A Food Chain with Lethal Prey

A Food Chain with Lethal Prey

James P. Braselton

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Martha L. Abell

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Abstract

We form a model of a food chain in the chemist at where the prey species can defend itself against the predator by producing a toxin lethal to the predator. Numerically, we illustrate that if the toxin production by the prey is constant, toxin levels will not vary considerably. On the other hand, if the prey is able to adjust its toxin production based on the density of the predator, toxin levels can vary considerably and periodically. In the context of the biological example we reference, the results indicate that toxic algae blooms might be a regular and periodic occurrence in nature.

References

32 Cites in Article

Reference Format

James Braselton,Martha Abell (2019). Competition in the chemostat with an undesirable lethal competitor.
James Braselton,Paul Waltman (2001). A competition model with dynamically allocated inhibitor production.
Lin Chao,Bruce Levin (1981). Structured habitats and the evolution of anticompetitor toxins in bacteria..
A Fredrickson,Gregory Stephanopoulos (1981). Microbial Competition.
Myungsoo Han,Haeok Lee,Donald Anderson,Baikho Kim (2016). Paralytic shellfish toxin production by the dinoagellate alexandrium pacificum (chinhae bay, korea) in axenic, nutrient-limited chemostat cultures and nutrient-enriched batch cultures.
S Hansen,S Hubbell (1980). Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes.
S Hsu,Ting-Kung Luo,Paul Waltman (1995). Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor.
S Hsu,Paul Waltman (1998). Competition in the chemostat when one competitor produces a toxin.
S Hsu,Yen-Sheng Li,Paul Waltman (2000). Competition in the presence of a lethal external inhibitor.
S Hsu,Paul Waltman (1992). Analysis of a model of two competitors in a chemostat with an external inhibitor.
S-B Hsu,Paul Waltman (2004). A survey of mathematical models of competition with an inhibitor.
Sze-Bi Hsu,Paul Waltman (1997). Competition between plasmid-bearing and plasmid-free organisms in selective media.
Sze-Bi Hsu,Paul Waltman,Gail Wolkowicz (1994). Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat.
Richard Lenski,S E Hattingh (1986). Coexistence of two competitors on one resource and one inhibitor: a chemostat model based on bacteria and antibiotics.
B Levin (1196). Frequency-dependent selection in bacterial populations.
Zhiqi Lu,K Hadeler (1998). Model of plasmid-bearing, plasmid-free competition in the chemostat with nutrient recycling and an inhibitor.
Ting-Kung Luo,Sze-Bi Hsu (1995). Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat with inhibitions.
Catherine Macken,Simon Levin,Roland Waldst�tter (1994). The dynamics of bacteria-plasmid systems.
Xavier Mayali,Gregory Doucette (2002). Microbial community interactions and population dynamics of an algicidal bacterium active against Karenia brevis (Dinophyceae).
Richard Pierce,Michael Henry (2008). Harmful algal toxins of the orida red tide (karenia brevis): Natural chemical stressors in south orida coastal ecosystems.
Clare Redshaw,Denise Sutter,Krista Lim-Hing,Melanie Heckman,Stina Jakobsson,Jerome Naar,Julia Kubanek (2011). Tracking losses of brevetoxins on exposure to phytoplankton competitors: Ecological impacts.
Wolfram Research (2019). Unknown Title.
Patricia Roth,Michael Twiner,Christina Mikulski,Amanda Barnhorst,Gregory Doucette (2008). Comparative analysis of two algicidal bacteria active against the red tide dinoagellate karenia brevis.
Patricia Roth,Michael Twiner,Zhihong Wang,Marie-Yasmine Bottein Dechraoui,Gregory Doucette (2007). Fate and distribution of brevetoxin (PbTx) following lysis of Karenia brevis by algicidal bacteria, including analysis of open A-ring derivatives.
D Ryder,D Dibiasio (1984). An operational strategy for unstable recombinant dna cultures.
Hal Smith,Paul Waltman (2008). The Theory of the Chemostat: Dynamics of Microbial Competition.
Hal Smith (2008). Monotone dynamical systems.
Gregory Stephanopoulos,R Gary (1988). Lapudis. Chemostat dynamics of plasmid-bearing, plasmid-free mixed recombinant cultures.
G William,Cheska Sunda,D Burleson,Jeanine Hardison,Zhihong Morey,Wang,Alina Jenniferwolny,Leanne Corcoran,Frances Flewelling,Van Dolah (2013). Osmotic stress does not trigger brevetoxin production in the dinoagellate karenia brevis.
R Horst,Thieme (1992). Convergence results and a poincare-bendixson trichotomy for asymptotically autonomous differential equations.
R Horst,Thieme (1992). Persistence under relaxed point-dissipativity (with application to an endemic model).
Paul Waltman,James Braselton,Lorraine Braselton (2002). A Mathematical Model of a Biological Arms Race with a Dangerous Prey.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

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Not applicable for this article.

How to Cite This Article

James P. Braselton. 2019. \u201cA Food Chain with Lethal Prey\u201d. Global Journal of Science Frontier Research - D: Agriculture & Veterinary GJSFR-D Volume 19 (GJSFR Volume 19 Issue D1).

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GJSFR Volume 19 Issue D1

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-D Classification FOR Code: 079999

Submission ReceivedJune 8, 2019
Peer Review Double Blind
Handling Editor
Accepted July 2, 2019
Published July 16, 2019

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v1.2

Issue date

July 24, 2019

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