A non-stationary spatial generalized linear mixed model approach for studying plant diversity

We analyze the multivariate spatial distribution of plant species diversity, distributed across three ecologically distinct land uses, the urban residential, urban non-residential, and desert. We model these data using a spatial generalized linear mixed model. Here plant species counts are assumed to be correlated within and among the spatial locations. We implement this model across the Phoenix metropolis and surrounding desert. Using a Bayesian approach, we utilized the Langevin--Hastings hybrid algorithm. Under a generalization of a spatial log-Gaussian Cox model, the log-intensities of the species count processes follow Gaussian distributions. The purely spatial component corresponding to these log-intensities are jointly modeled using a cross-convolution approach, in order to depict a valid cross-correlation structure. We observe that this approach yields non-stationarity of the model ensuing from different land use types. We obtain predictions of various measures of plant diversity including plant richness and the Shannon--Weiner diversity at observed locations. We also obtain a prediction framework for plant preferences in urban and desert plots.