caa a22 4500 606164553 CHVBK 20210128100649.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10144-014-0471-0 doi (NATIONALLICENCE)springer-10.1007/s10144-014-0471-0 The stability-complexity relationship at age 40: a random matrix perspective [Elektronische Daten] [Stefano Allesina, Si Tang] Since the work of Robert May in 1972, the local asymptotic stability of large ecological systems has been a focus of theoretical ecology. Here we review May's work in the light of random matrix theory, the field of mathematics devoted to the study of large matrices whose coefficients are randomly sampled from distributions with given characteristics. We show how May's celebrated "stability criterion” can be derived using random matrix theory, and how extensions of the so-called circular law for the limiting distribution of the eigenvalues of large random matrix can further our understanding of ecological systems. Our goal is to present the more technical material in an accessible way, and to provide pointers to the primary mathematical literature on this subject. We conclude by enumerating a number of challenges, whose solution is going to greatly improve our ability to predict the stability of large ecological networks. The Society of Population Ecology and Springer Japan, 2015 Complexity nationallicence Eigenvalue nationallicence Food web nationallicence Random matrix nationallicence Stability nationallicence Allesina Stefano Department of Ecology and Evolution, University of Chicago, 1101 E. 57th, 60637, Chicago, IL, USA aut Tang Si Department of Ecology and Evolution, University of Chicago, 1101 E. 57th, 60637, Chicago, IL, USA aut Population Ecology Springer Japan 57/1(2015-01-01), 63-75 1438-3896 57:1<63 2015 57 10144 https://doi.org/10.1007/s10144-014-0471-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 review-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10144-014-0471-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Allesina Stefano Department of Ecology and Evolution, University of Chicago, 1101 E. 57th, 60637, Chicago, IL, USA aut NATIONALLICENCE 700 1- Tang Si Department of Ecology and Evolution, University of Chicago, 1101 E. 57th, 60637, Chicago, IL, USA aut NATIONALLICENCE 773 0- Population Ecology Springer Japan 57/1(2015-01-01), 63-75 1438-3896 57:1<63 2015 57 10144