It’s currently dewlapping mayhem down here at the moment, with all species except the late-rising Cuban knight anoles (A. equestris) out and showing off!
Visual displays such as dewlap extensions are often used to mediate physical interactions by acting as an indication of the relative size, strength, and fitness of each individual. This is beneficial for both parties; dominant individuals do not have to waste energy that a physical interaction would require, and weaker individuals avert the risk of physical injury (of course, both reasons are reciprocal to both individuals also).
However, when two individuals cannot determine dominance through visual communication, for example if two individuals are equally matched in size, then an aggressive and physical confrontation may occur (read a previous account of one such interaction between two equally-sized males here). The results of these interactions are apparent in many injurious forms, for example through extensive bite marks to the body (as previously discussed here and here), or perhaps even to the extent of tail loss (as discussed here).
Yesterday (9 March 2017) I observed this male Puerto Rican crested anole (A. cristatellus) below that looks like another male had taken a good bite at him!
Of course, there are many avenues through which such an injury may appear. However, the presence of a still-erect nuchal crest paired with how fresh the wound looks (and the time of year!) gives me the impression that this was probably the result of an intraspecific male-male interaction.