Attention! Your ePaper is waiting for publication!
By publishing your document, the content will be optimally indexed by Google via AI and sorted into the right category for over 500 million ePaper readers on YUMPU.
This will ensure high visibility and many readers!
<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011<br />
Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30<br />
Michael Sieber<br />
Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Systems Research, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics<br />
and Computer Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Osnabrück, 49069 Osnabrück,<br />
Germany<br />
e-mail: msieber@uni-osnabrueck.de<br />
Intraguild predati<strong>on</strong> or not? Taking a different perspective<br />
<strong>on</strong> some eco-epidemiological models<br />
The field <str<strong>on</strong>g>of</str<strong>on</strong>g> eco-epidemiology has integrated epidemiology wi<str<strong>on</strong>g>th</str<strong>on</strong>g> community ecology<br />
and similarities between host-parasitoid and host-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g><br />
classical intraguild predati<strong>on</strong> (IGP) have been noticed. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I want to show<br />
<str<strong>on</strong>g>th</str<strong>on</strong>g>at certain eco-epidemiological scenarios not <strong>on</strong>ly fit into <str<strong>on</strong>g>th</str<strong>on</strong>g>e IGP framework, but<br />
<str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may suggest a different perspective <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying community structure.<br />
After an appropriate transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> variables particular cases <str<strong>on</strong>g>of</str<strong>on</strong>g> IGP are<br />
found to be structurally similar to “simpler” community modules and <str<strong>on</strong>g>th</str<strong>on</strong>g>is structural<br />
similarity also translates into remarkably similar community dynamics.<br />
References.<br />
[1] Sieber, M. and Hilker, F. M. (2011). Prey, predators, parasites: intraguild predati<strong>on</strong> or simpler<br />
community modules in disguise? Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Animal Ecology, 80:414-421.<br />
<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011 Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical Models in Eco-epidemiology I; Wednesday, June 29, 08:30 Michael Sieber Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Envir<strong>on</strong>mental Systems Research, Department <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Science, University <str<strong>on</strong>g>of</str<strong>on</strong>g> Osnabrück, 49069 Osnabrück, Germany e-mail: msieber@uni-osnabrueck.de Intraguild predati<strong>on</strong> or not? Taking a different perspective <strong>on</strong> some eco-epidemiological models The field <str<strong>on</strong>g>of</str<strong>on</strong>g> eco-epidemiology has integrated epidemiology wi<str<strong>on</strong>g>th</str<strong>on</strong>g> community ecology and similarities between host-parasitoid and host-pa<str<strong>on</strong>g>th</str<strong>on</strong>g>ogen interacti<strong>on</strong>s wi<str<strong>on</strong>g>th</str<strong>on</strong>g> classical intraguild predati<strong>on</strong> (IGP) have been noticed. In <str<strong>on</strong>g>th</str<strong>on</strong>g>is talk I want to show <str<strong>on</strong>g>th</str<strong>on</strong>g>at certain eco-epidemiological scenarios not <strong>on</strong>ly fit into <str<strong>on</strong>g>th</str<strong>on</strong>g>e IGP framework, but <str<strong>on</strong>g>th</str<strong>on</strong>g>at <str<strong>on</strong>g>th</str<strong>on</strong>g>ey may suggest a different perspective <strong>on</strong> <str<strong>on</strong>g>th</str<strong>on</strong>g>e underlying community structure. After an appropriate transformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> variables particular cases <str<strong>on</strong>g>of</str<strong>on</strong>g> IGP are found to be structurally similar to “simpler” community modules and <str<strong>on</strong>g>th</str<strong>on</strong>g>is structural similarity also translates into remarkably similar community dynamics. References. [1] Sieber, M. and Hilker, F. M. (2011). Prey, predators, parasites: intraguild predati<strong>on</strong> or simpler community modules in disguise? Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Animal Ecology, 80:414-421. 896
<str<strong>on</strong>g>European</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>ference</str<strong>on</strong>g> <strong>on</strong> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematical and Theoretical Biology 2011 Neurosciences; Wednesday, June 29, 08:30 Justyna Signerska Institute <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics Polish Academy <str<strong>on</strong>g>of</str<strong>on</strong>g> Sciences, Warszawa, Poland Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Applied Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Technical Physics, Gdańsk University <str<strong>on</strong>g>of</str<strong>on</strong>g> Technology, Gdańsk, Poland e-mail: j.signerska@impan.pl Wacław Marzantowicz Faculty <str<strong>on</strong>g>of</str<strong>on</strong>g> Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>ematics and Computer Sci., Adam Mickiewicz University <str<strong>on</strong>g>of</str<strong>on</strong>g> Poznań, Poznań, Poland e-mail: marzan@amu.edu.pl Firing map for integrate–and–fire models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> almost periodic stimulus In integrate–and–fire systems <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>secutive spikes can be recovered via iterati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e so–called firing map. Until now analytical approaches mainly c<strong>on</strong>centrated <strong>on</strong> models <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e type ˙x = f(t, x) when <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> f was c<strong>on</strong>tinuous and periodic in <str<strong>on</strong>g>th</str<strong>on</strong>g>e time variable ([1],[2],[3]). We analyze firing maps and firing sequences for <str<strong>on</strong>g>th</str<strong>on</strong>g>e class <str<strong>on</strong>g>of</str<strong>on</strong>g> integrate–and–fire models wi<str<strong>on</strong>g>th</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e stimulus functi<strong>on</strong> almost periodic in time (ei<str<strong>on</strong>g>th</str<strong>on</strong>g>er uniformly almost periodic or in a Stepanov sense) and prove <str<strong>on</strong>g>th</str<strong>on</strong>g>at many required properties <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing map still hold for leaky integrate-and fire ˙x = −σx + f(t) or Perfect Integrator ˙x = f(t) models when <str<strong>on</strong>g>th</str<strong>on</strong>g>e functi<strong>on</strong> f is <strong>on</strong>ly locally integrable. We prepare a formal framework for <str<strong>on</strong>g>th</str<strong>on</strong>g>e study <str<strong>on</strong>g>of</str<strong>on</strong>g> discrete dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing map arising from almost periodically driven integrate–and–fire systems. In particular, results c<strong>on</strong>cerning almost periodic displacement <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing map and regularity properties (semi–/almost periodicity) <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>th</str<strong>on</strong>g>e sequence <str<strong>on</strong>g>of</str<strong>on</strong>g> interspike intervals will be shown. References. [1] R. Brette, Dynamics <str<strong>on</strong>g>of</str<strong>on</strong>g> <strong>on</strong>e–dimensi<strong>on</strong>al spiking neur<strong>on</strong> model, J.Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>.Biol., 48 (2004), 38– 56. [2] H. Carrillo, F. A. Ongay, On <str<strong>on</strong>g>th</str<strong>on</strong>g>e firing maps <str<strong>on</strong>g>of</str<strong>on</strong>g> a general class <str<strong>on</strong>g>of</str<strong>on</strong>g> forced integrate and fire neur<strong>on</strong>s, Ma<str<strong>on</strong>g>th</str<strong>on</strong>g>. Biosci., 172 (2001), 33–53. [3] S. Coombes, P. C. Bressl<str<strong>on</strong>g>of</str<strong>on</strong>g>f, Mode locking and Arnold t<strong>on</strong>gues in integrate–and–fire neural oscillators, Phys. Rev. E, 60 (1999), 2086–2096. [4] W. Marzantowicz, J.Signerska, Firing map <str<strong>on</strong>g>of</str<strong>on</strong>g> an almost periodic input functi<strong>on</strong>, AIMS Proceedings 2011, in print. 897
Change language