Exploring spatial vegetation dynamics using logistic regression and a multinomial logit model

1. This study presents statistical methodology that uses spatial explanator y variables to improve simpler estimates of transition probabilities from c ategorical data, such as vegetation type, that have been recorded as classi fied cells (pixels) in a grid or lattice at different times. 2. A specific application is to examine successions in semi-natural vegetat ion in north-east Scotland. Questions related to these data include: Do tra nsition probabilities of a pixel depend on the size of a patch of vegetatio n (polygon) and pixel location within the polygon? Do stable areas remain s table? Does the proximity of certain vegetation types influence transitions ? 3. We selected spatial variables that were likely to be important in this a pplication, where short-range vegetative spread was thought to be an import ant factor. 4. The multinomial logit model is used to estimate the transition probabili ties as a function of explanatory variables, including location, neighbourh ood information and other factors recorded at the start of the transition p eriod. This model allowed the testing of different assumptions about the dy namics of underlying processes leading to transitions. 5. When the number of categories, for example vegetation types, observed is large in comparison to the sample size, estimates of transition probabilit ies can be unreliable. We show that using change of category within the tim e period as the response in a logistic regression can still provide insight to the underlying dynamics of change in such a case. 6. The methods are illustrated with some Scottish vegetation classification data with pixels of size 5 x 5 in covering a square of area 0.25 km(2). Tw o contrasting squares were investigated: the first was upland moorland graz ed by sheep and the second was a lowland area with more varied vegetation a nd low intensity grazing by cattle. 7. In both squares there are strong spatial trends, and the neighbourhood o f a pixel affected its transition. Prediction misclassification rates estim ated from different models were compared using K-fold cross-validation. The multinomial model, including position in the square and number of neighbou ring pixels in the same category as the pixel modelled, reduced the misclas sification rate compared with the model without spatial explanatory variabl es. 8. The improved estimates of transition probabilities could be incorporated into Markov models used in simulation studies to predict future vegetation changes under different management strategies.