# American Institute of Mathematical Sciences

• Previous Article
Partial differential equations with Robin boundary condition in online social networks
• DCDS-B Home
• This Issue
• Next Article
Time-invariant and stochastic disperser-structured matrix models: Invasion rates of fleshy-fruited exotic shrubs
August  2015, 20(6): 1625-1638. doi: 10.3934/dcdsb.2015.20.1625

## Mathematical study of the effects of travel costs on optimal dispersal in a two-patch model

 1 212A Williams Hall, 953 Danby Road, Ithaca, NY 14850, United States

Received  November 2013 Revised  April 2014 Published  June 2015

The theoretical dispersal of organisms has been widely studied. It is well known for single species dispersal in a spatially heterogeneous and temporally constant environment that balanced dispersal'' is an evolutionarily stable strategy [36,10]. This assumes that organisms do not pay a cost to move from one part of the environment to another. We begin this paper by proving that the optimal strategy for organisms constrained by perceptual limitations, described by [19], is evolutionarily stable. Then, we extend this idea of optimal dispersal to a situation where constrained organisms pay a cost to move between two patches in a heterogeneous environment. For moderate travel costs, we find a convergent stable strategy that suggests an extension of the balanced dispersal concept. Furthermore, we show for high costs that the best strategy is to ignore information about the environment.
Citation: Theodore E. Galanthay. Mathematical study of the effects of travel costs on optimal dispersal in a two-patch model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1625-1638. doi: 10.3934/dcdsb.2015.20.1625
##### References:

show all references

##### References:
 [1] Alex Potapov, Ulrike E. Schlägel, Mark A. Lewis. Evolutionarily stable diffusive dispersal. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3319-3340. doi: 10.3934/dcdsb.2014.19.3319 [2] Jing-Jing Xiang, Yihao Fang. Evolutionarily stable dispersal strategies in a two-patch advective environment. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1875-1887. doi: 10.3934/dcdsb.2018245 [3] S.A. Gourley, Yang Kuang. Two-Species Competition with High Dispersal: The Winning Strategy. Mathematical Biosciences & Engineering, 2005, 2 (2) : 345-362. doi: 10.3934/mbe.2005.2.345 [4] Wendi Wang. Population dispersal and disease spread. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 797-804. doi: 10.3934/dcdsb.2004.4.797 [5] Yujing Wang, Changjun Yu, Kok Lay Teo. A new computational strategy for optimal control problem with a cost on changing control. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 339-364. doi: 10.3934/naco.2016016 [6] Peng Zhong, Suzanne Lenhart. Optimal control of integrodifference equations with growth-harvesting-dispersal order. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2281-2298. doi: 10.3934/dcdsb.2012.17.2281 [7] Chunmei Zhang, Wenxue Li, Ke Wang. Graph-theoretic approach to stability of multi-group models with dispersal. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 259-280. doi: 10.3934/dcdsb.2015.20.259 [8] Chiu-Yen Kao, Yuan Lou, Wenxian Shen. Random dispersal vs. non-local dispersal. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 551-596. doi: 10.3934/dcds.2010.26.551 [9] Long Zhang, Gao Xu, Zhidong Teng. Intermittent dispersal population model with almost period parameters and dispersal delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 2011-2037. doi: 10.3934/dcdsb.2016034 [10] Nancy Azer, P. van den Driessche. Competition and Dispersal Delays in Patchy Environments. Mathematical Biosciences & Engineering, 2006, 3 (2) : 283-296. doi: 10.3934/mbe.2006.3.283 [11] Robert Stephen Cantrell, Chris Cosner, Yuan Lou. Evolution of dispersal and the ideal free distribution. Mathematical Biosciences & Engineering, 2010, 7 (1) : 17-36. doi: 10.3934/mbe.2010.7.17 [12] Chiu-Yen Kao, Yuan Lou, Wenxian Shen. Evolution of mixed dispersal in periodic environments. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2047-2072. doi: 10.3934/dcdsb.2012.17.2047 [13] Ka Wo Lau, Yue Kuen Kwok. Optimal execution strategy of liquidation. Journal of Industrial & Management Optimization, 2006, 2 (2) : 135-144. doi: 10.3934/jimo.2006.2.135 [14] Jacques A. L. Silva, Flávia T. Giordani. Density-dependent dispersal in multiple species metapopulations. Mathematical Biosciences & Engineering, 2008, 5 (4) : 843-857. doi: 10.3934/mbe.2008.5.843 [15] Song Liang, Yuan Lou. On the dependence of population size upon random dispersal rate. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2771-2788. doi: 10.3934/dcdsb.2012.17.2771 [16] Fei-Ying Yang, Wan-Tong Li. Dynamics of a nonlocal dispersal SIS epidemic model. Communications on Pure & Applied Analysis, 2017, 16 (3) : 781-798. doi: 10.3934/cpaa.2017037 [17] Wan-Tong Li, Li Zhang, Guo-Bao Zhang. Invasion entire solutions in a competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1531-1560. doi: 10.3934/dcds.2015.35.1531 [18] Jian-Wen Sun, Wan-Tong Li, Zhi-Cheng Wang. A nonlocal dispersal logistic equation with spatial degeneracy. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3217-3238. doi: 10.3934/dcds.2015.35.3217 [19] Carmen Cortázar, Manuel Elgueta, Jorge García-Melián, Salomé Martínez. Finite mass solutions for a nonlocal inhomogeneous dispersal equation. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1409-1419. doi: 10.3934/dcds.2015.35.1409 [20] Yuan-Hang Su, Wan-Tong Li, Fei-Ying Yang. Effects of nonlocal dispersal and spatial heterogeneity on total biomass. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-8. doi: 10.3934/dcdsb.2019038

2017 Impact Factor: 0.972