Gnawed bark, Anguilla Minimize

March 2013. Can anyone suggest what might be causing the trees in these pictures to be gnawed/debarked like this? We have seen this recently, and believe it might be a monkey, but are also aware that rats are capable of this kind of damage. However, the level of debarking is extensive in some areas; We tried to set up a camera, but to no avail. The location is Anguilla, Caribbean.

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