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Von Mises
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This is NetLogo code that presents two alternative implementations of Correlated Random Walk (CRW):

- 1. drawing the turning angles from the uniform distribution, i.e. drawing the angle with the same probability from a certain given range;

- 2. drawing the turning angles from von Mises distribution.

The move lengths are drawn from the lognormal distribution with the specified parameters.

Correlated Random Walk is used to represent the movement of animal individuals in two-dimensional space. When modeled as CRW, the direction of movement at any time step is correlated with the direction of movement at the previous time step. Although originally used to describe the movement of insects, CRW was later shown to sufficiently well describe the empirical movement data of other animals, such as wild boars, caribous, sea stars.

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The first simple movement models used unbiased and uncorrelated random walks (RW). In such models of movement, the direction of the movement is totally independent of the previous movement direction. In other words, at each time step the direction, in which an individual is moving is completely random. This process is referred to as a Brownian motion.

On the other hand, in correlated random walks (CRW) the choice of the movement directions depends on the direction of the previous movement. At each time step, the movement direction has a tendency to point in the same direction as the previous one. This movement model fits well observational movement data for many animal species.

The presented agent based model simulated the movement of the agents as a correlated random walk (CRW). The turning angle at each time step follows the Von Mises distribution with a ϰ of 10. The closer ϰ gets to zero, the closer the Von Mises distribution becomes uniform. The larger ϰ gets, the more the Von Mises distribution approaches a normal distribution concentrated around the mean (0°).

In this script the turning angles (following the Von Mises distribution) are generated based on the the instructions from N. I. Fisher 2011.

This model is implemented in Javascript and can be used as a building block for more complex agent based models that would rely on describing the movement of individuals with CRW.

The first simple movement models used unbiased and uncorrelated random walks (RW). In such models of movement, the direction of the movement is totally independent of the previous movement direction. In other words, at each time step the direction, in which an individual is moving is completely random. This process is referred to as a Brownian motion.

On the other hand, in correlated random walks (CRW) the choice of the movement directions depends on the direction of the previous movement. At each time step, the movement direction has a tendency to point in the same direction as the previous one. This movement model fits well observational movement data for many animal species.

The presented agent based model simulated the movement of the agents as a correlated random walk (CRW). The turning angle at each time step follows the Von Mises distribution with a ϰ of 10. The closer ϰ gets to zero, the closer the Von Mises distribution becomes uniform. The larger ϰ gets, the more the Von Mises distribution approaches a normal distribution concentrated around the mean (0°).

This model is implemented in python and can be used as a building block for more complex agent based models that would rely on describing the movement of individuals with CRW.

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