Abstract
Migration is a key mechanism for expansion of communities. In spatially heterogeneous environments, rapidly gaining knowledge about the local environment is key to the evolutionary success of a migrating population. For historical human migration, environmental heterogeneity was naturally asymmetric in the north-south (NS) and east-west (EW) directions. We here consider the human migration process in the Americas, modelled as random, asymmetric, modularly correlated environments. Knowledge about the environments determines the fitness of each individual. We present a phase diagram for asymmetry of migration as a function of carrying capacity and fitness threshold. We find that the speed of migration is proportional to the inverse complement of the spatial environmental gradient, and in particular, we find that NS migration rates are lower than EW migration rates when the environmental gradient is higher in the NS direction. Communication of knowledge between individuals can help to spread beneficial knowledge within the population. The speed of migration increases when communication transmits pieces of knowledge that contribute in a modular way to the fitness of individuals. The results for the dependence of migration rate on asymmetry and modularity are consistent with existing archaeological observations. The results for asymmetry of genetic divergence are consistent with patterns of human gene flow.