TITLE:
Uncertainty in a Measurement of Density Dependence on Population Fluctuations
AUTHORS:
Hiro-Sato Niwa
KEYWORDS:
Population Dynamics, Stochastic Difference Equation, Noise Color, Coarse Graining, Ecological Time-Series
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.8,
April
29,
2014
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.