A good example is the convergent evolution of a whole range of mammal trades in the separate continents of South America, Australia, and the Old World.
When South America and Australia broke away to begin their long periods of isolation from the rest of the world, they each carried their own cargo of dinosaurs, and also of the less-prominent animals that were to become the ancestors of modern mammals. When, rather later, for reasons that are not understood and are the subject of much profitable speculation, the dinosaurs (with the exception of the group of dinosaurs that we now call birds) went extinct, they went extinct all over the world. This left a vacuum in the 'trades' open to land-dwelling animals. The vacuum was filled, over a period of millions of years of evolution, mostly by mammals. The interesting point for us here is that there were three independent vacuums, and they were independently filled by mammals in Australia, South America and the Old World.
The primitive mammals that happened to be around in the three areas when the dinosaurs more or less simultaneously vacated the great life trades, were all rather small and insignificant, probably nocturnal, previously overshadowed and overpowered by the dinosaurs. They could have evolved in radically different directions in the three areas. To some extent this is what happened. There is nothing in the Old World that resembles the giant ground sloth of South America, alas now extinct. The great range of South American mammals included an extinct giant guinea-pig, the size of a modern rhinoceros but a rodent (I have to say 'modern' rhinoceros because the Old World fauna included a giant rhinoceros the size of a two-storey house). But although the separate continents each produced their unique mammals, the general pattern of evolution in all three areas was the same. In all three areas the mammals that happened to be around at the start fanned out in evolution, and produced a specialist for each trade which, in many cases, came to bear a remarkable resemblance to the corresponding specialist in the other two areas. Each trade, the burrowing trade, the large hunter trade, the plains-grazing trade, and so on, was the subject of independent convergent evolution in two or three separate continents. In addition to these three major sites of independent evolution, smaller islands such as Madagascar have interesting parallel stories of their own, which I shall not go into.
Setting aside the strange egg-laying mammals of Australia - the duck-billed platypus and the spiny anteaters - modern mammals all belong to one of two great groups. These two are the marsupials (whose young are born very small and are then kept in a pouch) and the placentals (all the rest of us). The marsupials came to dominate the Australian story and the placentals the Old World, while the two groups played important roles alongside each other in South America. The South American story is complicated by the fact that it was subject to sporadic waves of invasion by mammals from North America.
