American Institute of Mathematical Sciences

Advanced
2007, 4(1): 67-84. doi: 10.3934/mbe.2007.4.67

An individual, stochastic model of growth incorporating state-dependent risk and random foraging and climate

William Wolesensky 1, and  J. David Logan 2,

1. 

Program in Mathematics, College of St. Mary, Omaha, NE 68134
2. 

Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130

Received  January 2006 Revised  March 2006 Published  November 2006

We model the effects of both stochastic and deterministic temperature variations on arthropod predator-prey systems. Specifically, we study the stochastic dynamics of arthropod predator-prey interactions under a varying temperature regime, and we develop an individual model of a prey under pressure from a predator, with vigilance (or foraging effort), search rates, attack rates, and other predation parameters dependent on daily temperature variations. Simulations suggest that an increase in the daily average temperature may benefit both predator and prey. Furthermore, simulations show that anti-predator behavior may indeed decrease predation but at the expense of reduced prey survivorship because of a greater increase in other types of mortality.
Keywords: vigilance, temperature, grasshoppers., foraging, nutritional state, stochastic.
Mathematics Subject Classification: 92D25, 92D40, 92D5.
Citation: William Wolesensky, J. David Logan. An individual, stochastic model of growth incorporating state-dependent risk and random foraging and climate. Mathematical Biosciences & Engineering, 2007, 4 (1) : 67-84. doi: 10.3934/mbe.2007.4.67
[1]

Chanakarn Kiataramkul, Graeme Wake, Alona Ben-Tal, Yongwimon Lenbury. Optimal nutritional intake for fetal growth. Mathematical Biosciences & Engineering, 2011, 8 (3) : 723-732. doi: 10.3934/mbe.2011.8.723
[2]

J. G. Ollason, N. Ren. A general dynamical theory of foraging in animals. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 713-720. doi: 10.3934/dcdsb.2004.4.713
[3]

J. A. López Molina, M. J. Rivera, E. Berjano. Electrical-thermal analytical modeling of monopolar RF thermal ablation of biological tissues: determining the circumstances under which tissue temperature reaches a steady state. Mathematical Biosciences & Engineering, 2016, 13 (2) : 281-301. doi: 10.3934/mbe.2015003
[4]

Brahim El Asri, Sehail Mazid. Stochastic impulse control Problem with state and time dependent cost functions. Mathematical Control & Related Fields, 2020, 10 (4) : 855-875. doi: 10.3934/mcrf.2020022
[5]

Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021066
[6]

W. Y. Tan, L.-J. Zhang, C.W. Chen. Stochastic modeling of carcinogenesis: State space models and estimation of parameters. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 297-322. doi: 10.3934/dcdsb.2004.4.297
[7]

Ming Chen, Hao Wang. Dynamics of a discrete-time stoichiometric optimal foraging model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 107-120. doi: 10.3934/dcdsb.2020264
[8]

Susmita Halder, Joydeb Bhattacharyya, Samares Pal. Predator-prey interactions under fear effect and multiple foraging strategies. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021206
[9]

Igor Chueshov, Peter E. Kloeden, Meihua Yang. Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 991-1009. doi: 10.3934/dcdsb.2018139
[10]

Shuang Li, Chuong Luong, Francisca Angkola, Yonghong Wu. Optimal asset portfolio with stochastic volatility under the mean-variance utility with state-dependent risk aversion. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1521-1533. doi: 10.3934/jimo.2016.12.1521
[11]

Haiyan Zhang. A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1287-1301. doi: 10.3934/jimo.2016.12.1287
[12]

Komi Messan, Yun Kang. A two patch prey-predator model with multiple foraging strategies in predator: Applications to insects. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 947-976. doi: 10.3934/dcdsb.2017048
[13]

Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 209-226. doi: 10.3934/dcdsb.2017011
[14]

Roberto Garra. Confinement of a hot temperature patch in the modified SQG model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2407-2416. doi: 10.3934/dcdsb.2018258
[15]

Stéphane Brull, Bruno Dubroca, Corentin Prigent. A kinetic approach of the bi-temperature Euler model. Kinetic & Related Models, 2020, 13 (1) : 33-61. doi: 10.3934/krm.2020002
[16]

Naveen K. Vaidya, Xianping Li, Feng-Bin Wang. Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 321-349. doi: 10.3934/dcdsb.2018099
[17]

Hung-Wen Kuo. Effect of abrupt change of the wall temperature in the kinetic theory. Kinetic & Related Models, 2019, 12 (4) : 765-789. doi: 10.3934/krm.2019030
[18]

Seiji Ukai, Tong Yang, Huijiang Zhao. Exterior Problem of Boltzmann Equation with Temperature Difference. Communications on Pure & Applied Analysis, 2009, 8 (1) : 473-491. doi: 10.3934/cpaa.2009.8.473
[19]

Ming Chen, Meng Fan, Xing Yuan, Huaiping Zhu. Effect of seasonal changing temperature on the growth of phytoplankton. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1091-1117. doi: 10.3934/mbe.2017057
[20]

Jingzhi Li, Masahiro Yamamoto, Jun Zou. Conditional Stability and Numerical Reconstruction of Initial Temperature. Communications on Pure & Applied Analysis, 2009, 8 (1) : 361-382. doi: 10.3934/cpaa.2009.8.361

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (27)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences