Trend analyses of hierarchical pin-point cover data.

The use of state-space models for analyzing longitudinal hierarchical pin-point plant cover data is demonstrated. The main advantages of using a state-space model are (1) that the observed variance is separated into sampling variance and the more interesting structural variance which are needed for quantifying prediction uncertainty, (2) that missing values or an unbalanced sampling design readily may be accounted for, and (3) that the structural equation easily may be expanded and made as complex as necessary for modeling longitudinal pin-point cover data, thus allowing the incorporation of the most important ecological processes in the state-space model without technical difficulties. Typically, there is considerable spatial variation in plant abundance, and this variation is modeled using the Pólya-Eggenberger distribution (a generalization of the beta-binomial distribution). To illustrate this method, longitudinal hierarchical pin-point data of Erica tetralix in wet Danish heathlands were analyzed, including and excluding autocorrelation and an environmental covariable in the state-space model. The pin-point plant cover data showed a significant decrease in the plant cover of E. tetralix in the period from 2004 to 2009, with an annual decrease of about 10% in the logit-transformed cover. The distribution of predicted plant cover at a given site the following year was calculated, including and excluding the information of an environmental covariable.