Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/the-origin-of-species-by-means-of-mathematical-modelling-o7ITMWAtt1
References (49)
-
M. Banerjee, V. Volpert (2017)
Spatio-temporal pattern formation in Rosenzweig–MacArthur model: Effect of nonlocal interactionsEcological Complexity, 30
-
F. Thomas, Daniel Fisher, P. Fort, J. Marie, S. Daoust, B. Roche, C. Grunau, C. Cosseau, G. Mitta, S. Baghdiguian, F. Rousset, P. Lassus, E. Assenat, Damien Grégoire, D. Missé, A. Lorz, F. Billy, W. Vainchenker, F. Delhommeau, S. Koscielny, R. Itzykson, R. Tang, Fanny Fava, A. Ballesta, T. Lepoutre, L. Krasinska, V. Dulić, Peggy Raynaud, P. Blache, C. Quittau-Prévostel, E. Vignal, Helene Trauchessec, B. Perthame, J. Clairambault, V. Volpert, E. Solary, U. Hibner, M. Hochberg (2012)
Applying ecological and evolutionary theory to cancer: a long and winding roadEvolutionary Applications, 6
-
N. Bessonov, N. Reinberg, V. Volpert (2014)
Mathematics of Darwin’s DiagramMathematical Modelling of Natural Phenomena, 9
-
Grégoire Nadin, L. Rossi, L. Ryzhik, B. Perthame (2013)
Wave-like Solutions for Nonlocal Reaction-diffusion Equations: a Toy ModelMathematical Modelling of Natural Phenomena, 8
-
M. Doebeli, U. Dieckmann (2000)
Evolutionary Branching and Sympatric Speciation Caused by Different Types of Ecological InteractionsThe American Naturalist, 156
-
S. Gourley, M. Chaplain, F. Davidson (2007)
Spatio-temporal pattern formation in a nonlocal reaction-diŒusion equation -
V. Volpert, S. Petrovskii (2009)
Reaction-diffusion waves in biology.Physics of life reviews, 6 4
-
Juncheng Wei, M. Winter (2007)
Existence, Classification and Stability Analysis of Multiple-peaked Solutions for the Gierer-Meinhardt System in R 1Methods and applications of analysis, 14
-
S Genieys, V Volpert, P Auger (2006)
Adaptive dynamics: modelling Darwin’s divergence principleCR Biol, 329
-
L. Desvillettes, P. Jabin, S. Mischler, G. Raoul (2008)
On selection dynamics for continuous structured populationsCommunications in Mathematical Sciences, 6
-
S. Méléard (2011)
Random Modeling of Adaptive Dynamics and Evolutionary Branching -
V. Volpert (2011)
Fredholm theory of elliptic problems in unbounded domains -
M. Banerjee, V. Volpert (2016)
Prey-predator model with a nonlocal consumption of prey.Chaos, 26 8
-
S. Gourley (2000)
Travelling front solutions of a nonlocal Fisher equationJournal of Mathematical Biology, 41
-
V. Volpert, N. Apreutesei, N. Bessonov, V. Vougalter (2010)
Spatial structures and generalized travelling waves for an integro-differential equationDiscrete and Continuous Dynamical Systems-series B, 13
-
Z. Cai, R. Falgout, Shun Zhang (2014)
Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential EquationsSIAM J. Numer. Anal., 53
-
U. Dieckmann, M. Doebeli (1999)
On the origin of species by sympatric speciationNature, 400
-
(2008)
Publication prepared on the basis of the first edition -
M. Banerjee, V. Vougalter, V. Volpert (2016)
Doubly nonlocal reaction-diffusion equations and the emergence of speciesApplied Mathematical Modelling, 42
-
V. Volpert, V. Vougalter (2013)
Emergence and Propagation of Patterns in Nonlocal Reaction-Diffusion Equations Arising in the Theory of Speciation -
S. Génieys, V. Volpert, P. Auger (2006)
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of ResourcesMathematical Modelling of Natural Phenomena, 1
-
(2004)
Fitness Landscape and the Origin of Species -
N. Britton (1990)
Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population modelSiam Journal on Applied Mathematics, 50
-
V Volpert, N Reinberg, M Benmir, S Boujena (2015)
On pulse solutions of a reactiondiffusion system in population dynamics nonlinearAnalysis, 120
-
Aizik Volpert, V. Volpert, V. Volpert (1994)
Traveling Wave Solutions of Parabolic Systems -
B. Perthame, S. Génieys (2007)
Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi LimitMathematical Modelling of Natural Phenomena, 2
-
S. Génieys, N. Bessonov, V. Volpert (2009)
Mathematical model of evolutionary branchingMath. Comput. Model., 49
-
Y. Nec, M. Ward (2013)
The Stability and Slow Dynamics of Two-Spike Patterns for a Class of Reaction-Diffusion SystemMathematical Modelling of Natural Phenomena, 8
-
B. Segal, V. Volpert, A. Bayliss (2013)
Pattern formation in a model of competing populations with nonlocal interactionsPhysica D: Nonlinear Phenomena, 253
-
V. Volpert, N. Reinberg, M. Benmir, S. Boujena (2015)
On pulse solutions of a reaction-diffusion system in population dynamicsNonlinear Analysis-theory Methods & Applications, 120
-
R. Siegel, G. Edelman (1992)
Bright Air, Brilliant Fire: On the Matter of the MindBioScience
-
H. Berestycki, Grégoire Nadin, B. Perthame, L. Ryzhik (2009)
The non-local Fisher–KPP equation: travelling waves and steady statesNonlinearity, 22
-
S. Atamas (1996)
Self-organization in computer simulated selective systems.Bio Systems, 39 2
-
V. Volpert (2015)
Pulses and waves for a bistable nonlocal reaction-diffusion equationAppl. Math. Lett., 44
-
N. Apreutesei, A. Ducrot, V. Volpert (2009)
Travelling Waves for Integro-differential EquationsDiscrete and Continuous Dynamical Systems-series B, 11
-
N. Eymard, V. Volpert, V. Vougalter (2017)
Existence of Pulses for Local and Nonlocal Reaction-Diffusion EquationsJournal of Dynamics and Differential Equations, 29
-
V. Volpert (2014)
Elliptic Partial Differential Equations: Volume 2: Reaction-Diffusion Equations -
N. Bessonov, I. Demin, Laurent Pujo-Menjouet, V. Volpert (2009)
A multi-agent model describing self-renewal of differentiation effects on the blood cell populationMath. Comput. Model., 49
-
S. Gourley, M. Chaplain, F. Davidson (2001)
Spatio-temporal pattern formation in a nonlocal reaction-diffusion equationDynamical Systems, 16
-
(2014)
Birkhäuser/Springer Basel, pp 175–192 -
D. Iron, M. Ward (2000)
A Metastable Spike Solution for a Nonlocal Reaction-Diffusion ModelSIAM J. Appl. Math., 60
-
Trenton Holliday (2018)
SpeciationThe International Encyclopedia of Biological Anthropology
-
A. Ducrot, M. Marion, V. Volpert (2011)
Spectrum of some integro-differential operators and stability of travelling wavesFuel and Energy Abstracts
-
AsaHG Gray, A. Dupree (1963)
I. THE ORIGIN OF SPECIES BY MEANS OF NATURAL SELECTION -
S Gavrilets (2004)
10.1515/9780691187051 -
S. Génieys, V. Volpert, P. Auger (2006)
Adaptive dynamics: Modelling Darwin's divergence principle.Comptes rendus biologies, 329 11
-
V. Volpert (2011)
Elliptic Partial Differential Equations -
N. Apreutesei, A. Ducrot, V. Volpert (2008)
Competition of Species with Intra-Specific CompetitionMathematical Modelling of Natural Phenomena, 3
-
Mark Lewis, P. Maini, S. Petrovskii (2013)
Dispersal, Individual Movement and Spatial Ecology
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
- Subject
- Philosophy; Philosophy of Biology; Evolutionary Biology
- ISSN
- 0001-5342
- eISSN
- 1572-8358
- DOI
- 10.1007/s10441-018-9328-9
- Publisher site
- See Article on Publisher Site
Abstract
Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in Darwin’s diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin’s definition of species, stated above, and Mayr’s definition of species (group of individuals that can reproduce) is also discussed.
Journal
Acta Biotheoretica – Springer Journals
Published: Apr 30, 2018