Applications of Fractal Theory to Ecology

Abstract

Forms with fractal geometric properties are found in ecosystems. Fractal geometry seems to be a basic space occupation property of biological systems. The surface area of the contact zones between interacting parts of an ecosystem is considerably increased if it has a fractal geometry, resulting in enhanced fluxes of energy, matter, and information. The interface structure often develops into a particular type of ecosystem, becoming an “interpenetration volume” that manages the fluxes and exchanges. The physical environment of ecosystems may also have a fractal morphology. This is found for instance in the granulometry of soils and sediments, and in the phenomenon of turbulence. On the other hand, organisms often display patchiness in space, which may be a fractal if patches are hierarchically nested.

A statistical fractal geometry appears along trips and trajectories of mobile organisms. This strategy diversifies the contact points between organisms and a heteregeneous environment, or among individuals in predator-prey systems. Finally, fractals appear in abstract representational spaces, such as the one in which strange attractors are drawn in population dynamics, or in the case of species diversity. The “evenness” component of diversity seems to be a true fractal dimension of community structure. Species distributions, at least at some scales of observation, often fit a Mandelbrot model fr = f ₀ (r + β)^-γ, where fr is the relative frequency of the species of rank r, and 1/γ is the fractal dimension of the distribution of individuals among species.

Fractal theory is likely to become of fundamental interest for global analysis and modelling of ecosystems, in the future.