Parameter esimation for stage-structured projection models using real data

Herbivores, particularly introduced ones such as sheep and rabbits, have reduced the levels of regeneration of a number of species of native trees and shrubs in the arid rangelands of southern Australia since European settlement. These reduced levels of regeneration mean that populations of some species are declining whilst others, less palatable to herbivores, are being maintained, hence gradually altering the composition and/or overall cover of vegetation. In the long term, this could result in loss of palatable species valuable to the pastoral industry for animal production. To investigate the effects of grazing, we describe a model which projects the age-structured populations of some native Australian tree and shrub species under grazing and non-grazing regimes. The technique we are applying is an extension of the Leslie growth model, where the grazing and rainfall events are incorporated by the use of separate transition matrices. The preliminary results indicate that rangeland management practices will need to be adjusted to ensure the longterm sustainability, biodiversity and usability of the arid regions. The purpose of this paper is to frame the context for study in the application of this methodology, as well as to indicate the problems involved in parameter estimation and delineate the extent of our deliberation thus far.