caa a22 4500 445330007 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00285-010-0387-z doi (NATIONALLICENCE)springer-10.1007/s00285-010-0387-z A stability analysis of the power-law steady state of marine size spectra [Elektronische Daten] [Samik Datta, Gustav Delius, Richard Law, Michael Plank] This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth” equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems. Springer-Verlag, 2010 Marine ecosystem nationallicence Stability nationallicence Size-spectrum nationallicence McKendrick-von Foerster equation nationallicence Predator-prey nationallicence Growth diffusion nationallicence Eigenvalues nationallicence Datta Samik Departments of Biology and Mathematics, University of York, YO10 5DD, Heslington, York, UK aut Delius Gustav Department of Mathematics, University of York, YO10 5DD, Heslington, York, UK aut Law Richard Department of Biology, University of York, YO10 5DD, Heslington, York, UK aut Plank Michael Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand aut Journal of Mathematical Biology Springer-Verlag 63/4(2011-10-01), 779-799 0303-6812 63:4<779 2011 63 285 https://doi.org/10.1007/s00285-010-0387-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0387-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Datta Samik Departments of Biology and Mathematics, University of York, YO10 5DD, Heslington, York, UK aut NATIONALLICENCE 700 1- Delius Gustav Department of Mathematics, University of York, YO10 5DD, Heslington, York, UK aut NATIONALLICENCE 700 1- Law Richard Department of Biology, University of York, YO10 5DD, Heslington, York, UK aut NATIONALLICENCE 700 1- Plank Michael Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/4(2011-10-01), 779-799 0303-6812 63:4<779 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer