Knowledge Base

Definition

Meander is the change in direction of movement of a subject relative to the distance moved by that subject. It provides an indication of how convoluted the subject's trajectory is. Meander can be relative or absolute:

• Relative Meander: The change in direction is signed. With a default position of the Calibration axes (x-axis pointing to the right; y-axis pointing upward), a clockwise turn is scored as negative value because turn angle is negative; a counterclockwise turn is scored as positive. With other orientations of the x- and y-axes, the same turn may have different sign, depending on the relative turn angle. See Turn angle for how turns are given positive vs. sign.
• Absolute Meander: The turn angle that measures the change in direction is unsigned. Meander is therefore always positive.

Calculation

Where RMk is Relative Meander, RTAk is the Relative Turn angle and DMk is the Distance moved at sample k. Absolute Meander is the absolute value of the Relative Meander.

You can calculate Meander in two ways:

• Based on body points: Meander is calculated from the turn angle and the distance moved of the specified body point, as shown in the figure above.
• Based on Head direction: Meander is calculated from the turn angle based on the Head direction line and the distance moved by the nose point.

Range

Given the formula above, Relative Meander can range from -∞º/cm to +∞º/cm, while Absolute Meander from 0°/cm to +∞°/cm. When DM is very small, Meander can get high, unrealistic values. One case when DM is very small is when you use a high sample rate and the subject does not move significantly.

TIP: Before running analysis, make sure you use Track Smoothing to remove very small values of distance moved from your tracks.

See also Troubleshooting: Statistics > I get unrealistic values of path shape and direction.

How to Specify Meander

1. Click the Add button next to Meander and click the Meander tab. Select Absolute or Relative.
2. Select Head direction meander (body point is ignored) if you want to calculate meander based on the head direction line.
3. Click the Body points tab and select the body points for which you want to calculate meander. By default, Center-point is selected.
4. Complete the procedure to add the variable. See Calculate statistics: procedure.

Notes

• If your experiment is set to Only center-point detection or Color marker tracking, the Body points tab is absent. Calculations are based on the center point.
• Meander is very sensitive to small, random movements of the body points. When the animal sits still, Meander can get very high, unrealistic values. To remove such small movements from your data, smooth the tracks, then run analysis.

Application

• The Relative Meander is a measure for the direction of turning per unit distance. This dependent variable can be of additional value to other turn bias variables, such as relative Turn angle and relative Angular velocity, since the turn bias is 'corrected' for the distance moved. For instance, if two individuals move at different speeds, the two can have very different values for the mean relative Turn angle, but at the same time have identical values for the mean relative meander.
• The Absolute Meander is often used in combination with the dependent variables absolute Turn angle and absolute Angular velocity to study turning rates. Bell (1991) reports that in most studies, when plotting the values, absolute Meander generates a smoother curve than absolute Angular velocity. This is caused by the fact that the latter dependent variable is influenced both by speed as well as by real turning rate. See Bell (1991). Searching Behaviour: The Behavioural Ecology of Finding Resources. Chapman & Hall, London.
• In rodent models of aging, the average meander is used to calculate the frailty index. See Parks et al. (2012) J. Gerontol. A 67(3): 217-227.

Definition

The direction of movement of the nose, center or tail-base point of the current sample relative to a line parallel to the x-axis in the coordinate system. 'Compass heading' and 'compass angle' are synonyms for Heading. See also Heading to point.

Calculation

Heading is calculated in three steps:

1. The smallest angle α is found between the reference line and the vector connecting the samples k–1 and k. The figure below shows the relationship between the angle α formed by the segment joining samples k-1 and k, the horizontal line parallel to the x-axis, and the dependent variable Heading (HE). Four cases are illustrated, corresponding to the possible directions an animal's body point can be moving relative to the x-axis. Here, it is assumed the x-axis is horizontal and pointing to the right, and the y-axis is pointing upward.

2. The value of α is calculated according to the formula, where:

   • DMk is the distance moved at sample k.
   • Xk and Xk-1 are the x-coordinates of the center, nose or tail-base point at sample k and k–1, respectively.

   Because the way α is defined, it can only range from 0° to 90°.

3. How to convert α to Heading depends on the direction of movement between samples k–1 and k. The relation between Heading and α is determined by the following rules:

   • If ΔX > 0 and ΔY ≥ 0, then Heading = α.
   • If ΔX ≥ 0 and ΔY < 0, then Heading = -α.
   • If ΔX < 0 and ΔY ≤ 0, then Heading = -(180 - α).
   • If ΔX ≤ 0 and ΔY > 0, then Heading = 180 - α.

   Where ΔX = Xk - Xk-1 and ΔY = Yk - Yk-1.

Range

Heading ranges from -180° to +180°.

How to Specify Heading

1. Click the Add button next to Heading.
2. Complete the procedure to add the variable. See Calculate statistics: procedure.

Notes

• If your experiment is set to Center-point, nose-point and tail-base detection, click the Body points tab and select the body points for which you want to calculate heading.
• The mean, standard deviation and variance are calculated with circular statistics. See Statistics available.
• Heading is calculated relative to the orientation of the x-axis you have chosen in the Arena Settings used for that trial. By default, the x-axis is horizontal and pointing to the right. If the x-axis is not horizontal or is pointing to another direction, Heading is calculated based on that axis direction.

Application

Heading is used in studies of spatial orientation. For example, you can use it to determine the direction of flight of a moth relative to the direction of the air flow in a wind tunnel. In a Morris water maze test, you can use this variable to measure initial heading of the path after releasing the animal in the basin.

Source: EthoVision XT 19 Help, Noldus Information Technology