The Pre-Settlement Vegatation of the Western and Central Wimmera Plains of Victoria,Australia

Historical records indicate that the fertile soils of the western and central Wimmera Plains of Victoria, Australia formerly supported grassy woodlands on rises and flats, and grasslands on shallow depressions and clay plains. Soil type and micro-relief appear to have been the major factors that determined the distribution of these communities. Burning of the woodlands by Aborigines may have contributed to their open grassy nature. The few ungrazed remnants of Buloke (Allocasuarina luehmannii) woodland support a suite of species that are absent from or uncommon in other Buloke woodland remnants in the region. This work demonstrates that in districts where little intact native vegetation remains, investigation of the distribution and floristic composition of the pre-settlement vegetation can provide useful information for the maintenance and restoration of remnant vegetation.     

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.