##
COS 13-1
Robustness of Taylor's law under spatial hierarchical groupings of forest tree samples

**Background/Question/Methods**

Interpreting the spatial variations of the population size or density of species in nature is a central challenge in ecology. One of the well-tested empirical patterns that quantify population fluctuations is Taylor’s law (TL). TL states that the variance of population density for a single (or a group of) species is a power-law function of the mean density. Testing TL requires grouping sampling areas of the species habitat into “blocks”, so that the means and variances of species densities over all sampling areas within a block can be calculated, and the linearity between the log mean and the log variance across blocks can be tested. How specific grouping of sampling areas into blocks affects TL and its parameters remains unknown. Using tree basal area density data from the Black Rock Forest, we analyzed the impact of 4 biologically distinct grouping methods on TL. To test if the agreement to TL was a statistical artifact or an ecological consequence of the biological method, 4 kinds of randomizations were performed to the biological groupings and tree census. These randomizations randomly assigned sampling areas to blocks, and/or randomized the species composition within or across sampling areas.

**Results/Conclusions**

** **We found that TL held for tree basal area densities under 4 biological methods of grouping sampling areas into blocks, and all 4 methods yielded statistically similar estimates of the slope of TL. Thus the form (i.e., the linear relationship between log mean and log variance) and the slope of TL were robust with respect to the method of grouping. To our surprise, none of the randomized groupings of sampling areas into blocks destroyed the form of TL or altered the slope of TL. These results implied that the form and the slope of TL cannot reflect the biological assumptions or details of the grouping methods. However, when we randomly permuted tree species within and among sampling areas, the slope parameter of TL changed significantly. This result showed that the species composition of sampling areas has a bigger impact on the slope of TL than does any particular grouping method. Overall, the robustness of the form of TL under various grouping methods suggested that TL must intrinsically relate to the shared or common frequency distribution of all observed basal area densities, since this frequency distribution was the only information left unchanged in the testing of TL after randomizations.