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Net distances to other cows
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Mean
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Median
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Minimum
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# cows within 2 m radius
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# cows within 4 m radius
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# cows within 8 m radius
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# cows within 16 m radius
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All mean cow coordinates
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Group elongation index, φ
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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 non-elongated, 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.
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Group area proxy
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πσ2(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 non-elongated the area is πσ2 (where the variance σ2 is a proxy for the extent of the direction of elongation) and when fully elongated the area is 0.
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Directions to other cows
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ρ
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Length of the mean resultant vector
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Periphery index
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Maximum difference between consecutive directions, minus \( \frac{2\pi }{\# cows-1} \) and divided by 2π
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