Possibly Longest Food Chain: Analysis of a Mathematical Model
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 4, pp. 131-160
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We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases, we find that the possibly longest chain is such that the lower trophic level has a greater energy reserve than the higher has, so that the distribution of energy reserves can be regarded to have a pyramid shape, whereas, if any of its trophic levels is removed, the pyramid shape cannot be maintained. Further, we find the condition that arbitrary long chain can be established. In such unbounded case, we prove that any chain could not have the pyramid shape of energy reserve distribution.
@article{10_1051_mmnp:2008067,
author = {T. Matsuoka and H. Seno},
title = {Possibly {Longest} {Food} {Chain:} {Analysis} of a {Mathematical} {Model}},
journal = {Mathematical modelling of natural phenomena},
pages = {131--160},
publisher = {mathdoc},
volume = {3},
number = {4},
year = {2008},
doi = {10.1051/mmnp:2008067},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008067/}
}
TY - JOUR AU - T. Matsuoka AU - H. Seno TI - Possibly Longest Food Chain: Analysis of a Mathematical Model JO - Mathematical modelling of natural phenomena PY - 2008 SP - 131 EP - 160 VL - 3 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008067/ DO - 10.1051/mmnp:2008067 LA - en ID - 10_1051_mmnp:2008067 ER -
%0 Journal Article %A T. Matsuoka %A H. Seno %T Possibly Longest Food Chain: Analysis of a Mathematical Model %J Mathematical modelling of natural phenomena %D 2008 %P 131-160 %V 3 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008067/ %R 10.1051/mmnp:2008067 %G en %F 10_1051_mmnp:2008067
T. Matsuoka; H. Seno. Possibly Longest Food Chain: Analysis of a Mathematical Model. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 4, pp. 131-160. doi: 10.1051/mmnp:2008067
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