Net distances to other cows

Mean
 
Median
 
Minimum
 
# cows within 2 m radius
 
# cows within 4 m radius
 
# cows within 8 m radius
 
# cows within 16 m radius
 
All mean cow coordinates

Group elongation index, φ

Variance explained by the first principal component through the mean x and y coordinates of all cows. Value lies by definition between 0.5 (when completely nonelongated, e.g., an exact circle) and 1 (when all coordinates lie on a straight line). Afterwards scaled between 0 and 1, by subtracting 0.5 and multiplying by 2.

Group area proxy

πσ^{2}(1 − φ); where σ is the standard deviation of the first principal component values. This measure assumes that the area can be estimated by considering the group as an ellipse. When completely nonelongated the area is πσ^{2} (where the variance σ^{2} is a proxy for the extent of the direction of elongation) and when fully elongated the area is 0.

Directions to other cows

ρ

Length of the mean resultant vector

Periphery index

Maximum difference between consecutive directions, minus \( \frac{2\pi }{\# cows1} \) and divided by 2π
