Cs: Coefficient of Sociality

Description Usage Arguments Details Value References See Also Examples


The function Cs computes the coefficient of sociality between two moving objects following the methods outlined by Kenward et al. (1993). It also uses a signed Wilcoxon-rank test to test for significance.


Cs(traj1, traj2, tc = 0)



an object of the class ltraj which contains the time-stamped movement fixes of the first object. Note this object must be a type II ltraj object. For more information on objects of this type see help(ltraj).


same as traj1.


time threshold for determining simultaneous fixes – see function: GetSimultaneous.


This function can be used to calculate the Kenward et al. (1993) coefficient of sociality (Cs) between two animals. The Cs statistic tests the observed mean distance between simultaneous fixes against that expected by the overall distribution of distances between all fixes.


Where Do is the mean observed distance between simultaneous fixes, and De is the mean expected distance between all fixes. Kenward et al. (1993) propose Cs as a useful metric for exploring attraction or avoidance behaviour. Values for Cs closer to 1 indicate attraction, while values for Cs closer to -1 indicate avoidance. Values of Cs near 0 indicate that the two animals' movements have no influence on one another.

Further, the difference between the observed and expected distances are compared using a paired signed-rank test (both one-sided tests, indicative of attraction or avoidance). See the function GetSimultaneous for details on how simultaneous fixes are determined from two trajectories.


This function returns a list of objects representing the calculated values from the Cs statistic and associated p-values from the signed rank test.

  • Do – The mean distance of simultaneous fixes.

  • De – The mean expected distance, from all fixes.

  • Cs – The coefficient of sociality, see Details.

  • p.Attract – One sided p-value from signed rank test, testing for attraction.

  • p.Avoid – One sided p-value from signed rank test, testing for avoidance.


Kenward, R.E., Marcstrom, V. and Karlbom, M. (1993) Post-nestling behaviour in goshawks, Accipiter gentilis: II. Sex differences in sociality and nest-switching. Animal Behaviour. 46, 371–378.

See Also



deer37 <- deer[1]
deer38 <- deer[2]
#tc = 7.5 minutes
Cs(deer37, deer38, tc = 7.5*60)

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