Possibly longest food chain : Analysis of a mathematical model
Mathematical Modelling of Natural Phenomena 3 巻 4 号
131-160 頁
2008 発行
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| ファイル情報(添付) | |
| タイトル ( eng ) |
Possibly longest food chain : Analysis of a mathematical model
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| 作成者 |
Matsuoka T.
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| 収録物名 |
Mathematical Modelling of Natural Phenomena
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| 巻 | 3 |
| 号 | 4 |
| 開始ページ | 131 |
| 終了ページ | 160 |
| 抄録 |
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.
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| 著者キーワード |
food chain
energy reserve
trophic level
mathematical model
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| NDC分類 |
生物科学・一般生物学 [ 460 ]
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| 言語 |
英語
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| 資源タイプ | 学術雑誌論文 |
| 出版者 |
EDP Sciences
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| 発行日 | 2008 |
| 権利情報 |
Copyright (c) 2008 EDP Sciences
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| 出版タイプ | Version of Record（出版社版。早期公開を含む） |
| アクセス権 | オープンアクセス |
| 収録物識別子 |
[DOI] 10.1051/mmnp:2008067
[DOI] http://dx.doi.org/10.1051/mmnp:2008067
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