Abstract
A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a "life-boat strategy" phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 347-361 |
| Number of pages | 15 |
| Journal | Theoretical Population Biology |
| Volume | 42 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1992 |
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ASJC Scopus subject areas
- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics
Cite this
A size-structured model for cannibalism. / Cushing, Jim M.
In: Theoretical Population Biology, Vol. 42, No. 3, 1992, p. 347-361.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A size-structured model for cannibalism
AU - Cushing, Jim M
PY - 1992
Y1 - 1992
N2 - A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a "life-boat strategy" phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.
AB - A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a "life-boat strategy" phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.
UR - http://www.scopus.com/inward/record.url?scp=0027011809&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0027011809&partnerID=8YFLogxK
U2 - 10.1016/0040-5809(92)90020-T
DO - 10.1016/0040-5809(92)90020-T
M3 - Article
AN - SCOPUS:0027011809
VL - 42
SP - 347
EP - 361
JO - Theoretical Population Biology
JF - Theoretical Population Biology
SN - 0040-5809
IS - 3
ER -