Department of Mathematics, University of Miami, Coral Gables, FL33124, USA.
J Biol Dyn. 2007 Jul;1(3):249-71. doi: 10.1080/17513750701450227.
We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.
我们研究了在异质斑块环境中扩散的策略或在连续或离散时间的种群动态或物种相互作用模型中在离散状态（例如防御和无防御）之间切换的策略的进化稳定性。有许多理论研究支持这样的观点，即在空间异质但时间不变的环境中，将对无条件的，即随机的扩散进行选择，但可能会选择某些类型的扩散，这些扩散在某种意义上是有条件的，即扩散率取决于环境因素。已经证明在某些情况下可以进化稳定的一种特定类型的扩散策略是平衡扩散，其中无论是否存在扩散，每个斑块上生物的平衡密度都是相同的。平衡扩散导致种群分布是理想自由的，因为在平衡时所有个体的适应性相同，并且个体之间没有斑块或状态之间的净运动。我们发现，在关于基础种群动态或物种相互作用的相当一般的假设下，只有这样的理想自由策略才能进化稳定。在稍微更严格的假设下（但仍然相当普遍），我们表明理想自由策略确实是进化稳定的。我们的主要数学方法是使用常微分方程和非负矩阵理论的入侵性分析。我们的分析统一并扩展了关于扩散或状态切换策略的进化稳定性的先前结果。
