2006, 3(1): 51-65. doi: 10.3934/mbe.2006.3.51

Simulation of structured populations in chemically stressed environments


Department of Ecology and Evolutional Biology, University of Tennessee, Knoxville, TN 37996, United States


The Institute for Environmental Modeling, University of Tennessee, Knoxville, TN 37996, United States

Received  January 2005 Revised  April 2005 Published  November 2005

A heterogenous environment usually impacts, and sometimes determines, the structure and function of organisms in a population. We simulate the effects of a chemical on a population in a spatially heterogeneous environment to determine perceived stressor and spatial effects on dynamic behavior of the population. The population is assumed to be physiologically structured and composed of individuals having both sessile and mobile life history stages, who utilize energetically-controlled, resource-directed, chemical-avoidance advective movements and are subjected to random or density dependent diffusion. From a modeling perspective, the presence of a chemical in the environment requires introduction of both an exposure model and an effects module. The spatial location of the chemical stressor determines the exposure levels and ultimately the effects on the population while the relative location of the resource and organism determines growth. We develop a mathematical model, the numerical analysis for this model, and the simulation techniques necessary to solve the problem of population dynamics in an environment where heterogeneity is generated by resource and chemical stressor. In the simulations, the chemical is assumed to be a nonpolar narcotic and the individuals respond to the chemical via both physiological response and by physical movement. In the absence of a chemical stressor, simulation experiments indicate that despite a propensity to move to regions of higher resource density, organisms need not concentrate in the vicinity of high levels of resource. We focus on the dynamical variations due to advection induced by the toxicant. It is demonstrated that the relationship between resource levels and toxicant concentrations is crucial in determining persistence or extinction of the population.
Citation: Thomas G. Hallam, Qingping Deng. Simulation of structured populations in chemically stressed environments. Mathematical Biosciences & Engineering, 2006, 3 (1) : 51-65. doi: 10.3934/mbe.2006.3.51

Juan Pablo Aparicio, Juan Carlos Corley, Jorge Eduardo Rabinovich. Life history traits of Sirex Noctilio F. (Hymenoptera: Siricidae) can explain outbreaks independently of environmental factors. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1265-1279. doi: 10.3934/mbe.2013.10.1265


Enrico Gerlach, Charlampos Skokos. Comparing the efficiency of numerical techniques for the integration of variational equations. Conference Publications, 2011, 2011 (Special) : 475-484. doi: 10.3934/proc.2011.2011.475


B. Wiwatanapataphee, Theeradech Mookum, Yong Hong Wu. Numerical simulation of two-fluid flow and meniscus interface movement in the electromagnetic continuous steel casting process. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1171-1183. doi: 10.3934/dcdsb.2011.16.1171


Mauro Cesa. A brief history of quantitative finance. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 6-. doi: 10.1186/s41546-017-0018-3


Paula Federico, Dobromir T. Dimitrov, Gary F. McCracken. Bat population dynamics: multilevel model based on individuals' energetics. Mathematical Biosciences & Engineering, 2008, 5 (4) : 743-756. doi: 10.3934/mbe.2008.5.743


Lambertus A. Peletier, Xi-Ling Jiang, Snehal Samant, Stephan Schmidt. Analysis of a complex physiology-directed model for inhibition of platelet aggregation by clopidogrel. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 945-961. doi: 10.3934/dcds.2017039


Vera Ignatenko. Homoclinic and stable periodic solutions for differential delay equations from physiology. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3637-3661. doi: 10.3934/dcds.2018157


A. Chauviere, T. Hillen, L. Preziosi. Modeling cell movement in anisotropic and heterogeneous network tissues. Networks & Heterogeneous Media, 2007, 2 (2) : 333-357. doi: 10.3934/nhm.2007.2.333


F. H. Clarke, Yu. S . Ledyaev, R. J. Stern. Proximal techniques of feedback construction. Conference Publications, 1998, 1998 (Special) : 177-194. doi: 10.3934/proc.1998.1998.177


Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020264


Russell Betteridge, Markus R. Owen, H.M. Byrne, Tomás Alarcón, Philip K. Maini. The impact of cell crowding and active cell movement on vascular tumour growth. Networks & Heterogeneous Media, 2006, 1 (4) : 515-535. doi: 10.3934/nhm.2006.1.515


Thomas Hillen, Peter Hinow, Zhi-An Wang. Mathematical analysis of a kinetic model for cell movement in network tissues. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1055-1080. doi: 10.3934/dcdsb.2010.14.1055


Meng-Rong Li. Estimates for the life-span of the solutions for some semilinear wave equations. Communications on Pure & Applied Analysis, 2008, 7 (2) : 417-432. doi: 10.3934/cpaa.2008.7.417


Tsanou Berge, Samuel Bowong, Jean Lubuma, Martin Luther Mann Manyombe. Modeling Ebola Virus Disease transmissions with reservoir in a complex virus life ecology. Mathematical Biosciences & Engineering, 2018, 15 (1) : 21-56. doi: 10.3934/mbe.2018002


Xiaoliang Cheng, Stanisław Migórski, Anna Ochal, Mircea Sofonea. Analysis of two quasistatic history-dependent contact models. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2425-2445. doi: 10.3934/dcdsb.2014.19.2425


Baowei Feng. On the decay rates for a one-dimensional porous elasticity system with past history. Communications on Pure & Applied Analysis, 2019, 18 (6) : 2905-2921. doi: 10.3934/cpaa.2019130


Gongwei Liu, Baowei Feng, Xinguang Yang. Longtime dynamics for a type of suspension bridge equation with past history and time delay. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4995-5013. doi: 10.3934/cpaa.2020224


Stanisław Migórski, Yi-bin Xiao, Jing Zhao. Fully history-dependent evolution hemivariational inequalities with constraints. Evolution Equations & Control Theory, 2020, 9 (4) : 1089-1114. doi: 10.3934/eect.2020047


B. E. Ainseba, W. E. Fitzgibbon, M. Langlais, J. J. Morgan. An application of homogenization techniques to population dynamics models. Communications on Pure & Applied Analysis, 2002, 1 (1) : 19-33. doi: 10.3934/cpaa.2002.1.19


Santanu Sarkar, Subhamoy Maitra. Some applications of lattice based root finding techniques. Advances in Mathematics of Communications, 2010, 4 (4) : 519-531. doi: 10.3934/amc.2010.4.519

2018 Impact Factor: 1.313


  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]