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.
 Sibly, R.M. and Hone, J. (2002) Population Growth Rate and its Determinants: An Overview. Philosophical Transactions of the Royal Society of London B, 357, 1153-1170.
 Hassell, M.P., Latto, J. and May, R.M. (1989) Seeing the Wood for the Trees: Detecting Density Dependence from Existing Life-Table Studies. Journal of Animal Ecology, 58, 883-892.
 Brook, B.W. and Bradshaw, C.J.A. (2006) Strength of Evidence for Density Dependence in Abundance Time Series of 1198 Species. Ecology, 87, 1445-1451.
 Connell, J.H. and Sousa, W.P. (1983) On the Evidence Needed to Judge Ecological Stability or Persistence. American Naturalist, 121, 789-824.
 Hixon, M.A., Pacala, S.W. and Sandin, S.A. (2002) Population Regulation: Historical Context and Contemporary Challenges of Open vs. Closed Systems. Ecology, 83, 1490-1508.
 Solow, A.R. (1990) Testing for Density Dependence: A Cautionary Note. Oecologia, 83, 47-49.
 Beddington, J.R. and May, R.M. (1977) Harvesting Natural Populations in a Randomly Fluctuating Environment. Science, 197, 463-465.
 Shepherd, J.G. and Horwood, J.W. (1979) The Sensitivity of Exploited Populations to Environmental “Noise”, and the Implications for Management. Journal du Conseil International pour l’Exploration de la Mer, 38, 318-323.
 Ives, A.R., Dennis, B., Cottingham, K.L. and Carpenter, S.R. (2003) Estimating Community Stability and Ecological Interactions from Time-Series Data. Ecological Monographs, 73, 301-330.
 Ives, A.R., Abbott, K.C. and Ziebarth, N.L. (2010) Analysis of Ecological Time Series with ARMA(p, q) Models. Ecology, 91, 858-871.
 Roughgarden, J. (1975) A Simple Model for Population Dynamics in Stochastic Environments. American Naturalist, 109, 713-736.
 Royama, T. (1981) Fundamental Concepts and Methodology for the Analysis of Animal Population Dynamics, with Particular Reference to Univoltine Species. Ecological Monographs, 51, 473-493. http://dx.doi.org/10.2307/2937325
 McArdle, B.H. (1989) Bird Population Densities. Nature, 338, 628.
 Lundberg, P., Ranta, E., Ripa, J. and Kaitala, V. (2000) Population Variability in Space and Time. Trends in Ecology & Evolution, 15, 460-464.
 Jonzén, N., Ripa, J. and Lundberg, P. (2002) A Theory of Stochastic Harvesting in Stochastic Environments. American Naturalist, 159, 427-437.
 Lande, R., Engen, S., Sather, B.-E., Filli, F., Matthysen, E. and Weimerskirch, H. (2002) Estimating Density Dependence from Population Time Series Using Demographic Theory and Life-History Data. American Naturalist, 159, 321337.
 Edelstein-Keshet, L. (2005) Mathematical Models in Biology. Society for Industrial and Applied Mathematics.
 Shepherd, J.G. and Cushing, D.H. (1990) Regulation in Fish Populations: Myth or Mirage? Philosophical Transactions of the Royal Society of London B, 330, 151-164.
 Walters, C. and Parma, A.M. (1996) Fixed Exploitation Rate Strategies for Coping with Effects of Climate Change. Canadian Journal of Fisheries and Aquatic Sciences, 53, 148-158.
 Dixon, P.A., Milicich, M.J. and Sugihara, G. (1999) Episodic Fluctuations in Larval Supply. Science, 283, 1528-1530.
 Niwa, H.S. (2006) Recruitment Variability in Exploited Aquatic Populations. Aquatic Living Resources, 19, 195-206.
 von Neumann, J. (1941) Distribution of the Ratio of the Mean Square Successive Difference to the Variance. Annals of Mathematical Statistics, 12, 367-395.
 Bulmer, M.G. (1975) The Statistical Analysis of Density Dependence. Biometrics, 31, 901-911.
 Kubo, R., Toda, M. and Hashitsume, N. (1991) Statistical Physics II. Nonequilibrium Statistical Mechanics. 2nd Edition, Springer-Verlag, Berlin.
 Niwa, H.S. (2007) Random-Walk Dynamics of Exploited Fish Populations. ICES Journal of Marine Science, 64, 496502.
 Sparholt, H., Bertelsen, M. and Lassen, H. (2007) A Meta-Analysis of the Status of ICES Fish Stocks during the Past Half Century. ICES Journal of Marine Science, 64, 707-713.
 ICES (2008) Report of the ICES Advisory Committee, ICES Advice 2008, Books 1-10.