Analysis of prehistoric biological variation under a model of isolation by geographic and temporal distance

Biological distances calculated between archeologically recovered human skeletal collections are often used to assess the effects of temporal and spatial distance on subpopulation divergence. Although there are many previous empirical studies that examine skeletal material arrayed across time and/or space, the theoretical expectations for temporally or spatially related variation in biological characteristics have not been formally developed. In this paper I present the infinite island model, the unidimensional stepping-stone model, and the migration matrix method in forms that allow prediction of the genetic distance between groups separated by a given spatial and temporal lag. These models demonstrate that, if there is isolation by geographic distance, then the correlation between genetic and spatial distance (controlling for temporal distance) should be positive and the correlation between genetic and temporal distance (controlling for spatial distance) should be negative. I use observations of nonmetric traits in a sample of prehistoric crania from west-central Illinois to demonstrate the expected relationships among biological, temporal, and spatial distance. The results indicate that, once the effects of temporal trend are removed, biological and spatial distance are positively correlated and biological and temporal distance negatively correlated within this sample.