Post-glacial environmental change and hunting-gathering societies of the southern Prairie Peninsula

Evidence from several disciplines supports the proposition that following the Wisconsinan and an initial but brief moist phase of the Holocene, there was a gradual drying trend in the mid-continent Prairie Peninsula that peaked about 7000 years ago, a pattern that was not reversed until about 4000 years ago. Except for minor perturbations, conditions during the past four millennia have essentially been similar to those of the present. Studies in palynology and geomorphology have shown that the climatic regimes of the early/mid Post-glacial had a marked influence on both the biota and landscape erosional patterns, especially along the margins of the Prairie Peninsula. Measurable changes in the landscape and attendant biota show a time-transgressive pattern of drought related phenomena recorded palaeo-ecologically from west to east.Few studies of archaeological sites in the Prairie Peninsula have examined the evidence in and around the sites themselves for data reflecting local environmental dynamics. In fact, earlier models proposed for explaining the evolution of food-procuring systems in eastern North America virtually ignored potential changes in the natural environment. This paper examines data from two archaeological sites along the prairie-forest border in Missouri that contain long cultural sequences. Evidence is presented that pronounced changes in the natural environment occurred and that these biophysical variables are indeed critical for understanding the evolution of food-procuring societies in the American Midwest.     

Gravity-Type Interactive Markov Models—Part II: Lyapunov Stability of Steady States

In Part I of this paper (Smith and Hsieh, 1997) a programming formulation of steady states was developed for gravity-type interactive Markov chains in terms of their associated spatial-flow chains. These results are here applied to analyze the stability properties of interactive Markov chains. In particular, the objective function for this programming formulation is shown to constitute a Lyapunov function for an appropriately defined continuous-time version of spatial-flow chains. The Lyapunov stability properties of these spatial flows are then shown to yield corresponding stability properties for the continuous-time versions of interactive Markov chains. In particular, these processes always exhibit global convergence to steady states. Finally, it is shown that when steady states are unique, these convergence results are inherited by those interactive Markov chains that are 'sufficiently close' to their continuous-time versions.