We consider a simple mathematical model of gradual Darwinian evolution in
continuous time and continuous trait space, due to intraspecific competition
for common resource in an asexually reproducing population in constant
environment, while far from evolutionary stable equilibrium. The model admits
exact analytical solution. In particular, Gaussian distribution of the trait
emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

A Calsina

A Sasaki

EV Koonin

GP Karev

GR Price

I Gudelj

JAJ Metz

KM Page

LH Liow

M Kimura

M Turelli

N Champagnat

NH Barton

O Hallatschek

P Schuster

PD Taylor

R Dawkins

R Lande

RA Fisher

RG Bowers

SAH Geritz

U Dieckmann

Vadim N. Biktashev

Journal of Mathematical Biology

English

arXiv

Copyright © 2013 Springer Verlag. The final publication is available at link.springer.comWe consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions

Biktashev, V. N.

Open Research Exeter

A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient

There is another ORE record for this article at http://hdl.handle.net/10871/26441We propose a solution to a long standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.The research leading to the results
has received funding from Max Planck Gesellschaft,
the European Community Seventh Framework Pro-
gramme FP7/2007-2013 under Grant Agreement 17 No.
HEALTH-F2-2009-241526, EUTrigTreat (DH, TB, SB,
VIK, SL), and from EPSRC (UK) grant EP/I029664
(VNB).We also acknowledge support from the German
Federal Ministry of Education and Research (BMBF)
(project FKZ 031A147, GO-Bio), the German Research
Foundation (DFG) (Collaborative Research Centres SFB
1002 Project C3 and SFB 937 Project A18), the Ger-
man Center for Cardiovascular Research (DZHK e.V.)
(DH, TB, SB, VIK, SL), Science & Engineering Research
Board of Department of Science & Technology, Govern-
ment of India (TKS), EPSRC (UK) grant EP/N014391
(VNB) and U.S. NIH Grant No. R01HL089271 (NFO)

Hornung, D

Biktashev, VN

Otani, NF

Shajahan, TK

Baig, T

Berg, S

Han, S

Krinsky, V

Luther, S

Mechanisms of vortices termination in the cardiac muscle

We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation

Hornung, Daniel

Otani, N. F.

Shajahan, T. K.

Baig, T.

Berg, S.

Han, Sang Who

Krinsky, V. I.

Luther, Stefan

GRO.publications

GRO.publications (Univ. Göttingen)

We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.</jats:p

D. Hornung

V. N. Biktashev

N. F. Otani

T. K. Shajahan

T. Baig

S. Berg

S. Han

V. I. Krinsky

S. Luther

Crossref

Royal Society Open Science

Hornung, D.

Biktashev, V.

Otani, N.

Shajahan, T.

Han, S.

Krinski, V.

Luther, S.

MPG.PuRe

A simple mathematical model of gradual Darwinian evolution: Emergence of
  a Gaussian trait distribution in adaptation along a fitness gradient

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

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Open Research Exeter

Open Research Exeter

GRO.publications

GRO.publications (Univ. Göttingen)

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MPG.PuRe