Components of error in predictions of species compositional change

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Abstract
A method is given for measuring two components of error (rate and direction) in predictions of compositional change through time. Observed compositional change between two times can be represented as a vector between two points in multidimensional species space. The point at the tail of this vector is the species composition at one particular time. A vector of predicted compositional change will diverge from the vector of observed change to some degree. The error in the predicted rate of change is measured by the difference between the lengths of the two vectors. The error in the predicted direction of change is measured by the angle between the vectors. The cosine of this angle is a non‐standardized correlation coefficient (rn) between the predicted and observed species compositions. The quantity 1 ‐ rn2 measures the error in direction of the predicted dynamics without being influenced by the overall rate of change. These measures in Euclidean space have useful counterparts in city‐block space. The method is illustrated by comparing actual long‐term changes in Midwestern old‐growth forests with the changes predicted by a growth and yield model, TWIGS.