Search dynamics at the edge of extinction: Anomalous diffusion as a critical survival stateC. L. Faustino1, L. R. da Silva2, M. G. E. da Luz3, E. P. Raposo4 and G. M. Viswanathan1
1 Instituto de Física, Universidade Federal de Alagoas - 57072-970, Maceió-AL, Brazil
2 Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970, Natal-RN, Brazil
3 Departamento de Física, Universidade Federal do Paraná - 81531-990, Curitiba-PR, Brazil
4 Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife-PE, Brazil
received 14 July 2006; accepted in final form 28 November 2006; published February 2007
published online 23 January 2007
We investigate the general problem of autonomous random walkers whose sole source of energy are search targets that are themselves diffusing random walkers. We study how the energy accumulated by the searcher varies with the target density via numerical simulations and compare the results with an analytical model for fixed targets. We report that superdiffusion of either searcher or target confers substantial energetic advantages to the former. While superdiffusion may not play a crucial role for high target densities, in contrast it confers a vital advantage in the limit of low densities at the edge of extinction: diffusive searchers rapidly die but superdiffusive searchers can survive for long periods without entering into the extinction state. The validity and relevance of our findings in broader contexts are also discussed.
05.40.Fb - Random walks and Levy flights .
87.23.-n - Ecology and evolution .
© Europhysics Letters Association 2007