After the first mission, the number of cats remaining on the island was 1800-600 = <<1800-600=1200>>1200.
If half of the remaining cats on the island were relocated to a rescue center inland, the number of cats taken by the wildlife service on the second mission is 1200/2 = <<1200/2=600>>600 cats.
The number of cats remaining on the island is 1200-600 = <<1200-600=600>>600
#### 600