Mathematical Biosciences and Engineering, 2015, 12(3): 585-607. doi: 10.3934/mbe.2015.12.585

Primary: 92B99, 60H10, 60H35; Secondary: 65C30, 97M60.

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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

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.
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