“  The comprehension of noise's role in the dynamics of nonlinear systems plays a key aspect in the efforts devoted to understand and then to model so-called complex ecosystems.”

In the past, the study of deterministic mathematical models of ecosystems has clearly revealed a large variety of phenomena, ranging from deterministic chaos to the presence of a spatial organization. These models, however, do not account for the effects of noise despite the fact that it is always present in actual population dynamics and that it arises from different sources, such as the intrinsic stochasticity associated with the random variability of the environment. Frequently, its effects have been assumed to be only a source of disorder.

Ecological systems are open systems in which the interaction between the component parts is nonlinear and the interaction with the environment is noisy. This intrinsic nonlinearity can give rise to the complex behavior of the system, which becomes very sensitive to initial conditions, various deterministic external perturbations, and to fluctuations always present in nature. The comprehension of noise’s role in the dynamics of nonlinear systems plays a key aspect in the efforts devoted to the understanding and modeling of so-called complex ecosystems.

  Does it describe a new discovery, methodology, or synthesis of knowledge?

The noise, through its interaction with the nonlinearity of the living systems, can give rise to new counter-intuitive phenomena like noise-enhanced stability, stochastic resonance, noise-delayed extinction, temporal oscillations and spatial patterns. In addition, the analysis of the experimental data of population dynamics frequently requires a consideration of spatial heterogeneity.

Characterizing the resultant spatio-temporal patterns is, perhaps, the major challenge for ecological time-series analysis and for dynamics modeling. In our article we briefly reviewed some 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 were analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment.

We found noise-induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise-delayed extinction, and noise-induced pattern formation with nonmonotonic behaviors of patterns areas and of the density correlation as a function of the multiplicative noise intensity.

To describe complex ecosystems it is fundamental to understand the interplay between noise, along with the periodic and random modulations of some environmental parameters and the intrinsic nonlinearity of simple models of ecosystems. It is fundamental also to understand spatio-temporal dynamics.

The interplay between noise and periodic modulations of some environmental parameters can change drastically as, in an unexpected way, the dynamics of fish populations, for example. The noise-induced effects found should be useful in explaining the time evolution of species whose dynamics are strongly affected by the noisy environment.