Uncertainty in a Measurement of Density Dependence on Population Fluctuations

• 作者: Hiro-Sato Niwa
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: POPULATION Dynamics STOCHASTIC DIFFERENCE Equation Noise Color Coarse GRAINING ECOLOGICAL Time-Series
• 年，卷（期）: yysxyw_2014,（8）
• 页码范围: 1108-1119
• 页数: 12页
• 分类号: O1

摘要

This article discusses the question of how elasticity of the system is intertwined with external stochastic disturbances. The speed at which a displaced system returns to its equilibrium is a measure of density dependence in population dynamics. Population dynamics in random environments, linearized around the equilibrium point, can be represented by a Langevin equation, where populations fluctuate under locally stable (not periodic or chaotic) dynamics. I consider a Langevin model in discrete time, driven by time-correlated random forces, and examine uncertainty in locating the population equilibrium. There exists a time scale such that for times shorter than this scale the dynamics can be approximately described by a random walk;it is difficult to know whether the system is heading toward the equilibrium point. Density dependence is a concept that emerges from a proper coarse-graining procedure applied for time-series analysis of population data. The analysis is illustrated using time-series data from fisheries in the North Atlantic, where fish populations are buffeted by stochastic harvesting in a random environment.