Patagonia narrates the journeys of two women - one looking for her past, the other for her future. The film inter-cuts between their stories, in which one of them travels south to north through the Welsh springtime and the other east to west through the Argentine autumn.
There is a scene after Rhys leaves Gwen, he is driving and comes across a dead dog in the middle of the road. He runs towards the dog hoping to help it but it probably died of dehydration or something. It is later hinted that the dog could be Martin’s dog.
Martin likely suffers from PTSD due to being a soldier in the folklands war. The film does not explicitly tell us that he has PTSD but when we first meet him he steals Rhys’ belongings and they get in a fight which Martin pulls a knife on Rhys.