Appendix C. Derivation of Theorem 4.

Derivation of Theorem 4

Appendix D. A discussion of the statistical significance of results.

A discussion of the statistical significance of results

Appendix E. Division-specific estimate of aggregation parameter.

Division-specific estimate of aggregation parameter

Appendix A. Derivation of Theorem 1.

Derivation of Theorem 1

Appendix B. Derivation of Theorem 2.

Derivation of Theorem 2

Conlisk_etal_richness

Species cove

Map of plot and transects on elevation contour map (in meters above sea level).

<p>Burned area is shaded.</p

Non-metric multidimensional scaling (NMDS) of vegetation composition (in % aboveground cover for each species) in unburned (dark blue arrows) and burned (light blue arrows) communities, moving from 2012 (tail of arrow) to 2013 (point of arrow) for all plots (faint arrows) and the mean and standard error of the burn by year combination (stress = 0.24).

<p>Error bars are standard deviations across plots of the NMDS1 and NMDS2 values. Species abbreviations are defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162777#pone.0162777.t001" target="_blank">Table 1</a> and color coded by their functional type (green are the native annual forbs, dark blue are native perennial forbs, light blue codes are native shrubs, red codes are non-native grasses, and black codes are non-native forbs). The location of the abbreviation on the plot shows its correlation with the axes.</p

Average percent cover of each species in burned and unburned plots.

<p>Average percent cover of each species in burned and unburned plots.</p

Appendix A. Derivation of the hypothesis of equal allocation probabilities (HEAP) from an assembly function.

Derivation of the hypothesis of equal allocation probabilities (HEAP) from an assembly function