A stability analysis of the power-law steady state of marine size spectra

Journal of Mathematical Biology

Volumn 63, Issue 4, 2011, Pages 779-799

  Datta, Samik ^a   Delius, Gustav W ^a   Law, Richard ^a   Plank, Michael J ^b  

^a UNIVERSITY OF YORK   (United Kingdom)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

Eigenvalues; Growth diffusion; Marine ecosystem; McKendrick von Foerster equation; Predator prey; Size spectrum; Stability

Indexed keywords

ANIMAL; AQUATIC SPECIES; ARTICLE; BIOLOGICAL MODEL; BIOMASS; ECOSYSTEM; GROWTH, DEVELOPMENT AND AGING; POPULATION DYNAMICS; PREDATION; STATISTICS;

ANIMALS; AQUATIC ORGANISMS; BIOMASS; ECOSYSTEM; MODELS, BIOLOGICAL; POPULATION DYNAMICS; PREDATORY BEHAVIOR; STOCHASTIC PROCESSES;

EID: 80052708674     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-010-0387-z     Document Type: Article

References (25)

1. Andersen KH, Beyer JE (2006) Asymptotic size determines species abundance in the marine size spectrum. Am Nat 168: 54-61.
2. Anderson CNK, Hsieh C, Sandin SA, Hewitt R, Hollowed A, Beddington J, May RM, Sugihara G (2008) Why fishing magnifies fluctuations in fish abundance. Nature 452: 835-839.
3. Arino O, Shin Y, Mullon C (2004) A mathematical derivation of size spectra in fish populations. C R Biol 327(3): 245-254.
4. Aulbach B, Garay BM (1993) Linearizing the expanding part of noninvertible mappings. Z angew Math Phys 44(3): 469-494.
5. Benoît E, Rochet M (2004) A continuous model of biomass size spectra governed by predation and the effects of fishing on them. J Theor Biol 226(1): 9-21.
6. Blanchard JL, Jennings S, Law R, Castle MD, McCloghrie P, Rochet M, Benoît E (2009) How does abundance scale with body size in coupled size-structured food webs?. J Anim Ecol 78(1): 270-280.
7. Boudreau P, Dickie L (1992) Biomass spectra of aquatic ecosystems in relation to fisheries yield. Can J Fish Aquat Sci 49(8): 1528-1538.
8. Camacho J, Solé RV (2001) Scaling in ecological size spectra. Europhys Lett 55(6): 774-780.
9. Capitan JA, Delius GW (2010) Scale-invariant model of marine population dynamics. Phys Rev E 81(6): 061901.
10. Cohen JE, Jonsson T, Carpenter SR (2003) Ecological community description using the food web, species abundance, and body size. Proc Natl Acad Sci USA 100(4): 1781-1786.
11. Datta S, Delius GW, Law R (2010) A Jump-Growth model for PredatorPrey dynamics: derivation and application to marine ecosystems. Bull Math Biol 72(6): 1361-1382. http://arxiv. org/abs/0812. 4968.
12. Hsieh C, Reiss CS, Hunter JR, Beddington JR, May RM, Sugihara G (2006) Fishing elevates variability in the abundance of exploited species. Nature 443: 859-862.
13. Kirchgraber U, Palmer KJ (1990) Geometry in the neighborhood of invariant manifolds of maps and flows and linearization. Longman Scientific & Technical, Harlow.
14. Law R, Plank MJ, James A, Blanchard JL (2009) Size-spectra dynamics from stochastic predation and growth of individuals. Ecology 90(3): 802-811.
15. McKane AJ, Newman TJ (2005) Predator-prey cycles from resonant amplification of demographic stochasticity. Phys Rev Lett 94: 218102.
16. Murray JD (2002) Mathematical biology, I: an introduction, 3rd edn. Springer, Berlin.
17. Platt T, Denman K (1978) The structure of pelagic marine ecosystems. Rapports et Procés-Verbaux Des Réunions, Conseil International Pour l'Exploration de la Mer 173: 60-65.
18. Rooney N, McCann K, Gellner G, Moore JC (2006) Structural asymmetry and the stability of diverse food webs. Nature 442: 265-269.
19. Samoilov M, Plyasunov S, Arkin AP (2005) Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc Natl Acad Sci USA 102(7): 2310-2315.
20. Sheldon R, Parsons T (1967) A continuous size spectrum for particulate matter in the sea. J Fish Res Board Canada 24(5): 909-915.
21. Sheldon RW, Prakash A, Sutcliffe WH Jr (1972) The size distribution of particles in the ocean. Limnol Oceanogr 17(3): 327-340.
22. Silvert W (1980) Dynamic energy-flow model of the particle size distribution in pelagic ecosystems. In: Kerfoot W (eds) Evolution and ecology of zooplankton communities. University Press of New England, Hanover, pp 754-763.
23. Silvert W, Platt T (1978) Energy flux in the pelagic ecosystem: a time-dependent equation. Limnol Oceanogr 23(4): 813-816.
24. van Kampen NG (1992) Stochastic processes in physics and chemistry. Elsevier, Amsterdam.
25. Ware DM (1978) Bioenergetics of pelagic fish: theoretical change in swimming speed and ration with body size. J Fisher Res Board Canada 35: 220-228.