Noise in ecosystems: A short review - B. Spagnolo; D. Valenti; A. Fiasconaro (Mathematical Biosciences and Engineering)
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) twocompeting 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 multiplicativenoise, which models the interaction between the species and the environment. Theinteraction parameter between the species is random in cases (i) and (iii), and aperiodical function, which accounts for the environmental temperature, in case (ii).We find noise-induced phenomena such as quasi-deterministic oscillations, stochasticresonance, noise-delayed extinction, and noise-induced pattern formation with non-monotonic behaviors of patterns areas and of the density correlation as a functionof the multiplicative noise intensity. The asymptotic behavior of the time average ofthe$ i^{th}$population when the ecosystem is composed of a great number of interactingspecies is obtained and the effect of the noise on the asymptotic probability distri-butions of the populations is discussed.