Neolithic Transition Single-Species Models

In order to make a comparison with archaeological data possible for this process, one needs a more detailed microscopic model than the RD model. Such a model should (i) apply to two-dimensional (2D) spaces and (ii) relate the macroscopic parameters of the evolution equation to the microscopic properties of the system [87]. We consider here the RT model and compare its predictions with observations [137]. The RT equation in 2D reads 

Mendez et al., Reaction-Transport Systems, Springer Series in Synergetics, DOI 10.1007/978-3-642-11443-4 7, Springer-Verlag Berlin Heidelberg 2010 

The time T is estimated as the time of travel, on the order of days or weeks, plus the time of residence, i.e., the time interval between the arrival of a family and the subsequent migration, on the order of a generation [358]. This implies that in our case T is approximately the time of residence or the waiting time during the rest phase of the population. 

We assume that the population growth can be described by the logistic growth function F p) = p( - /o/Pmax) where p is the saturation density or carrying capacity. This growth function compares favorably with a wealth of experimental results [256]. Equation (7.1) leads to wavefronts with asymptotic velocity, see (5.60), 

Here r /r is the invaded area during the time interval T that separates two successive migrations. Previous approaches did not take the factor 1/4 in (7.5) into account but relied on the approximation ) a /r [13], 

---