Population Expansion in the Western Pacific (Austronesia): A Wave of Advance Model
Fort, Joaquim, Antiquity
The wave of advance model is based on a mathematical formula, which was originally proposed by Fisher (1937) to explain the spread of advantageous genes. It has been applied to the expansion of agriculture in Neolithic Europe, leading to the conclusion that farming originated in the Near East, from where it spread over Europe at a speed of about 1 km/yr (Ammerman & Cavalli-Sforza 1984). Subsequent studies have set out to investigate whether the spread of agriculture was mainly a demic process (physical diffusion of human populations), as opposed to a purely cultural process (diffusion of ideas between neighboring populations) (see Gkiasta et al. 2003). The present paper further investigates the way that the model reports changes in culture and population, by applying it to island communities in the western Pacific. The investigation concerns the Neolithic expansion in western Oceania (Austronesia) as indicated by Lapita pottery and its derivatives. This expansion is also equated to the expansion of population and farming, and in this case, given the distances involved, the expansion is certainly demic, involving the movement of people across the sea. The fact that the populations must farm islands of land separated by sea poses an interesting problem.
Character of the wave of advance model
The intuitive basis for the wave of advance model is as follows. To understand the development of agriculture in the place where a population lives, one needs to take into account two factors: mobility and reproduction. If individuals move, the area occupied will increase in time, and if a population reproduces very quickly its geographical expansion will be faster, because there are more individuals to disperse. Mobility is usually represented by the symbol m, whereas reproduction is taken into account by means of a parameter with the symbol a. These symbols will be explained in more detail below.
The wave of advance model has been recently refined (Fort & Mendez 1999a; 1999b) by taking into account (i) that it is currently applied to two-dimensional population expansions, and (ii) the effect of the diffusive delay due to the mean generation time [tau]. The predicted speed is (Fort & Mendez 1999a)
(1) v = [square root of (am)]/1 + a[tau]/2
where the reproductive parameter a is usually called the initial growth rate of the population the mobility m is the mean square displacement per generation, and [tau] is the mean generation time (mean age difference between parents and their progeny). The reason why [tau] appears in Equation (1) is that usually sons have to grow before they leave their parents. Note that if this point were neglected (i.e., if [tau] were assumed so small that it can be approximately set equal to zero), then Equation (1) would become v = [square root of (am)]. This is almost the formula used by Ammerman and Cavalli-Sforza (1984: 68), namely v = 2 [square root of (am)]. The only additional difference is the factor 2, and is due to the following point. It has been shown (Fort & Mendez 1999a) v = [square root of (am)] that holds in two dimensions (e.g. the Earth's surface), whereas Fisher's result v = 2 [square root of (am)] can be used for populations dispersing in one dimension (e.g. along a coast). When applied to the European Neolithic, Equation (1) leads to a speed of 1 km/yr, which agrees with the value observed from archaeological data (Fort & Mendez 1999a).
The theory which leads to Equation (1) is a straightforward extension of the classical model due to Fisher (1937) and widely used in ecology (Shigesada & Kawasaki 1997; Turchin 1998; Williamson 1996). In both cases, one assumes a tabula ram, or level playing field, in the sense that all areas of two-dimensional space are assumed equally suitable in principle for the settlement of human populations. This provides a macro-model, an approximation to a large-scale, space-averaged description of the observed clustered distribution of sites (Ammerman 2001). …