ECOLOGY

GLOBAL WARMING

Climate Plan in U.S. Threatens European Goals for Global Deal on Emissions

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Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression

A major focus of geographical ecology and macroecology is to understand the causes of spatially structured ecological patterns. However, achieving this understanding can be complicated when using multiple regression, because the relative importance of explanatory variables, as measured by regression coefficients, can shift depending on whether spatially explicit or non-spatial modeling is used. However, the extent to which coefficients may shift and why shifts occur are unclear. Here, we analyze the relationship between environmental predictors and the geographical distribution of species richness, body size, range size and abundance in 97 multi-factorial data sets. Our goal was to compare standardized partial regression coefficients of non-spatial ordinary least squares regressions (i.e. models fitted using ordinary least squares without taking autocorrelation into account; “OLS models” hereafter) and eight spatial methods to evaluate the frequency of coefficient shifts and identify characteristics of data that might predict when shifts are likely. We generated three metrics of coefficient shifts and eight characteristics of the data sets as predictors of shifts. Typical of ecological data, spatial autocorrelation in the residuals of OLS models was found in most data sets. The spatial models varied in the extent to which they minimized residual spatial autocorrelation. Patterns of coefficient shifts also varied among methods and datasets, although the magnitudes of shifts tended to be small in all cases. We were unable to identify strong predictors of shifts, including the levels of autocorrelation in either explanatory variables or model residuals. Thus, changes in coefficients between spatial and non-spatial methods depend on the method used and are largely idiosyncratic, making it difficult to predict when or why shifts occur. We conclude that the ecological importance of regression coefficients cannot be evaluated with confidence irrespective of whether spatially explicit modelling is used or not. Researchers may have little choice but to be more explicit about the uncertainty of models and more cautious in their interpretation.

http://www3.interscience.wiley.com/journal/122261991/abstract?CRETRY=1&SRETRY=0

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THE SMALL ISLAND EFFECT : FACT OR ARTIFACT?

Positive relationships between species richness and sampling area are perhaps the most pervasive patterns in nature. However, the shape of species–area relationships is often highly variable, for reasons that are poorly understood. One such source of variability is the “small-island effect”, which refers to a decrease in the capacity of sampling area to predict species richness on small islands. Small-island effects have been attributed to a variety of processes, including spatial subsidies, habitat characteristics and ocean-born disturbances. Here, we show that small-island effects can be generated by logarithmic data transformations, which are commonly applied to both axes of species–area relationships. To overcome this problem, we derive several null models to test for non-random variability in the capacity of island area to predict species richness and apply them to data sets on island plant communities in Canada and New Zealand. Both archipelagos showed evidence for small-island effects using traditional breakpoint regression techniques on log-log axes. However, null model analyses revealed different results. The capacity of sampling area to predict species richness in the Canadian archipelago was actually lowest at intermediate island size classes. In the New Zealand archipelago, island area was similarly capable of predicting species richness across the full range of island sizes, indicating the small-island effect detected by breakpoint regression is an artifact of logarithm data transformation. Overall results show that commonly used regression techniques can generate spurious small-island effects and that alternative analytic procedures are needed to detect non-random patterns in species richness on small islands.

Abstract

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