The first species to go extinct as a result of human-caused climate change anywhere in the world appears to have been Australian.  The tiny rodent called the Bramble Cay Melomys might be the tip of the rapidly melting iceberg.

The Melomys lived on Bramble Cay, a tiny island in the eastern Torres Strait.  Situated closer to Papua New Guinea than the Australian mainland at Queensland, the small coral cay is just 340 meters long and 150 meters wide and is only three meters above the water line at its highest point. 

Europeans first noticed the Melomys in 1845, and several hundred were believed to live on the island in 1978.  But these appeared to be gone by 2009; and in 2014, an exhaustive survey of the island concluded that that rats wouldn't bounce back.  A report (.pdf link) from Queensland's Department of Environment and Heritage Protection - in partnership with the University of Queensland - determined that Bramble Cay had been inundated several times by sea water, killing the animals and destroying their vegetation in their habitat.  

Globally, averaged sea level has risen by almost 20 centimeters from 1901 to 2010.  But the Sea Level around the Torres Strait appears to be rising twice as fast as the rest of the world. "Significantly, this probably represents the first recorded mammalian extinction due to anthropogenic climate change," the researchers said in their report.

Ecologist John White from Deakin University in Australia says, "I am of absolutely no doubt we will lose species due to the increasing pressures being exerted by climate change."  He added, "Species restricted to small, low lying islands, or those with very tight environmental requirements are likely to be the first to go," cautioning that the Melomys wouldn't be the last.

A study published two months ago said that one in six of the world's species will be lost as a result of man-made global warming.  And creatures in Australia, New Zealand and South America will be hit much harder than North American and Europe, due to a high number of species not found anywhere else.