# American Institute of Mathematical Sciences

2004, 1(1): 185-211. doi: 10.3934/mbe.2004.1.185

## Noise in ecosystems: A short review

 1 Dipartimento di Fisica e Tecnologie Relative, Istituto Nazionale di Fisica della Materia, Unità di Palermo, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy, Italy, Italy

Received  February 2004 Revised  March 2004 Published  March 2004

Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we briefly review the noise-induced effects in three different ecosystems: (i) two competing species; (ii) three interacting species, one predator and two preys, and (iii) N-interacting species. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is random in cases (i) and (iii), and a periodical function, which accounts for the environmental temperature, in case (ii). We find noise-induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise-delayed extinction, and noise-induced pattern formation with non-monotonic behaviors of patterns areas and of the density correlation as a function of the multiplicative noise intensity. The asymptotic behavior of the time average of the$i^{th}$ population when the ecosystem is composed of a great number of interacting species is obtained and the effect of the noise on the asymptotic probability distri- butions of the populations is discussed.
Citation: B. Spagnolo, D. Valenti, A. Fiasconaro. Noise in ecosystems: A short review. Mathematical Biosciences & Engineering, 2004, 1 (1) : 185-211. doi: 10.3934/mbe.2004.1.185
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