Theoretical Ecology

, Volume 5, Issue 4, pp 465–480 | Cite as

Ecological drivers of stability and instability in marine ecosystems

  • Michael John PlankEmail author
  • Richard Law
Original Paper


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.


Food 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.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of CanterburyChristchurchNew Zealand
  2. 2.University of YorkYorkUK

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