This plant was originally planted in UBC Botanical Garden as Acaena magellanica, which is native to both New Zealand and Patagonia. A subsequent determination suggested the species is closer to Acaena tenera, a species of Tierra del Fuego and South Georgia Island. The identification remains elusive with the resources we have on hand. However, it has been transplanted in UBC Botanical Garden from the Australasian section of the Alpine Garden into the South American section for the time being.
Botany resource link: Adaptations and economic uses of rainforest plants via the Missouri Botanical Garden.