Competition with Evolution in Ecology and Finance

J. C. Sprott
Department of Physics, University of Wisconsin- Madison, Madison, WI 53706, USA

(Received 9 December 2003; received in revised form 11 March 2004; accepted 12 March 2004)


A variant of the multi-species Lotka–Volterra model is studied in which species competing for fixed finite resources are replaced by new randomly chosen species whenever they become extinct. The model exhibits chaos, punctuated equilibria, leptokurtosis, and self-organized criticality. It has application to ecology, finance, and possibly other diverse systems.

Ref: J. C. Sprott, Phys. Lett. A 325, 329-333 (2004)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.

Fig. 1. Typical temporal variation of 48 species without evolution.

Fig. 2. Fluctuations in average biomass and biodiversity for 48 species with evolution.

Fig. 3. Fluctuations in biomass for two initial conditions that differ by 10-9.

Fig. 4. Fluctuation of the stock market (1930-2002), a Gaussian distribution, and the model, all normalized to the same standard deviation.

Fig. 5. Probability distribution function of volatility showing a power-law scaling.