A Stochastic Model of Ocean-Drift Migration

Abstract

At this stage of the conference it seems a good idea to introduce some history, geography and perhaps a dash of anthropology. The historical content is concerned with the sixteenth and seventeenth centuries when European explorers 'discovered' the Pacific Ocean and found that almost all the habitable islands were or had been occupied. At first this may not seem very startling. But since then, anthropologists have established that the Pacific islands, typically thousands of miles from any continental coastline, were first inhabited about 3,000 years before Europeans had either the technology or the confidence to even attempt trans-oceanic voyages. So it is understandable that the question of the origins of the Pacific islanders has been a centre of debate among Europeans for several centuries. As one author has written '... the controversy has generated much heat, some light and innumerable papers, monographs and books.' Over the years the argument has developed, intensified and particularly centred on the settlement of Polynesia, the triangular region bounded by the Hawaiian Islands in the north, New Zealand in the south and Easter Island in the east (see Figure 1). Until half way through this century the most popular theories for the settlement of Polynesia suggested island-hopping routes from Asia via Melanesia or Micronesia. Any other route from a continent was considered impossible, due to the long ocean voyages involved. It was this attitude which faced Heyerdahl in the 1940's when he postulated the settlement of Polynesia by ocean-drift voyages from the Americas. His theory was not taken seriously until the famous Kon Tiki expedition, in which he sailed a balsa raft from Peru to the Tuomotu Archipelago, which is at about the centre of the Polynesian region. However, as Heyerdahl himself noted, although the Kon Tiki expedition established the plausibility of his theory it was not conclusive proof. In fact such a theory is impossible to prove-all one can do is build up evidence for or against it. That is, one aims to establish the probability of the theory. Levison, Ward and Webb (1973) set up a model for Monte Carlo simulation to estimate the probabilities of successful ocean-drift voyages to and between the islands of Polynesia. Their model had the advantage of simplicity, at least in concept, but suffered from the disadvantage of requiring a very large