×

Evolution of dispersal distance. (English) Zbl 1311.60115

Summary: The problem of how often to disperse in a randomly fluctuating environment has long been investigated, primarily using patch models with uniform dispersal. Here, we consider the problem of choice of seed size for plants in a stable environment when there is a trade off between survivability and dispersal range. H. Ezoe [“Optimal dispersal range and seed size in a stable environment”, J. Theor. Biol. 190, No. 3, 287–293 (1998)] and S. A. Levin and H. C. Muller-Landau [“The evolution of dispersal and seed size in plant communities”, Evol. Ecol. Res. 2, No. 4, 409–435 (2000)] approached this problem using models that were essentially deterministic, and used calculus to find optimal dispersal parameters. Here, we follow D. Hiebeler [“Competition between near and far dispersers in spatially structured habitats”, Theor. Pop. Biol. 66, No. 3, 205–218 (2004)] and use a stochastic spatial model to study the competition of different dispersal strategies. Most work on such systems is done by simulation or nonrigorous methods such as pair approximation.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
92D40 Ecology

Citations:

Zbl 1277.60004
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aronson DG, Weinberger HF (1975) Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In: Partial differential equations and related topics, Springer Lecture Notes in Math 446, pp 5–49. Springer, New York
[2] Cohen D, Levin SA (1991) Dispersal in patchy environments: the effects of temporal and spatial structure. Theor Pop Biol 39: 63–99 · Zbl 0714.92025 · doi:10.1016/0040-5809(91)90041-D
[3] Cox JT, Durrett R, Perkins EA (2011) Voter model perturbations and reaction diffusion equations. arXiv:1103.1676
[4] Durrett R, Remenik D (2011) Voter model perturbations in two dimensions. Manuscript in preparation
[5] Durrett R, Neuhauser C (1994) Particle systems and reaction-diffusion equations. Ann Probab 22: 289–333 · Zbl 0799.60093 · doi:10.1214/aop/1176988861
[6] Ezoe H (1998) Optimal dispersal range and seed size in a stable environment. J Theor Biol 190: 287–293 · doi:10.1006/jtbi.1997.0553
[7] Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugen 7: 355–369 · JFM 63.1111.04 · doi:10.1111/j.1469-1809.1937.tb02153.x
[8] Hamilton WD, May RM (1977) Dispersal in stable habitats. Nature 269: 578–581 · doi:10.1038/269578a0
[9] Hiebeler D (2004) Competition between near and far dispersers in spatially structured habitats. Theor Pop Biol 66: 205–218 · doi:10.1016/j.tpb.2004.06.004
[10] Holley RA, Liggett TM (1975) Ergodic theorems for weakly interacting infinite systems and the voter model. Ann Probab 3: 643–663 · Zbl 0367.60115 · doi:10.1214/aop/1176996306
[11] Kipnis C, Landim C (1999) Scaling limits of particle systems. Springer, New York · Zbl 0927.60002
[12] Kolmogoroff A, Petrovsky P, Piscounov N (1937) Étude de l’equations de la diffusion avec croissance de la quantité de matière et son application a un problème biologique. Bull Univ Etat Moscou Ser Int Set A 1: 1–25
[13] Levin SA, Cohen D, Hastings A (1984) Dispersal strategies in patchy environments. Theor Pop Biol 26: 165–191 · Zbl 0541.92022 · doi:10.1016/0040-5809(84)90028-5
[14] Levin SA, Muller-Landau HC (2000) The evolution of dispersal and seed size in plant communities. Evol Ecol Res 2: 409–435
[15] Levin SA, Muller-Landau HC, Nathan R, Chave J (2003) The ecology and evolution of seed dispersal: a theoretical perscpective. Annu Rev Ecol Syst 34: 575–604 · doi:10.1146/annurev.ecolsys.34.011802.132428
[16] Ludwig D, Levin SA (1991) Evolutionary stability of plant communities and maintenance of multiple dispersal types. Theor Pop Biol 40: 285–307 · Zbl 0737.92022 · doi:10.1016/0040-5809(91)90057-M
[17] Neuhauser C, Pacala SW (1999) An explicitly spatial version of the Lotka-Volterra model with interspecific competition. Ann Appl Probab 9: 1226–1259 · Zbl 0948.92022 · doi:10.1214/aoap/1029962871
[18] Spitzer F (1976) Principles of random walks. In: Graduate texts in mathematics, 2nd edn, vol 34. Springer, New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.