Scale collapse and the emergence of the power law species-area relationship

Background/Question/Methods

The recently proposed Maximum Entropy Theory of Ecology predicts that all
nested species-area relationships (SARs) will collapse to a single, universal
curve that exhibits decreasing log-log slope with increasing scale, suggesting
that the power law form of the SAR is invalid at any scale. In this analysis
we test the generality of this scale collapse behavior and determine the scale
at which approximate power law behavior of the SAR is predicted to occur. We
use common SAR models to recursively upscale SARs to 1) look for scale collapse
of SARs built from different community assumptions and 2) identify the scale at
which approximate power law SARs are recovered. We explore four SAR models in
which species abundance distributions and the spatial aggregation of species
vary within and across scales according to observed patterns.

Results/Conclusions

We show that scale-collapse is a property of nested SARs, not of maximum
entropy theory, and that many types of SARs can exhibit scale collapsed curves
that follow the general pattern of empirical communities. Moreover, we use the
scale collapsed curves to show that power law behavior is not predicted to
occur at the scale of most SAR studies and that variation in species spatial
aggregation or the scaling of species abundance distributions are needed to
produce power law SARs at realistic scales. Our findings show that power law
behavior of nested SARs is rare and that communities displaying approximate
power law SARs may exhibit predictable characteristics within and across scale,
such as interspecific variation in aggregation. Our findings regarding the
general rarity of power law behavior suggests that careful consideration of the
curvature of an SAR and the scale of an ecological community are necessary
before using power law SARs to predict biodiversity across scales.