Department of Physics, Bar-Ilan University, Ramat-Gan, Israel.
PLoS One. 2013 May 21;8(5):e62699. doi: 10.1371/journal.pone.0062699. Print 2013.
We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an implicit cost of dispersal, due to the tendency to leave favorable locations. Then, as in the Hamilton-May model with its explicit dispersal cost, the tradeoff between dispersal case and the beneficial role of dispersal in limiting fluctuations, leads to an advantage of one dispersal rate over another, and the eventual extinction of the disadvantaged species. In two dimensions we find that while the competition leads to the elimination of one species at high and low population density, at intermediate densities the two species can coexist essentially indefinitely. This is a new phenomenon not present in either the one-dimensional form of the Kessler-Sander model nor in the totally connected Hamilton-May model, and points to the importance of geometry in the question of dispersal.
我们考察了 Kessler 和 Sander 模型的二维扩展，该模型研究了两种除扩散率外完全相同的物种之间的竞争。在这类模型中，由于倾向于离开有利位置，繁殖率的空间非均质性导致了扩散的隐含成本。然后，就像具有显式扩散成本的 Hamilton-May 模型一样，扩散与扩散在限制波动中的有益作用之间的权衡，导致一种扩散率优于另一种扩散率，从而最终使劣势物种灭绝。在二维空间中，我们发现，尽管竞争导致在高和低种群密度下一种物种的灭绝，但在中等密度下，两种物种基本上可以无限期共存。这是在 Kessler-Sander 模型的一维形式或完全连通的 Hamilton-May 模型中都不存在的新现象，它指出了在扩散问题中几何形状的重要性。
