An aggregate stochastic model incorporating individual dynamics for predation movements of anelosimus studiosus
-
1.
Department of Mathematics & Statistics, East Tennessee State University, Johnson City, TN, 37614
-
2.
Department of Biological Sciences, East Tennessee State University, Johnson City, TN, 37614
-
Received:
01 July 2014
Accepted:
29 June 2018
Published:
01 February 2015
-
-
MSC :
Primary: 92B99, 60H10, 60H35; Secondary: 65C30, 97M60.
-
-
In this paper, we discuss methods for developing a stochastic model which incorporates behavior differences in the predation movements of Anelosimus studiosus (a subsocial spider). Stochastic models for animal movement and, in particular, spider predation movement have been developed previously; however, this paper focuses on the development and implementation of the necessary mathematical and statistical methods required to expand such a model in order to capture a variety of distinct behaviors. A least squares optimization algorithm is used for parameter estimation to fit a single stochastic model to an individual spider during predation resulting in unique parameter values for each spider. Similarities and variations between parameter values across the spiders are analyzed and used to estimate probability distributions for the variable parameter values. An aggregate stochastic model is then created which incorporates the individual dynamics. The comparison between the optimal individual models to the aggregate model indicate the methodology and algorithm developed in this paper are appropriate for simulating a range of individualistic behaviors.
Citation: Alex John Quijano, Michele L. Joyner, Edith Seier, Nathaniel Hancock, Michael Largent, Thomas C. Jones. An aggregate stochastic model incorporating individual dynamics for predation movements of anelosimus studiosus[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 585-607. doi: 10.3934/mbe.2015.12.585
Related Papers:
| [1] |
Michele L. Joyner, Chelsea R. Ross, Colton Watts, Thomas C. Jones .
A stochastic simulation model for Anelosimus studiosus during prey capture: A case study for determination of optimal spacing. Mathematical Biosciences and Engineering, 2014, 11(6): 1411-1429.
doi: 10.3934/mbe.2014.11.1411
|
| [2] |
Gianni Gilioli, Sara Pasquali, Fabrizio Ruggeri .
Nonlinear functional response parameter estimation in a stochastic predator-prey model. Mathematical Biosciences and Engineering, 2012, 9(1): 75-96.
doi: 10.3934/mbe.2012.9.75
|
| [3] |
Laura Martín-Fernández, Gianni Gilioli, Ettore Lanzarone, Joaquín Míguez, Sara Pasquali, Fabrizio Ruggeri, Diego P. Ruiz .
A Rao-Blackwellized particle filter for joint parameter estimation and biomass tracking in a stochastic predator-prey system. Mathematical Biosciences and Engineering, 2014, 11(3): 573-597.
doi: 10.3934/mbe.2014.11.573
|
| [4] |
Linda J. S. Allen, P. van den Driessche .
Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences and Engineering, 2006, 3(3): 445-458.
doi: 10.3934/mbe.2006.3.445
|
| [5] |
Yan Zhang, Wanbiao Ma, Hai Yan, Yasuhiro Takeuchi .
A dynamic model describing heterotrophic culture of chorella and its stability analysis. Mathematical Biosciences and Engineering, 2011, 8(4): 1117-1133.
doi: 10.3934/mbe.2011.8.1117
|
| [6] |
Jeong-Mi Yoon, Volodymyr Hrynkiv, Lisa Morano, Anh Tuan Nguyen, Sara Wilder, Forrest Mitchell .
Mathematical modeling of Glassy-winged sharpshooter population. Mathematical Biosciences and Engineering, 2014, 11(3): 667-677.
doi: 10.3934/mbe.2014.11.667
|
| [7] |
Xuan Zhang, Huiqin Jin, Zhuoqin Yang, Jinzhi Lei .
Effects of elongation delay in transcription dynamics. Mathematical Biosciences and Engineering, 2014, 11(6): 1431-1448.
doi: 10.3934/mbe.2014.11.1431
|
| [8] |
Tuan Anh Phan, Jianjun Paul Tian .
Basic stochastic model for tumor virotherapy. Mathematical Biosciences and Engineering, 2020, 17(4): 4271-4294.
doi: 10.3934/mbe.2020236
|
| [9] |
Damilola Olabode, Jordan Culp, Allison Fisher, Angela Tower, Dylan Hull-Nye, Xueying Wang .
Deterministic and stochastic models for the epidemic dynamics of COVID-19 in Wuhan, China. Mathematical Biosciences and Engineering, 2021, 18(1): 950-967.
doi: 10.3934/mbe.2021050
|
| [10] |
Yang Kuang, Jef Huisman, James J. Elser .
Stoichiometric Plant-Herbivore Models and Their Interpretation. Mathematical Biosciences and Engineering, 2004, 1(2): 215-222.
doi: 10.3934/mbe.2004.1.215
|
-
Abstract
In this paper, we discuss methods for developing a stochastic model which incorporates behavior differences in the predation movements of Anelosimus studiosus (a subsocial spider). Stochastic models for animal movement and, in particular, spider predation movement have been developed previously; however, this paper focuses on the development and implementation of the necessary mathematical and statistical methods required to expand such a model in order to capture a variety of distinct behaviors. A least squares optimization algorithm is used for parameter estimation to fit a single stochastic model to an individual spider during predation resulting in unique parameter values for each spider. Similarities and variations between parameter values across the spiders are analyzed and used to estimate probability distributions for the variable parameter values. An aggregate stochastic model is then created which incorporates the individual dynamics. The comparison between the optimal individual models to the aggregate model indicate the methodology and algorithm developed in this paper are appropriate for simulating a range of individualistic behaviors.
References
|
[1]
|
CRC Press, Boca Raton, 2014.
|
|
[2]
|
Technical Report 610, Department of Statistics, University of California, Berkeley, 2001.
|
|
[3]
|
Journal of Agricultural, Biological, and Environmental Statistics, 8 (2003), 387-419.
|
|
[4]
|
Tracker version 4.80, Copyright(c), 2013, URL http://www.cabrillo.edu/~dbrown/tracker.
|
|
[5]
|
3rd edition, Oxford University Press, 2011.
|
|
[6]
|
Proceedings of the Royal Society B, 280 (2013).
|
|
[7]
|
John Wiley & Sons, Inc., New York, 1988.
|
|
[8]
|
John Wiley & Sons, Inc., New York, 1971.
|
|
[9]
|
Journal of Arachnology, 28 (2000), 61-69.
|
|
[10]
|
Behavioral Ecology, 13 (2002), 142-148.
|
|
[11]
|
Mathematical Biosciences and Engineering, 11 (2014), 1411-1429.
|
|
[12]
|
6th edition, Brooks/Cole, Belmont CA, 2010.
|
|
[13]
|
Biological Macromolecules, 24 (1999), 289-293.
|
|
[14]
|
Animal Behaviour, 76 (2008), 871-879.
|
|
[15]
|
R Foundation for Statistical Computing, Vienna, Austria, 2013, URL http://www.R-project.org/.
|
|
[16]
|
Phi.l Trans.R. Soc. B., 365 (2010), 2201-2211.
|
-
-
This article has been cited by:
| 1.
|
David Jaurès Fotsa-Mbogne,
Estimation of anthracnose dynamics by nonlinear filtering,
2018,
11,
1793-5245,
1850005,
10.1142/S1793524518500055
|
|
| 2.
|
Kongshu Deng, Yicheng Ding, Zhurong Yin, Lu Zeng, Hailaing Wu, Dilei Qian,
Force transmission characteristics in a multiple-fulcrum supporting platform with heavy loads,
2020,
17,
1551-0018,
3329,
10.3934/mbe.2020189
|
|
-
-
DownLoad: