Appendix A. Literature sources for height data.

Literature sources for height data

Appendix B. The results of the principal components analysis of the six functional traits quantified for all of the species in the LFDP.

The results of the principal components analysis of the six functional traits quantified for all of the species in the LFDP

Appendix A. Tables showing (1) scaling relationship, species, sample size (n), R2 value, slope, intercept, and lower and upper 95% slope confidence limits for the species in this study, and (2) species, observation number, and log-transformed values (save bulk tissue density) for the leaf dimensions considered in this study.

Tables showing (1) scaling relationship, species, sample size (n), R2 value, slope, intercept, and lower and upper 95% slope confidence limits for the species in this study, and (2) species, observation number, and log-transformed values (save bulk tissue density) for the leaf dimensions considered in this study

First and second order effects.

<p>First-order effects describe all datasets, while second-order effects may provide scale-dependent approaches for distinguishing datasets.</p><p>First and second order effects.</p

Distribution of objects across categories and space.

<p>Left column, site locations for each dataset (colored as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0112850#pone-0112850-t002" target="_blank">Table 2</a>). Site brightness is proportional to richness. Right column, relative abundance distribution for log-transformed abundance data at full scale (a first-order effect). All datasets are shown with the same axes.</p

Central moments of the species-abundance distribution for log-transformed data.

<p>Line colors are described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0112850#pone-0112850-t002" target="_blank">Table 2</a>.</p

Summary statistics for each economic, ecological, and geological dataset.

<p>Maps display higher species richness at each site in brighter colors. In all subsequent graphs we have used the line-coloring scheme shown here.</p><p>Summary statistics for each economic, ecological, and geological dataset.</p

A general model for metabolic scaling in self-similar asymmetric networks

<div><p>How a particular attribute of an organism changes or scales with its body size is known as an allometry. Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. Perhaps the most central biological allometry is how metabolic rate scales with body size. A core assumption of the WBE model is that networks are symmetric with respect to their geometric properties. That is, any two given branches within the same generation in the network are assumed to have identical lengths and radii. However, biological networks are rarely if ever symmetric. An open question is: Does incorporating asymmetric branching change or influence the predictions of the WBE model? We derive a general network model that relaxes the symmetric assumption and define two classes of asymmetrically bifurcating networks. We show that asymmetric branching can be incorporated into the WBE model. This asymmetric version of the WBE model results in several theoretical predictions for the structure, physiology, and metabolism of organisms, specifically in the case for the cardiovascular system. We show how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber’s Law can still be attained within many asymmetric networks.</p></div

The fraction of species for which intra-specific clumping is consistently high at very small and very large scales.

<p>Among datasets, the clumping varies widely in magnitude with spatial scale. Line colors are described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0112850#pone-0112850-t002" target="_blank">Table 2</a>.</p

Appendix C. Example of bias resulting from fitting discrete data with continuous maximum likelihood solutions.

Example of bias resulting from fitting discrete data with continuous maximum likelihood solutions