无序环境中的物种生存与尺度律
Species survival and scaling laws in hostile and disordered environments
摘要：
在这项工作中，我们研究的可能性生存的单一物种的背景下，敌对和无序的环境。在这种环境中的种群动力学，由Fisher方程模拟，其特征是负的平均增长率，除了在一些随机的空间分布的斑块，可能支持生命。特别是，我们感兴趣的是生存概率的相图和临界尺寸问题，即，在长时间动态中生存所需的最小斑块大小。我们提出了一个措施的关键补丁大小成正比的参与率（PR）的特征向量对应的最大特征值的线性化Fisher动力学。我们得到了两种拓扑结构，即一维系统和分形Peano盆地的（抑制-生存）相图和概率分布函数（PDF）的临界补丁大小。我们发现，这两种拓扑结构具有相同的定性特征，但分形拓扑结构需要更高的空间波动，以保证物种的生存。我们执行一个有限大小的缩放，我们获得相关的缩放指数。此外，我们表明，PDF的关键补丁大小有一个通用的形状为1D的情况下，在模型参数（扩散，增长率等）。相反，扩散系数有一个剧烈的影响的PDF的分形Peano盆地的临界斑块大小，它不服从相同的标度律的一维情况。
英文摘要：
In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio (PR) of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.
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