American Institute of Mathematical Sciences

Advanced
2014, 11(6): 1411-1429. doi: 10.3934/mbe.2014.11.1411

A stochastic simulation model for Anelosimus studiosus during prey capture: A case study for determination of optimal spacing

Michele L. Joyner 1, , Chelsea R. Ross 2, , Colton Watts 3, and  Thomas C. Jones 3,

1. 

Department of Mathematics & Statistics and Institute for Quantitative Biology, East Tennessee State University, Johnson City, TN, 37659
2. 

Department of Mathematics & Statistics, East Tennessee State University, Johnson City, TN, 37659, United States
3. 

Department of Biological Sciences, East Tennessee State University, Johnson City, TN, 37659, United States, United States

Received  November 2013 Revised  August 2014 Published  September 2014

In this paper, we develop a stochastic differential equation model to simulate the movement of a social/subsocial spider species, Anelosimus studiosus, during prey capture using experimental data collected in a structured environment. In a subsocial species, females and their maturing offspring share a web and cooperate in web maintenance and prey capture. Furthermore, observations indicate these colonies change their positioning throughout the day, clustered during certain times of the day while spaced out at other times. One key question was whether or not the spiders spaced out ``optimally'' to cooperate in prey capture. In this paper, we first show the derivation of the model where experimental data is used to determine key parameters within the model. We then use this model to test the success of prey capture under a variety of different spatial configurations for varying colony sizes to determine the best spatial configuration for prey capture.
Keywords: social spider, Anelosimus studiosus, animal movement., cooperative foraging, Stochastic differential equation, mathematical model.
Mathematics Subject Classification: Primary: 92B99, 60H10; Secondary: 97M6.
Citation: 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 & Engineering, 2014, 11 (6) : 1411-1429. doi: 10.3934/mbe.2014.11.1411
References:
[1]

L. Aviles, The Evolution of Social Behavior in Insects and Arachnids,, ch. Causes and consequences of cooperation and permanent-sociality in spiders, (1997), 477.   Google Scholar

[2]

D. R. Billinger, H. K. Preisler, A. A. Ager, J. G. Kie and B. S. Stewart, Modelling Movements of Free-Ranging Animals,, Tech. Report 610, (2001).   Google Scholar

[3]

D. R. Brillinger, H. K. Preisler, A. A. Ager and J. G. Kie, An exploratory data analysis (eda) of the paths of moving animals,, Journal of Statistical Planning and Inference, 122 (2004), 43.  doi: 10.1016/j.jspi.2003.06.016.  Google Scholar

[4]

V. Brach, Anelosimus studiosus (araneae: Theridiidae) and the evolution of quasisociality in theridiid spiders,, Evolution, 31 (1977), 154.  doi: 10.2307/2407553.  Google Scholar

[5]

D. R. Brillinger, A particle migrating randomly on a sphere,, Journal of Theoretical Probability, 10 (1997), 429.  doi: 10.1023/A:1022869817770.  Google Scholar

[6]

D. R. Brillinger and B. S. Stewart, Elephant-seal movements: Modelling migrations,, The Canadian Journal of Statistics, 26 (1998), 431.  doi: 10.2307/3315767.  Google Scholar

[7]

R. Furey, Two cooperatively social populations of the theridiid spider Anelosimus studiosus in a temperate region,, Animal Behavior, 55 (1998), 727.   Google Scholar

[8]

L. Grinstead, J. N. Pruitt, V. Settepani and T. Bilde, Individual personalities shape task differentiation in a social spider,, Proceedings of the Royal Society B, 280 (2013).  doi: 10.1098/rspb.2013.1407.  Google Scholar

[9]

F. Heppner and U. Grenander, Ubiquity of Chaos,, ch. A stochastic nonlinear model for coordinated bird flocks, (1990), 233.   Google Scholar

[10]

D. Halliday and R. Resnick, Fundamentals of Physics,, John Wiley & Sons, (1988).  doi: 10.1063/1.3070817.  Google Scholar

[11]

T. Jones, S. Riechert, S. Dalrymple and P. Parker, Fostering model explains variation in levels of sociality in a spider system,, Animal Behavior, 73 (2007), 195.  doi: 10.1016/j.anbehav.2006.06.006.  Google Scholar

[12]

D. G. Kendall, Pole-seeking brownian motion and bird navigation,, Journal of the Royal Statistical Society Series B, 36 (1974), 365.   Google Scholar

[13]

P. M. Kareiva and N. Shigesada, Analyzing insect movement as a correlated random walk,, Oecologia, 56 (1983), 234.  doi: 10.1007/BF00379695.  Google Scholar

[14]

MATLAB, Version 8.1.0.604 (r2013a),, The MathWorks Inc., (2013).   Google Scholar

[15]

Inc Minitab, Minitab,, Minitab, (2013).   Google Scholar

[16]

S. A. Naftilan, Transmission of vibrations in funnel and sheet spider webs,, Biological Macromolecules, 24 (1999), 289.  doi: 10.1016/S0141-8130(98)00092-0.  Google Scholar

[17]

K. B. Newman, State-space modeling of animal movement and mortality with application to salmon,, Biometrics, 54 (1998), 1290.  doi: 10.2307/2533659.  Google Scholar

[18]

OSP, Tracker Video Analysis and Modeling Too,, 2013., ().   Google Scholar

[19]

H. K. Preisler, A. A. Ager, B. K. Johnson and J. G. Kie, Modeling animal movements using stochastic differential equations,, Environmetrics, 15 (2004), 643.  doi: 10.1002/env.636.  Google Scholar

[20]

H. R. Pulliam and T. Caraco, Behavioural Ecology, an Evolutionary Approach,, ch. Living in Groups: Is there Optimal Group Size?, (1984), 122.  doi: 10.1016/0003-3472(79)90082-4.  Google Scholar

[21]

C. Ross, Ontongeny and Diel Rhythm in Spacing Within a Subsocial web of Anelosimus Studiosus (Araneael Therididdae),, Honor's Thesis, (2013).   Google Scholar

[22]

L. S. Rayor and G. W. Uetz, Trade-offs in foraging success and predation risk with spatial position in colonial spiders,, Behavioral Ecology Sociobiology, 27 (1990), 77.  doi: 10.1007/BF00168449.  Google Scholar

[23]

P. E. Smouse, S. Focardi, P. R. Moorcroft, J. G. Kie, J. D. Forester and J. M. Morales, Stochastic modelling of animal movement,, Phi.l Trans. R. Soc. B., 365 (2010), 2201.  doi: 10.1098/rstb.2010.0078.  Google Scholar

[24]

G. W. Uetz and C. S. Hieber, Evolution of social behaviour in insects and arachnids,, ch. Colonial Web-building Spiders: Balancing the Costs and Benefits of Group Living, (1997), 458.   Google Scholar

show all references

References:
[1]

L. Aviles, The Evolution of Social Behavior in Insects and Arachnids,, ch. Causes and consequences of cooperation and permanent-sociality in spiders, (1997), 477.   Google Scholar

[2]

D. R. Billinger, H. K. Preisler, A. A. Ager, J. G. Kie and B. S. Stewart, Modelling Movements of Free-Ranging Animals,, Tech. Report 610, (2001).   Google Scholar

[3]

D. R. Brillinger, H. K. Preisler, A. A. Ager and J. G. Kie, An exploratory data analysis (eda) of the paths of moving animals,, Journal of Statistical Planning and Inference, 122 (2004), 43.  doi: 10.1016/j.jspi.2003.06.016.  Google Scholar

[4]

V. Brach, Anelosimus studiosus (araneae: Theridiidae) and the evolution of quasisociality in theridiid spiders,, Evolution, 31 (1977), 154.  doi: 10.2307/2407553.  Google Scholar

[5]

D. R. Brillinger, A particle migrating randomly on a sphere,, Journal of Theoretical Probability, 10 (1997), 429.  doi: 10.1023/A:1022869817770.  Google Scholar

[6]

D. R. Brillinger and B. S. Stewart, Elephant-seal movements: Modelling migrations,, The Canadian Journal of Statistics, 26 (1998), 431.  doi: 10.2307/3315767.  Google Scholar

[7]

R. Furey, Two cooperatively social populations of the theridiid spider Anelosimus studiosus in a temperate region,, Animal Behavior, 55 (1998), 727.   Google Scholar

[8]

L. Grinstead, J. N. Pruitt, V. Settepani and T. Bilde, Individual personalities shape task differentiation in a social spider,, Proceedings of the Royal Society B, 280 (2013).  doi: 10.1098/rspb.2013.1407.  Google Scholar

[9]

F. Heppner and U. Grenander, Ubiquity of Chaos,, ch. A stochastic nonlinear model for coordinated bird flocks, (1990), 233.   Google Scholar

[10]

D. Halliday and R. Resnick, Fundamentals of Physics,, John Wiley & Sons, (1988).  doi: 10.1063/1.3070817.  Google Scholar

[11]

T. Jones, S. Riechert, S. Dalrymple and P. Parker, Fostering model explains variation in levels of sociality in a spider system,, Animal Behavior, 73 (2007), 195.  doi: 10.1016/j.anbehav.2006.06.006.  Google Scholar

[12]

D. G. Kendall, Pole-seeking brownian motion and bird navigation,, Journal of the Royal Statistical Society Series B, 36 (1974), 365.   Google Scholar

[13]

P. M. Kareiva and N. Shigesada, Analyzing insect movement as a correlated random walk,, Oecologia, 56 (1983), 234.  doi: 10.1007/BF00379695.  Google Scholar

[14]

MATLAB, Version 8.1.0.604 (r2013a),, The MathWorks Inc., (2013).   Google Scholar

[15]

Inc Minitab, Minitab,, Minitab, (2013).   Google Scholar

[16]

S. A. Naftilan, Transmission of vibrations in funnel and sheet spider webs,, Biological Macromolecules, 24 (1999), 289.  doi: 10.1016/S0141-8130(98)00092-0.  Google Scholar

[17]

K. B. Newman, State-space modeling of animal movement and mortality with application to salmon,, Biometrics, 54 (1998), 1290.  doi: 10.2307/2533659.  Google Scholar

[18]

OSP, Tracker Video Analysis and Modeling Too,, 2013., ().   Google Scholar

[19]

H. K. Preisler, A. A. Ager, B. K. Johnson and J. G. Kie, Modeling animal movements using stochastic differential equations,, Environmetrics, 15 (2004), 643.  doi: 10.1002/env.636.  Google Scholar

[20]

H. R. Pulliam and T. Caraco, Behavioural Ecology, an Evolutionary Approach,, ch. Living in Groups: Is there Optimal Group Size?, (1984), 122.  doi: 10.1016/0003-3472(79)90082-4.  Google Scholar

[21]

C. Ross, Ontongeny and Diel Rhythm in Spacing Within a Subsocial web of Anelosimus Studiosus (Araneael Therididdae),, Honor's Thesis, (2013).   Google Scholar

[22]

L. S. Rayor and G. W. Uetz, Trade-offs in foraging success and predation risk with spatial position in colonial spiders,, Behavioral Ecology Sociobiology, 27 (1990), 77.  doi: 10.1007/BF00168449.  Google Scholar

[23]

P. E. Smouse, S. Focardi, P. R. Moorcroft, J. G. Kie, J. D. Forester and J. M. Morales, Stochastic modelling of animal movement,, Phi.l Trans. R. Soc. B., 365 (2010), 2201.  doi: 10.1098/rstb.2010.0078.  Google Scholar

[24]

G. W. Uetz and C. S. Hieber, Evolution of social behaviour in insects and arachnids,, ch. Colonial Web-building Spiders: Balancing the Costs and Benefits of Group Living, (1997), 458.   Google Scholar

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