Cantrell Robert Stephen, Cosner Chris, Lou Yuan, Schreiber Sebastian J
Department of Mathematics, University of Miami, Coral Gables, FL 33124, United States.
Institute for Mathematical Sciences, Renmin University of China, Beijing 100872, PRC, China; Department of Mathematics, Ohio State University, Columbus, OH 43210, United States.
Math Biosci. 2017 Jan;283:136-144. doi: 10.1016/j.mbs.2016.11.003. Epub 2016 Nov 10.
Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a "source-sink" spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.
理解扩散的进化是进化生态学中的一个重要问题。对于个体在其一生中持续扩散的连续时间模型，已经表明，导致理想自由分布的平衡扩散策略在空间变化但时间恒定的环境中是进化稳定的。然而，许多物种主要在繁殖前扩散（出生扩散），而在繁殖事件之间扩散（繁殖扩散）的情况较少。这些物种包括鸟类和珊瑚礁鱼类等领域性物种，以及植物和软体动物等固着性物种。由于出生扩散模型中的人口统计学和扩散项以乘法方式结合，而不是先前研究模型中的加法方式，我们开发了新的数学方法来研究连续时间和离散时间模型中出生扩散的进化。对于这些模型的非平凡平衡，确定了一个基本的生态二分法：（i）所有斑块中个体的人均增长率等于零，或者（ii）一些斑块中的个体经历负的人均增长率，而其他斑块中的个体经历正的人均增长率。第一种可能性对应于理想自由分布，而第二种可能性对应于“源 - 汇”空间结构。我们证明，具有导致理想自由分布的扩散策略的种群会取代具有导致源 - 汇空间结构的扩散策略的种群。当存在无法维持种群的斑块时，久坐不动的种群可以实现理想自由策略，并且我们表明这些种群可以取代具有任何不可约扩散策略的种群。总体而言，这些结果支持进化选择导致在空间异质但时间同质的环境中实现理想自由分布的出生或繁殖扩散策略。
