Environmental Stochasticity

Masami Fujiwara, Southwest Fisheries Science Center, Santa Cruz, California, USA

Published online: March 2009

DOI: 10.1002/9780470015902.a0021220

Environmental stochasticity is unpredictable spatiotemporal fluctuation in environmental conditions, and it is one of the main sources of fluctuation in ecological processes. The term is often used in the ecology and evolution literature. Unpredictability is defined as a lack of ability to predict the future state precisely so that only its distribution can be known. Environment is typically defined as any set of physical, chemical and biological conditions that organisms experience, such as temperature, nutrient availability and the abundance of predators. Environmental stochasticity influences how population abundance fluctuates and affects the fate (e.g. persistence or extinction) of populations. In an evolutionary time scale, environmental stochasticity also affects life history strategy of organisms. Incorporating environmental stochasticity into analysis requires some care. Stochastic equations sometimes do not have explicit solutions so that simulations are required, and statistical analysis must separate other confounding factors such as stochastic sampling errors and demographic stochasticity.

Key Concepts

  • Environmental stochasticity is unpredictable spatiotemporal fluctuations in environmental conditions.
  • Correlation between time-lagged environmental states is one statistical measure of its predictability.
  • Environmental stochasticity is reflected in the fluctuations in ecological processes and affects their fate (e.g. extinction or persistence of populations).
  • Observed population dynamics consist of fluctuation due to environmental stochasticity, but it is often confounded with other factors such as sampling errors and demographic stochasticity.
  • All of the fluctuations in ecological data are often erroneously attributed to environmental stochasticity alone.
  • Evolutionary dynamics are also affected by environmental stochasticity.
  • Autoregressive moving average (ARMA) models are an example of statistical models incorporating environmental stochasticity.
  • Using stochastic differential and difference equation models, mechanistic ecological models incorporating environmental stochasticity can be built.

Keywords: autocorrelation; ecological models; ecological statistics; environmental fluctuation; stochastic time series

Figure 1. Simulated time series and their spectra. (a) Negatively autocorrelated time series, (b) spectrum of negatively autocorrelated time series, (c) simulated white noise, (d) spectrum of the white noise, (e) positively autocorrelated time series and (f) spectrum of the positively autocorrelated time series.
Figure 2. River flow rate of the Klamath River, California, from 1932 to 2005. (a) River flow rate, (b) spectrum of river flow rate, (c) difference (Xt+1–Xt) of river flow rate and (d) spectrum of the differenced time series.
Figure 3. Life history graph of fall-run Chinook salmon (Oncorhyncus tshawytscha). Numbers indicate stage of individuals (1: juvenile; 2–4: adults in the ocean; 5–7 spawning adults), solid arrows indicate potential transition of individuals from 1 year to the next and the arrows with dashed lines indicate reproduction.
close
 References
    Allen JC, Schaffer WM and Rosko D (1993) Chaos reduces species extinction by amplifying local-population noise. Nature 364: 229–232.
    Boyce MS (1992) Population viability analysis. Annual Review of Ecology and Systematics 23: 481–506.
    book Caswell H (1997) "Matrix methods for population analysis". In: Tuljapurkar S and Caswell H (eds) Structured-population Models in Marine, Terrestrial, and Freshwater Systems, pp. 19–58. New York: Chapman & Hall.
    Caswell H and Fujiwara M (2004) Beyond survival estimation: mark-recapture, matrix population models, and population dynamics. Animal Biodiversity and Conservation 27: 471–487.
    De Valpine P and Hastings A (2002) Fitting population models incorporating process noise and observation error. Ecological Monographs 72: 57–76.
    Doak DF, Morris WF, Pfister C, Kendall BE and Bruna EM (2005) Correctly estimating how environmental stochasticity influences fitness and population growth. American Naturalist 166: E14–E21.
    Fieberg J and Ellner SP (2000) When is it meaningful to estimate an extinction probability? Ecology 81: 2040–2047.
    Franklin AB, Anderson DR, Gutierrez RJ and Burnham KP (2000) Climate, habitat quality, and fitness in Northern Spotted Owl populations in northwestern California. Ecological Monographs 70: 539–590.
    Fujiwara M (2007) Extinction-effective population index: incorporating life-history variations in population viability analysis. Ecology 88: 2345–2353.
    Fujiwara M (2008) Effects of an autocorrelated stochastic environment and fisheries on the age at maturity of Chinook salmon. Theoretical Ecology 1: 89–101.
    Fujiwara M and Caswell H (2002) Estimating population projection matrices from multi-stage mark-recapture data. Ecology 83: 3257–3265.
    Gimenez O, Rossi V, Choquet R et al. (2007) State-space modeling of data on marked individuals. Ecological Modelling 206: 431–438.
    Halley JM (1996) Ecology, evolution and 1/f-noise. Trends in Ecology & Evolution 11: 33–37.
    Hastings A, Hom CL, Ellner S, Turchin P and Godfray HCJ (1993) Chaos in ecology – is mother nature a strange attractor. Annual Review of Ecology and Systematics 24: 1–33.
    Heyde CC and Cohen JE (1985) Confidence-intervals for demographic projection based on products of random matrices. Theoretical Population Biology 27: 120–153.
    Higham DJ (2001) An algorithmic introduction to numerical simulation of stochastic differential equations. Siam Review 43: 525–546.
    Lebreton JD, Burnham KP, Clobert J and Anderson DR (1992) Modeling survival and testing biological hypotheses using marked animals – a unified approach with case-studies. Ecological Monographs 62: 67–118.
    Lindley ST (2003) Estimation of population growth and extinction parameters from noisy data. Ecological Applications 13: 806–813.
    Mantua NJ and Hare SR (2002) The Pacific decadal oscillation. Journal of Oceanography 58: 35–44.
    Mantua NJ, Hare SR, Zhang Y, Wallace JM and Francis RC (1997) A Pacific interdecadal climate oscillation with impacts on salmon production. Bulletin of the American Meteorological Society 78: 1069–1079.
    May RM (1976) Simple mathematical-models with very complicated dynamics. Nature 261: 459–467.
    book Morris WF and Doak DF (2002) Quantitative Conservation Biology. Sunderland, MA: Sinauer Associates.
    Morris WF, Pfister CA, Tuljapurkar S et al. (2008) Longevity can buffer plant and animal populations against changing climatic variability. Ecology 89: 19–25.
    Nichols JD, Sauer JR, Pollock KH and Hestbeck JB (1992) Estimating transition-probabilities for stage-based population projection matrices using capture recapture data. Ecology 73: 306–312.
    book NRC – National Research Council of the National Academies (2004) Endangered and Threatened Fishers in the Klamath River Basin: Causes of Decline and Strategies for Recovery. Washington DC: The National Academies Press. National Research Council of the National Academies.
    Orzack SH and Tuljapurkar S (2001) Reproductive effort in variable environments, or environmental variation is for the birds. Ecology 82: 2659–2665.
    Solow AR (1994) Detecting changes in the composition of a multispecies community. Biometrics 50: 556–565.
    Steele JH (1985) A comparison of terrestrial and marine ecological systems. Nature 313: 355–358.
    Tuljapurkar SD and Orzack SH (1980) Population-dynamics in variable environments. 1. Long-run growth-rates and extinction. Theoretical Population Biology 18: 314–342.
    Vasseur DA and Yodzis P (2004) The color of environmental noise. Ecology 85: 1146–1152.
    White GC and Burnham KP (1999) Program MARK: survival estimation from populations of marked animals. Bird Study 46: 120–139.
 Further Reading
    book Caswell H (2001) Matrix Population Models: Construction, Analysis, and Interpretation, 2nd edn. Sunderland, MA: Sinauer Associates.
    book Diggle PJ (1990) Time Series: A Biostatistical Introduction. Oxford, UK: Oxford University Press.
    book Harvey AC (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge, UK: Cambridge University Press.
    book Kot M (2001) Elements of Mathematical Ecology. Cambridge, UK: Cambridge University Press.
    book Nisbet RM and Gurney WCS (2003) Modelling Fluctuating Populations. Caldwell, NJ: The Blackburn Press.
    book Williams BK, Nichols JD and Conroy MJ (2002) Analysis and Management of Animal Populations. London, UK: Academic Press.

Related Sub-Topics:

Life History and Reproduction | Organisms and the Physical Environment | Population Ecology
Contact Editor close
Submit a note to the editor about this article by filling in the form below.

* Required Field

Article Title: Environmental Stochasticity
 
How to Cite close
Fujiwara, Masami(Mar 2009) Environmental Stochasticity. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0021220]