Discreteness of populations enervates biodiversity in evolution
msra(2010)
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.
更多查看译文
关键词
replicator equation,statistical physics,fluctuation theorem,kinetic energy,evolutionary game theory,economic model
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要