种群的离散性削弱了biodiversity的进化
Discreteness of populations enervates biodiversity in evolution
摘要：
生物多样性是生态系统中常见的现象，其本质是物种间竞争的动态平衡。在演化博弈论中，相互作用物种的时变种群常常被一组确定性的复制子方程很好地描述。然而，由于种群的离散性而产生的内在波动会导致光滑演化轨迹的随机衍生。这些波动的作用被证明是至关重要的，在造成灭绝和生态系统的生物多样性恶化。我们使用儿童的石头剪刀布游戏来演示离散种群的内在波动是如何产生的，以及为什么生态系统的生物多样性呈指数衰减，而不考虑竞争机制和初始分布的细节参数。生物多样性的耗散趋势可以类比为由于空气阻力或流体粘性而导致的运动粒子动能的逐渐侵蚀。统计物理学中的耗散涨落定理决定了这些原本守恒量的命运。物理学中的这一概念可以推广到仔细检查在生态学、生物学和定量经济模型中可能发生的错误，因为这些模型的成分在数量上都是离散的。
英文摘要：
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic replicator equations in the evolutionary game theory. However, intrinsic fluctuations arisen from the discreteness of populations lead to stochastic derivations from the smooth evolution trajectories. The role of these fluctuations is shown to be critical at causing extinction and deteriorating the biodiversity of ecosystem. We use children's rock-paper-scissors game to demonstrate how the intrinsic fluctuations arise from the discrete populations and why the biodiversity of the ecosystem decays exponentially, disregarding the detail parameters for competing mechanism and initial distributions. The dissipative trend in biodiversity can be analogized to the gradual erosion of kinetic energy of a moving particle due to air drag or fluid viscosity. The dissipation-fluctuation theorem in statistical physics seals the fate of these originally conserved quantities. This concept in physics can be generalized to scrutinize the errors that might be incurred in the ecological, biological, and quantitative economic modeling for which the ingredients are all discrete in number.
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