The cats were brought to remove snakes by Agia Eleni . this is the reason of their population . This is from Cyprus tourist organistaion :
Situated on Cape Gata south east of Akrotiri Salt Lake near Lemesos (Limassol), Agios Nikolaos ton Gaton (St Nicholas of the Cats) is perhaps the first monastery in Cyprus. The present church probably dates to the late 14th century. Abandoned in the late 16th century, it was re-occupied by Orthodox nuns in the early 1980s. According to tradition, the monastery was founded in the 4th century by Agia Eleni, mother of Constantine the Great, who left a piece of wood from the Holy Cross there. At the time, the island was experiencing a severed rought, forcing many people to leave the island. Snakes multiplied and life in Cyprus, particularly at Akrotiri peninsula was unbearable. According to the medieval historian Stephen Lusignan, after Agia Eleni's departure, Constantine the Great sent governor Kalokeros to Cyprus who brought thousands of cats to the island to exterminate the snakes.
There are still thousands of cats in that place, probably direct descendants from the snakes’ exterminators. And judging by the look of some, there must have been some wild cross-breeding between cats, snakes and perhaps even nuns involved…