Uncertainty in a Measurement of Density Dependence on Population Fluctuations

Author(s)
Hiro-Sato Niwa

Abstract

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.

Keywords

Population Dynamics, Stochastic Difference Equation, Noise Color, Coarse Graining, Ecological Time-Series

Population Dynamics, Stochastic Difference Equation, Noise Color, Coarse Graining, Ecological Time-Series

Cite this paper

Niwa, H. (2014) Uncertainty in a Measurement of Density Dependence on Population Fluctuations.*Applied Mathematics*, **5**, 1108-1119. doi: 10.4236/am.2014.58104.

Niwa, H. (2014) Uncertainty in a Measurement of Density Dependence on Population Fluctuations.

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