Noise in ecosystems: A short review
TLDR
In this article, 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.Abstract:
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.read more
Citations
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Mathematical models of vegetation pattern formation in ecohydrology
TL;DR: In this paper, an extensive analysis of deterministic and stochastic mechanisms for the formation of vegetation patterns is presented, along with some examples of applications relevant to the environmental sciences.
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WKB theory of large deviations in stochastic populations
Michael Assaf,Baruch Meerson +1 more
TL;DR: In this article, the authors review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems.
Journal ArticleDOI
Dynamics of two competing species in the presence of Lévy noise sources.
TL;DR: A Lotka-Volterra system of two competing species subject to multiplicative α-stable Lévy noise is considered, which is characterized by two different regimes, exclusion of one species and coexistence of both.
Journal ArticleDOI
Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion Model
G. Denaro,Davide Valenti,Bernardo Spagnolo,Gualtiero Basilone,Salvatore Mazzola,S. Zgozi,Salvatore Aronica,Angelo Bonanno +7 more
TL;DR: A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, and real distributions are well reproduced by theoretical profiles.
Journal ArticleDOI
Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics
G. Denaro,Davide Valenti,A. La Cognata,Bernardo Spagnolo,Angelo Bonanno,Gualtiero Basilone,Salvatore Mazzola,S. Zgozi,Salvatore Aronica,Christophe Brunet +9 more
TL;DR: By using a stochastic reaction-diffusion-taxis model, the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters, shows good agreement with experimental data sampled in two different sites of the Sicily Channel.
References
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Book
Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences
TL;DR: The Handbook of Stochastic Methods as mentioned in this paper covers the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations, and quatum-mechanical Markov processes.
Book
Nonlinear Dynamics of Interacting Populations
TL;DR: A brief outline of the ideas and methods of mathematical modelling of populations growth dynamics of isolated population predator- prey interaction competition and symbiosis local systems of three populations dissipative structures in predator-prey systems is provided.
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Stochastic Processes in Physics, Chemistry, and Biology
Jan A. Freund,Thorsten Pöschel +1 more
TL;DR: In this paper, the Lighthouse model of a neural net with delay is used to estimate phase coherence in ensembles of Stochastic Resonators, and the Kramers Oscillator is revisited.
Journal ArticleDOI
A high-resolution record of the last deglaciation in the Sicily Channel based on foraminifera and calcareous nannofossil quantitative distribution
TL;DR: In this article, relative abundance fluctuations in planktic foraminiferal and calcareous nannofossil assemblages are reported on the basis of a high-resolution study of ODP Leg 160 Hole 963D, drilled in the Sicily Strait, near Capo Rossello (southern Sicily).