Abstract:
:This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick-von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation, and the McKendrick-von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Datta S,Delius GW,Law Rdoi
10.1007/s11538-009-9496-5subject
Has Abstractpub_date
2010-08-01 00:00:00pages
1361-82issue
6eissn
0092-8240issn
1522-9602journal_volume
72pub_type
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