Wang Yuanshi, DeAngelis Donald L
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, PR China.
U.S. Geological Survey, Wetland and Aquatic Research Center, Gainesville, FL 32653, USA.
Theor Popul Biol. 2019 Feb;125:30-37. doi: 10.1016/j.tpb.2018.11.003. Epub 2018 Dec 5.
Previous mathematical analyses have shown that, for certain parameter ranges, a population, described by logistic equations on a set of connected patches, and diffusing among them, can reach a higher equilibrium total population when the local carrying capacities are heterogeneously distributed across patches, than when carrying capacities having the same total sum are homogeneously distributed across the patches. It is shown here that this apparently paradoxical result is explained when the resultant differences in energy inputs to the whole multi-patch system are taken into account. We examine both Pearl-Verhulst and Original Verhulst logistic models and show that, when total input of energy or limiting resource, is constrained to be the same in the homogeneous and heterogeneous cases, the total population in the heterogeneous patches can never reach an asymptotic equilibrium that is greater than the sum of the carrying capacities over the homogeneous patches. We further show that, when the dynamics of the limiting resources are explicitly modeled, as in a chemostat model, the paradoxical result of the logistic models does not occur. These results have implications concerning the use of some ubiquitous equations of population ecology in modeling populations in space.
以往的数学分析表明，在某些参数范围内，对于一组相互连接的斑块上由逻辑斯谛方程描述并在其间扩散的种群而言，当局部承载能力在各斑块间呈非均匀分布时，相较于承载能力总和相同但在各斑块间呈均匀分布的情况，该种群能够达到更高的平衡总种群数量。本文表明，当考虑到整个多斑块系统能量输入的最终差异时，就能解释这一明显矛盾的结果。我们研究了珀尔 - 弗尔胡尔斯特模型和原始弗尔胡尔斯特逻辑斯谛模型，并表明，当在均匀和非均匀情况下能量或限制资源的总输入被限制为相同时，非均匀斑块中的总种群数量永远无法达到一个大于均匀斑块承载能力总和的渐近平衡。我们进一步表明，当像在恒化器模型中那样明确对限制资源的动态进行建模时，逻辑斯谛模型的矛盾结果就不会出现。这些结果对于在空间中对种群进行建模时使用一些普遍存在的种群生态学方程具有启示意义。
