Spatial distribution of trees and landscapes of the past: A mixed spatially correlated multinomial logit model approach for the analysis of the public land survey data

Public Land Survey (PLS) data have been widely used in landscape studies of forest and woodlands in the pre- and early-European-settled Midwestern and Western United States. We aim to reconstruct presettlement forest vegetation at a finer spatial resolution than available from the PLS data using environmental covariates (slope, aspect, geology, and soil type) and the spatially correlated structure of witness tree data. To accommodate various data obtained from multiple sources while explicitly taking into account their spatial structures, we adopt a mixed spatially correlated multinomial logit model within the framework of a generalized linear mixed model. The application of the proposed model is illustrated using the three most abundant tree taxa from PLS data in the Arbuckle Mountains of south-central Oklahoma. To assess the influence of each source of information on the spatial prediction, we considered four variant multinomial/spatial models and evaluated their relative predictive power using a validation technique. The probabilistic information about the spatial distribution of tree species obtained from different models reveals the need to integrate information about witness tree data as well as environmental covariates, and the nature of tree species; that is, a tendency to cluster in space to share environmental conditions in the reconstruction of the presettlement forest vegetation surface.