# 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
 [1] Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016 [2] Francesca Sapuppo, Elena Umana, Mattia Frasca, Manuela La Rosa, David Shannahoff-Khalsa, Luigi Fortuna, Maide Bucolo. Complex spatio-temporal features in meg data. Mathematical Biosciences & Engineering, 2006, 3 (4) : 697-716. doi: 10.3934/mbe.2006.3.697 [3] Noura Azzabou, Nikos Paragios. Spatio-temporal speckle reduction in ultrasound sequences. Inverse Problems & Imaging, 2010, 4 (2) : 211-222. doi: 10.3934/ipi.2010.4.211 [4] Xiaoying Chen, Chong Zhang, Zonglin Shi, Weidong Xiao. Spatio-temporal keywords queries in HBase. Big Data & Information Analytics, 2016, 1 (1) : 81-91. doi: 10.3934/bdia.2016.1.81 [5] Lin Wang, James Watmough, Fang Yu. Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions. Mathematical Biosciences & Engineering, 2015, 12 (4) : 699-715. doi: 10.3934/mbe.2015.12.699 [6] Hirofumi Izuhara, Shunsuke Kobayashi. Spatio-temporal coexistence in the cross-diffusion competition system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 919-933. doi: 10.3934/dcdss.2020228 [7] Pietro-Luciano Buono, Daniel C. Offin. Instability criterion for periodic solutions with spatio-temporal symmetries in Hamiltonian systems. Journal of Geometric Mechanics, 2017, 9 (4) : 439-457. doi: 10.3934/jgm.2017017 [8] Buddhi Pantha, Judy Day, Suzanne Lenhart. Investigating the effects of intervention strategies in a spatio-temporal anthrax model. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1607-1622. doi: 10.3934/dcdsb.2019242 [9] Jingdong Wei, Jiangbo Zhou, Wenxia Chen, Zaili Zhen, Lixin Tian. Traveling waves in a nonlocal dispersal epidemic model with spatio-temporal delay. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2853-2886. doi: 10.3934/cpaa.2020125 [10] Wenjia Jing, Panagiotis E. Souganidis, Hung V. Tran. Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : 915-939. doi: 10.3934/dcdss.2018055 [11] Raimund BÜrger, Gerardo Chowell, Elvis GavilÁn, Pep Mulet, Luis M. Villada. Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents. Mathematical Biosciences & Engineering, 2018, 15 (1) : 95-123. doi: 10.3934/mbe.2018004 [12] Thomas Hillen, Jeffery Zielinski, Kevin J. Painter. Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2513-2536. doi: 10.3934/dcdsb.2013.18.2513 [13] Jinling Zhou, Yu Yang. Traveling waves for a nonlocal dispersal SIR model with general nonlinear incidence rate and spatio-temporal delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1719-1741. doi: 10.3934/dcdsb.2017082 [14] Zhi-Xian Yu, Rong Yuan. Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 709-728. doi: 10.3934/dcdsb.2010.13.709 [15] Rui Xu. Global convergence of a predator-prey model with stage structure and spatio-temporal delay. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 273-291. doi: 10.3934/dcdsb.2011.15.273 [16] Zelik S.. Formally gradient reaction-diffusion systems in Rn have zero spatio-temporal topological. Conference Publications, 2003, 2003 (Special) : 960-966. doi: 10.3934/proc.2003.2003.960 [17] Rodrigo A. Garrido, Ivan Aguirre. Emergency logistics for disaster management under spatio-temporal demand correlation: The earthquakes case. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2369-2387. doi: 10.3934/jimo.2019058 [18] Alain Miranville, Mazen Saad, Raafat Talhouk. Preface: Workshop in fluid mechanics and population dynamics. Discrete & Continuous Dynamical Systems - S, 2014, 7 (2) : i-i. doi: 10.3934/dcdss.2014.7.2i [19] Yiwen Tao, Jingli Ren. The stability and bifurcation of homogeneous diffusive predator–prey systems with spatio–temporal delays. Discrete & Continuous Dynamical Systems - B, 2022, 27 (1) : 229-243. doi: 10.3934/dcdsb.2021038 [20] Paolo Podio-Guidugli. On the modeling of transport phenomena in continuum and statistical mechanics. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1393-1411. doi: 10.3934/dcdss.2017074

2018 Impact Factor: 1.313