Evolutionary dynamics in a Lotka–Volterra competition model with impulsive periodic disturbance

In this paper, we develop a theoretical framework to investigate the influence of impulsive periodic disturbance on the evolutionary dynamics of a continuous trait, such as body size, in a general ...

[1]  U. Dieckmann,et al.  Evolutionary dynamics of predator-prey systems: an ecological perspective , 1996, Journal of mathematical biology.

[2]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[3]  Dynamical behaviors of a trimolecular response model with impulsive input , 2010 .

[4]  E. Benoît,et al.  Fishing destabilizes the biomass flow in the marine size spectrum , 2012, Proceedings of the Royal Society B: Biological Sciences.

[5]  J. Metz,et al.  Adaptive Dynamics: A Geometrical Study of the Consequences of Nearly Faithful Reproduction , 1995 .

[6]  Zhidong Teng,et al.  Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations , 2007 .

[7]  W. E. Ricker,et al.  Changes in the Average Size and Average Age of Pacific Salmon , 1981 .

[8]  M. Doebeli,et al.  Symmetric competition as a general model for single-species adaptive dynamics , 2012, Journal of Mathematical Biology.

[9]  Ruiqing Shi,et al.  The study of a ratio-dependent predator–prey model with stage structure in the prey , 2009 .

[10]  Jianjun Jiao,et al.  The dynamics of an age structured predator–prey model with disturbing pulse and time delays ☆ , 2008 .

[11]  Mats Gyllenberg,et al.  Necessary and sufficient conditions for evolutionary suicide , 2001, Bulletin of mathematical biology.

[12]  Sanyi Tang,et al.  Dynamical analysis of plant disease models with cultural control strategies and economic thresholds , 2010, Math. Comput. Simul..

[13]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[14]  I. Eshel Evolutionary and continuous stability , 1983 .

[15]  Matt K. Broadhurst,et al.  Working Laterally Towards Perfect Selectivity in Fishing Gears , 2006 .

[16]  Yasuhiro Takeuchi,et al.  On evolution under symmetric and asymmetric competitions. , 2008, Journal of theoretical biology.

[17]  U. Dieckmann,et al.  On the origin of species by sympatric speciation , 1999, Nature.

[18]  Stefan A H Geritz,et al.  Evolutionary branching and long-term coexistence of cycling predators: critical function analysis. , 2007, Theoretical Population Biology.

[19]  U Dieckmann,et al.  Evolutionary Cycling of Predator-Prey Interactions : Population Dynamics and the Red Queen , 1999 .

[20]  Juan J. Nieto,et al.  Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission , 2011, Math. Comput. Simul..

[21]  É. Kisdi,et al.  Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree , 2004, Evolutionary Ecology.

[22]  Zhen Jin,et al.  The persistence in a Lotka–Volterra competition systems with impulsive☆ , 2005 .

[23]  Ulf Dieckmann,et al.  Trade‐Off Geometries and Frequency‐Dependent Selection , 2004, The American Naturalist.

[24]  O. Leimar Multidimensional convergence stability , 2009 .

[25]  Andrew White,et al.  The geometric theory of adaptive evolution: trade-off and invasion plots. , 2005, Journal of theoretical biology.

[26]  U. Dieckmann,et al.  The Dynamical Theory of Coevolution : A Derivation from Stochastic Ecological Processes , 1996 .

[27]  Lansun Chen,et al.  Dynamic analysis of lactic acid fermentation in membrane bioreactor. , 2009, Journal of theoretical biology.

[28]  Éva Kisdi,et al.  Red Queen Evolution by Cycles of Evolutionary Branching and Extinction , 2000 .

[29]  C. Matessi,et al.  Long-term evolution of multilocus traits , 1996, Journal of mathematical biology.

[30]  É. Kisdi,et al.  Evolutionary branching under asymmetric competition. , 1999, Journal of theoretical biology.

[31]  A. White,et al.  The adaptive dynamics of Lotka-Volterra systems with trade-offs. , 2002, Mathematical biosciences.

[32]  George Sugihara,et al.  Why fishing magnifies fluctuations in fish abundance , 2008, Nature.

[33]  F. B. Christiansen On Conditions for Evolutionary Stability for a Continuously Varying Character , 1991, The American Naturalist.

[34]  R. Nisbet,et al.  How should we define 'fitness' for general ecological scenarios? , 1992, Trends in ecology & evolution.

[35]  Christopher A. Klausmeier,et al.  Floquet theory: a useful tool for understanding nonequilibrium dynamics , 2008, Theoretical Ecology.

[36]  Jianjun Jiao,et al.  GLOBAL ATTRACTIVITY OF A STAGE-STRUCTURE VARIABLE COEFFICIENTS PREDATOR-PREY SYSTEM WITH TIME DELAY AND IMPULSIVE PERTURBATIONS ON PREDATORS , 2008 .

[37]  Ulf Dieckmann,et al.  Evolutionary Branching and Sympatric Speciation Caused by Different Types of Ecological Interactions , 2000, The American Naturalist.