COS 74-7 - Exploring spatial autocorrelation and spatial random effects in tree species distribution models with the forest inventory and analysis data

Wednesday, August 10, 2011: 3:40 PM
8, Austin Convention Center
Sydne Record1, Matthew C. Fitzpatrick2, Aaron M. Ellison1 and Andrew O. Finley3, (1)Harvard Forest, Harvard University, Petersham, MA, (2)Appalachian Lab, University of Maryland Center for Environmental Science, Frostburg, MD, (3)Forestry and Geography, Michigan State University, East Lansing, MI

Spatial autocorrelation (SAC) - where locations closer together are more similar than places that are further apart – is a common occurrence in biology, but many models that forecast how species may respond to climate change do not account for such spatial structure. Sedentary organisms that are dispersal limited, such as many trees, are likely to exhibit spatial autocorrelation, but most published models of the responses of tree species’ range shifts to climate change are non-spatial. In this study, we hypothesize that the geographic distributions of trees in the eastern United States exhibit SAC. To test this, we calculated Moran’s I, a statistic that measured global spatial autocorrelation, for 137 species of trees using the United States Forest Service’s Forest Inventory and Analysis (FIA) data. To compute Moran’s I values, generalized least square models were fit for each species then we tested for SAC in the model’s residuals. For these models the response variable was the square-root transformed basal area per acre for a given FIA plot and the predictor variables were the current mean annual precipitation, minimum annual temperature, and slope of the plot. If SAC was significant, the second objective was to determine whether a spatial autoregressive linear model with spatial random effects performed better than the non-spatial model.


All 137 species of trees exhibited significant global SAC (Moran’s I P < 1 × 10-7) confirming our hypothesis that trees would exhibit non-random spatial structure. Moran’s I values can range between negative one and one where values of zero refer to random spatial structure, negative values refer to non-random spatial dispersion, and positive values indicate spatial clustering. The Moran’s I values for all of the species tested were positive suggesting clustered spatial structure. For many species, a spatial autoregressive linear model had a much lower Akaike Information Criteria value (for some species up to ~100 units) than the non-spatial generalized least squares model. This information suggests that the exclusion of a spatial random effect in species distribution models could lead to poor estimates of species distributions under future climates if the study organism exhibits spatial autocorrelation. Whether or not corrections for present day spatial autocorrelation are temporally and spatially transferable to novel situations is an open question. Projecting these models back in time then validating the results with the pollen record is an obvious next step in answering this question.

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