Ecological drivers of stability and instability in marine ecosystems
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A stability analysis of the steady state of marine ecosystems is described. The study was motivated by the approximate invariance of biomass in logarithmic size intervals, which is widely observed in marine ecosystems. This invariance is recovered as the steady state of dynamic models of size spectra, which, unlike traditional species-based models of food webs, explicitly account for the mass gained by an individual organism when it eats a prey item. Little is known about the ecological conditions affecting the stability of the steady state, and a new method is developed to examine this. The results show that stability is enhanced by: (a) decreasing the mean predator-to-prey mass ratio (PPMR), (b) increasing the diet breadth of predators, (c) increasing the strength of intrinsic mortality relative to predation mortality, (d) increasing the biomass conversion efficiency. When perturbed from steady state, size spectra develop a wave-like shape, with an average wavelength especially sensitive to the mean PPMR. These waves move from small to large body size at an average speed which depends on the rate of growth of organisms. In contrast to traditional food web models, stability is enhanced as connectance (diet breadth) increases and as food chain length is increased by reducing the PPMR.
KeywordsFood web Jump-growth equation Power law Predator-to-prey mass ratio Size-dependent predation Size spectrum
This research was supported by the RSNZ Marsden fund, grant number 08-UOC-034. We thank Gustav Delius for his contributions to the analytical calculations and derivation of the convolution kernel. We also thank David Wall for illuminating discussions and José Capitán and Julia Blanchard for comments on an earlier version of the manuscript.
- Barnes C, Bethea DM, Brodeur RD, Spitz J, Ridoux V, Pusineri C, Chase BC, Hunsicker ME, Juanes F, Kellermann A, Lancaster J, Ménard F, Bard F-X, Munk P, Pinnegar JK, Scharf FS, Rountree RA, Stergiou KI, Sassa C, Sabates A, Jennings S (2008) Predator and prey body sizes in marine food webs. Ecology 89:881CrossRefGoogle Scholar
- Blanchard JL (2008) The dynamics of size-structured ecosystems. Ph.D. thesis, University of YorkGoogle Scholar
- Cushing DH (1969) The regularity of the spawning season of some fishes. J Cons Int Explor Mer 33:81–92Google Scholar
- Guckenheimer J, and Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer, New YorkGoogle Scholar
- Kerr SR, Dickie LM (2001) The biomass spectrum: a predator–prey theory of aquatic production. Columbia University Press, New YorkGoogle Scholar
- McKendrick AG (1926) Applications of mathematics to medical problems. Proc Edinb Math Soc 40:98–130Google Scholar
- Platt T and Denman K (1978) The structure of pelagic marine ecosystems. Rapp P-v Réun Cons Int Explor Mer 173:60–65Google Scholar
- Silvert W, Platt T (1980) Dynamic energy-flow model of the particle size distribution in pelagic ecosystems. In: Kerfoot WC (ed) Evolution and ecology of zooplankton communities. University Press of New England, Hanover, pp 754–763Google Scholar
- Ursin E (1973) On the prey size preferences of cod and dab. Medd Dan Fisk Havunders 7:85–98Google Scholar
- von Foerster H (1959) Some remarks on changing populations. In: Stohlman JF (ed) The kinetics of cellular proliferation. Grune and Stratton, New York, pp 382–407Google Scholar