Michael Heads has calibrated the origin of the various primate groups to several tectonic events involved in the breakup of Pangaea.
New and Old World Monkeys diverged 120 million years ago when the Atlantic opened. Lemurs diverged from their closest relatives when the Mozambique Channel opened 160 million years ago, and the deepest split in the primate tree, between the haplorhines (monkey, apes, and tarsiers) and strepsirrhines (lemurs and lorises) is 180 million years ago in the Early Jurassic.
This is a problem. The earliest known primate fossil is Purgatorius from the Upper Cretaceous of the USA. (Well maybe. A recent paper in Nature indicates that it isn't a primate but the sister group to placentals as a whole.) Other than that the earliest primates turn up in the Eocene, about 56 million years ago. Molecular divergence times however put the split between primates and their closest living relatives the Dermopterans (the Colugos or "flying lemurs") at about 80 million years.
He is right in pointing out that the previously accepted dates are indeed the minimum dates. Any new fossil discovery could shift them by several million years. Just a week or so ago some tetrapod footprints were found that indicated that tetrapod evolution occurred about 10-20 million years earlier than we thought, creating "ghost lineages", spans of time where no fossils are known, but are expected.
If Heads' model of primate evolution is correct then it creates ghost lineages of 100 million years. This, to me, seems rather excessive. Defending this he points out that several groups do not have a fossil record, yet must be very old, while other modern groups are only known from a few very early fossils (he mentions proscopiid grasshoppers from 110 million years ago). Fair enough, but the molecular dates indicate a ghost lineage of about 25-30 million years from the earliest fossils to the latest divergence times. Increasing this by four times really needs rather more support than he gives it. A new fossil would be enough to make people think.
He is correct in his statements that molecular dates (however they are calibrated) are generally minimum dates, but he repeatedly states that they are "transmogrified" into maximum dates. I can't find any detailed criticism from this paper as to how this is done (do the authors just swap words around? Or are there mathematical tricks that can get you this result?)
Moreover where Heads' paper also falls down is in his refusal to accept that rafting can play a part in evolution and dispersal. It is generally accepted that chameleons originated on Madagascar and then spread. Frogs have made it to Madagascar from Indonesia, and this week a paper was published in Nature showing how ocean currents in the Eocene would have allowed lemurs to raft across the Mozambique Channel, but would prevent them doing so today. He also fails to take into account that the separation of continents is not a simple matter. The North Atlantic began to appear in the Cretaceous, but there were extensive connections between Europe and North America throughout the Eocene, allowing animals to island hop across. I see no reason why South America and Africa would be different.
He doesn't address the issue of why we have a nice transitional sequence of various primate groups in the Eocene, but that isn't necessarily a problem- the footprint paper in Nature gave us the same problem to deal with. However the footprints are evidence for the existence of tetrapods at a particular time period. Heads has not presented any physical evidence to back up his claims, rather he's taken the current distribution of primate groups as evidence that they always lived in these areas, and matched them up with past events. Would he have got the same results if he had used a different group? And if not what does that say about his methods?
Finally, other than ascribing a date of 185 million years to the split at the base of the Archonta (the larger group uniting Primates, Tree Shrews, and Colugos) he says nothing about what this data means for the diversification of other placentals, marsupials or indeed the origin of mammals as a whole. Without running the mathematics I can't help get the feeling that were this paper correct it would push the origin of mammals somewhere into the Permian. Which seems, shall we say, extremely unlikely given the fossil record we have there.
As they say, extraordinary claims require extraordinary evidence.
Michael Heads: Evolution and biogeography of primates: a new model based on molecular phylogenetics, vicariance and plate tectonics, Zoologica Scripta, Published Online: Nov 10 2009 4:44AM DOI: 10.1111/j.1463-6409.2009.00411.
J. R. Wible, G. W. Rougier, M. J. Novacek & R. J. Asher: Cretaceous eutherians and Laurasian origin for placental mammals near the K/T boundary, Nature 447, 1003 - 1006 (21 June 2007)