Iceland's Only Native Land Mammal Is The Arctic Fox
Iceland was first settled in the ninth century and then the only native land mammal was the Arctic Fox. These animals came to the island at the end of the ice age, walking over the frozen sea. Other animals were brought to the island by settlers. There are from 8,000 to 10,000 Arctic Foxes living in Iceland and their status in the International Union for Conservation of Nature Red List is Least Concern.
I can respect the need to control population growth. However, I am baffled by your choice to characterize the policy as "admirable in these times".