the 
negative side though, to really say that a system is a candidate for a 
fractal, the scale-invariant behaviour must hold for numerous decades of 
magnitude and I'd say that three is really the minimum. Keep this in mind 
when deciding over which scales you'll collect your data.

Handy refs:
Basillais E (1997) Coral surfaces and fractal dimensions: a new method. C R 
Acad Sc Paris, Life Sci 320:653-657
Bradbury RH, Reichelt RE (1983) Fractal dimension of a coral reef at 
ecological scales. Mar Ecol-Prog Ser 10:169-171

All the best,

Sam

Sam Purkis Ph.D.
National Coral Reef Institute
Oceanographic Center
Nova Southeastern University
8000 N. Ocean Drive, Dania
FL 33004

Formerly: Institute of Earth Sciences, Vrije Universiteit, Amsterdam, The 
Netherlands