Evolution of Mixed Dispersal in Periodic Environments

Random dispersal describes the movement of organisms between adjacent spatial locations. However, the movement of some organisms such as seeds of plants can occur between non-adjacent spatial locations and is thus non-local. We propose to study a mixed dispersal strategy, which is a combination of random dispersal and non-local dispersal. More specifically, we assume that a fraction of individuals in the population adopt random dispersal, while the remaining fraction assumes non-local dispersal. We investigate how such mixed dispersal affects the invasion of a single species and also how mixed dispersal strategy will evolve in spatially heterogeneous but temporally constant environment.

[1]  Thomas Nagylaki,et al.  Clines with partial panmixia. , 2012, Theoretical population biology.

[2]  J. G. Skellam.  Random dispersal in theoretical populations , 1951, Biometrika.

[3]  Roger Cousen.  Dispersal in Plants: A Population Perspective , 2008 .

[4]  S. Levin,et al.  The Ecology and Evolution of Seed Dispersal: A Theoretical Perspective , 2003 .

[5]  Wenxian Shen,et al.  Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats , 2010 .

[6]  Frithjof Lutscher.  Nonlocal dispersal and averaging in heterogeneous landscapes , 2010 .

[7]  Frithjof Lutscher,et al.  Average dispersal success: linking home range, dispersal, and metapopulation dynamics to reserve design. , 2006, Ecological applications : a publication of the Ecological Society of America.

[8]  J Umbanhowar,et al.  Non-local concepts and models in biology. , 2001, Journal of theoretical biology.

[9]  Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal , 2012 .

[10]  H. Kreiss,et al.  Time-Dependent Problems and Difference Methods , 1996 .

[11]  Michael Grinfeld,et al.  Non-Local dispersal and bistability , 2006, European Journal of Applied Mathematics.

[12]  Jérôme Coville,et al.  Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity , 2008, SIAM J. Math. Anal..

[13]  Chao Yang,et al.  ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.

[14]  Wenxian Shen,et al.  Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats , 2012 .

[15]  Wan-Tong Li,et al.  Entire solutions in the Fisher-KPP equation with nonlocal dispersal , 2010 .

[16]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[17]  Jerome Coville,et al.  Nonlocal anisotropic dispersal with monostable nonlinearity , 2008, 1106.4531.

[18]  Georg Hetzer,et al.  Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations , 2013 .

[19]  Mark A. Lewis,et al.  Integrodifference models for persistence in fragmented habitats , 1997 .

[20]  Konstantin Mischaikow,et al.  The evolution of slow dispersal rates: a reaction diffusion model , 1998 .

[21]  G. T. Vickers,et al.  Spectral Theory for Nonlocal Dispersal with Periodic or Almost-Periodic Time Dependence , 2008 .

[22]  Mark A. Lewis,et al.  The Effect of Dispersal Patterns on Stream Populations , 2005, SIAM J. Appl. Math..

[23]  Yuan Lou,et al.  Random dispersal vs. non-local dispersal , 2009 .

[24]  George Lindfield,et al.  Numerical Methods Using MATLAB , 1998 .

[25]  C. Cosner,et al.  Spatial Ecology via Reaction-Diffusion Equations , 2003 .

[26]  J. Coville,et al.  A nonlocal inhomogeneous dispersal process , 2007 .

[27]  Emmanuel Chasseigne,et al.  Asymptotic behavior for nonlocal diffusion equations , 2006 .

[28]  Daniel B. Henry.  Geometric Theory of Semilinear Parabolic Equations , 1989 .

[29]  Alan Hastings,et al.  Can spatial variation alone lead to selection for dispersal , 1983 .

[30]  C. Cosner,et al.  Evolutionary stability of ideal free nonlocal dispersal , 2012, Journal of biological dynamics.

[31]  Carmen Cortázar,et al.  Existence and Asymptotic Behavior of Solutions to Some Inhomogeneous Nonlocal Diffusion Problems , 2009, SIAM J. Math. Anal..

[32]  J. Coville.  On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators , 2010, 1106.5137.

[33]  N. Shigesada,et al.  Biological Invasions: Theory and Practice , 1997 .

[34]  Yu Jin,et al.  Seasonal Influences on Population Spread and Persistence in Streams: Critical Domain Size , 2011, SIAM J. Appl. Math..

[35]  V. Hutson,et al.  The evolution of dispersal , 2003, Journal of mathematical biology.