Abstract
The diversity of life and its organization in networks of interacting species has been a long-standing theoretical puzzle for ecologists. Ever since May's provocative paper challenging whether ‘large complex systems [are] stable' various hypotheses have been proposed to explain when stability should be the rule, not the exception. Spatial dynamics may be stabilizing and thus explain high community diversity, yet existing theory on spatial stabilization is limited, preventing comparisons of the role of dispersal relative to species interactions. Here we incorporate dispersal of organisms and material into stability–complexity theory. We find that stability criteria from classic theory are relaxed in direct proportion to the number of ecologically distinct patches in the meta-ecosystem. Further, we find the stabilizing effect of dispersal is maximal at intermediate intensity. Our results highlight how biodiversity can be vulnerable to factors, such as landscape fragmentation and habitat loss, that isolate local communities.
Highlights
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not
By contrasts, when elements of the random matrices arerdeuacllescotmo psleptelfficffiyðffiffiSffiiffinffiÀffiffidffiffieffi1ffipffiÞffiffi=effiffinnffiffidoenmt,(rth1⁄4at0)is,ththe estambailxitiymcarlitaedrimonissthibelne complexity parameter s2cðS À 1Þis multiplied by the number of patches
Our analyses reveal that meta-ecosystem dynamics are stabilizing because of the effects of dispersal on the structure of the Jacobian matrix and its corresponding eigenvalues
Summary
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. May[3,4] studied the dynamical properties of randomly assembled ecosystems He modelled them using the Jacobian matrix, which describes the pairwise effects of one species on another and could be used to investigate the rate at which the ecosystem returns to the equilibrium following a disturbance (as measured by the leading eigenvalue of the Jacobian). He found that stability should decrease with the number of species and interactions between them. By varying the number of species S, the connectance c (the proportion of potential interactions among all pairs of species that are realized), the s.d. of interspecific interaction strength (s) and the average intraspecific interaction strength (m), this theory indicates that for a community to be stable, it must respect the following inequality[3,16]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s cðS À 1Þom ð1Þ
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