Species biodiversity, being linked to ecosystem functioning and the resulting flow of ecosystem services, plays an important role in ecological and economic processes . One explanation for the effect of biodiversity lies in the spatial insurance hypothesis, which suggests that the stability of primary production in a meta-community increases with the biodiversity of each of its spatially distributed communities . Despite mixed empirical evidence, Loreau et al., in an influential theoretical analysis, present an illustration and corroboration of this hypothesis , . They show that at low dispersal rates, the species with the highest initial consumption rate will competitively exclude all others, resulting in low local biodiversity and high global biodiversity. High dispersal rates cause the meta-community to function as a single patch; the species with the consumption rate closest to the average will exclude all others in the meta-community. At intermediate dispersal rates, source-sink dynamics increase local biodiversity while preserving global biodiversity, leading to the highest net primary productivity and stability of productivity. However, little work has been conducted testing the robustness of this pivotal model. In this work, we reevaluated the Loreau  and updated Gonzalez et al.  models and tested the robustness of their results.
We numerically simulated the models of  and  using the Euler approximation method. We reproduced the original results, and tested their sensitivity to initial conditions and simulation time.
We found that the species coexistence result disappears at higher initial resource values - species experience unbounded exponential growth, then a steep decline in per capita growth rates that causes greater species extinction than if the resource was initially set to equilibrium values. Biodiversity also decreases as the number of iterations increases, but maintains the same trend. Net primary productivity and stability are robust to initial resource biomass and the number of iterations, suggesting that the net primary productivity and species coexistence results may not be as closely linked as previously believed.
Our work provided new insights into a pivotal ecological model and perspective on the spatial insurance hypothesis.
 Cardinale, B. J. et al. Biodiversity loss and its impact on humanity. Nature 486, 59-67 (2012).
 Yachi, S. & Loreau, M. Biodiversity and ecosystem productivity in a fluctuating environment: The insurance hypothesis. PNAS 96, 1463-1468 (1999).
 Loreau, M., Mouquet, N. & Gonzalez, A. Biodiversity as spatial insurance in heterogeneous landscapes. PNAS 100, 12765-12770 (2003).
 Gonzalez, A., Mouquet, N. & Loreau, M. in Biodiversity, Ecosystem Functioning, and Human Wellbeing (eds S. Naeem et al.) (Oxford University Press, 2009).
David Shanafelt, of Arizona State University, is a United States citizen. He was funded by IIASA's United States National Member Organization and worked in the Evolution and Ecology Program (EEP) during the YSSP.
Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.
Last edited: 19 August 2015
International Institute for Applied Systems Analysis (IIASA)
Schlossplatz 1, A-2361 Laxenburg, Austria
Phone: (+43 2236) 807 0 Fax:(+43 2236) 71 313