Environmental Stochasticity

Abstract

Environmental stochasticity refers to unpredictable spatiotemporal fluctuation in environmental conditions. The term is often used in the literature on ecology and evolution. Unpredictability is defined as an inability to predict the future state precisely such that only its distribution can be known. The environment is typically defined as any set of abiotic (e.g. temperature and nutrient availability) and biotic (e.g. predator, competitor and food) conditions that organisms experience. Environmental stochasticity influences how population abundance fluctuates and affects the fate (e.g. persistence or extinction) of populations. In an evolutionary timescale, environmental stochasticity also affects the life history strategy of organisms. Environmental stochasticity is included in population models using univariate difference equations, stochastic matrix population models, stochastic differential equations and partial differential equations. Ecological data are analysed to determine the effect of environmental stochasticity using methods such as spectral analysis, capture–recapture analysis, state‐space analysis, generalised linear models and multivariate statistical analyses.

Key Concepts

  • Environmental stochasticity is unpredictable spatiotemporal fluctuations in environmental conditions.
  • Observed population dynamics consist of fluctuation due to environmental stochasticity, but it is often confounded with other factors such as observational errors, deterministic fluctuation and demographic stochasticity.
  • Environmental stochasticity is reflected in the fluctuations in ecological processes and affects their fate (e.g. extinction or persistence of populations).
  • Environmental stochasticity plays an important role in the evolution of life history strategies of organisms by affecting their fitness.
  • Stochastic discrete‐time models, stochastic matrix population models, stochastic differential equation models and partial differential equation models are the four basic population models that include environmental stochasticity.
  • Spectral analysis, state‐space model analysis, capture–recapture analysis, generalised linear models and multivariate statistical analysis are commonly used for separating the effects of environmental stochasticity in data.

Keywords: ecological models; ecological statistics; environmental fluctuation; fitness; bet‐hedging; population extinction; population viability analysis; stochasticity; stochastic population growth

Figure 1. Stochastic and deterministic fluctuations: (a) purely stochastic fluctuation, (b) purely deterministic fluctuation, (c) mixture with high stochasticity, (d) mixture with intermediate stochasticity and (e) mixture low stochasticity.
Figure 2. Diagram depicting the sequence of ‘dry’ and ‘wet’ conditions and the number of viable seeds produced under the corresponding environmental condition.
Figure 3. Sample paths of logarithm of population size. Each solid line represents the sample path starting from the unique initial value. The thick lines are the normal distribution with mean t log λs and variance 2. The distribution expands with time.
close

References

Beissinger SR and McCullough DR (2002) Population Viability Analysis. Chicago, IL: The University of Chicago Press.

Bence JR (1995) Analysis of short‐time series – correcting for autocorrelation. Ecology 76: 628–639.

Boyce MS (1992) Population viability analysis. Annual Review of Ecology and Systematics 23: 481–506.

Caswell H (2001) Matrix Population Models. Sunderland, MA: John Wiley & Sons, Ltd.

Cohen JE (1977a) Ergodicity of age structure in populations with Markovian vital rates. II. General states. Advances in Applied Probability 9 (1): 18–37.

Cohen JE (1977b) Ergodicity of age structure in populations with Markovian vital rates, III: finite‐state moments and growth rate; an illustration. Advances in Applied Probability 9 (3): 462–475.

DeAngelis DL and Waterhouse JC (1987) Equilibrium and nonequilibrium concepts in ecological models. Ecological Monographs 57: 1–21.

Dennis B, Ponciano JM, Lele SR, Taper ML and Staples DF (2006) Estimating density dependence, process noise, and observation error. Ecological Monographs 76: 323–341.

de Roos AM (1997) A gentle introduction to physiologically structured population models. In: Tuljapurkar S and Caswell H (eds) Structured‐population Models in Marine, Terrestrial, and Freshwater Systems, pp. 119–204. New York, NY: Chapman & Hall.

Diggle PJ (1990) Time Series: A Biostatistical Introduction. Oxford, UK: Oxford Science Publications.

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.

Ellner SP and Holmes EE (2008) Commentary on holmes et al. (2007): resolving the debate on when extinction risk is predictable. Ecology Letters 11: E1–E5.

Engle RF and Granger CWJ (1987) Cointegration and error correction – representation, estimation, and testing. Econometrica 55: 251–276.

Fujiwara M and Mohr MS (2009) Identifying environmental signals from population abundance data using multivariate time‐series analysis. Oikos 118: 1712–1720.

Garcia SM (1994) The precautionary principle: its implications in capture fisheries management. Ocean & Coastal Management 22: 99–125.

Garthwaite PH (1994) An interpretation of partial least‐squares. Journal of the American Statistical Association 89: 122–127.

Gillespie JH (1974) Natural selection for within‐generation variance in offspring number. Genetics 76: 601–606.

Goel NS and Richter‐Dyn N (2016) Stochastic Models in Biology. London, UK: Academic Press.

Halley JM (1996) Ecology, evolution and 1/f‐noise. Trends in Ecology & Evolution 11: 33–37.

Harvey AC (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge, UK: Cambridge University Press.

Heyde CC and Cohen JE (1985) Confidence‐intervals for demographic projections 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.

Horvitz CC, Tuljapurkar S and Pascarella JB (2005) Plant–animal interactions in random environments: habitat stage elasticity, seed predators, and hurricanes. Ecology 86: 3312–3322.

Ives AR, Dennis B, Cottingham KL and Carpenter SR (2003) Estimating community stability and ecological interactions from time‐series data. Ecological Monographs 73: 301–330.

Knape J and de Valpine P (2011) Effects of weather and climate on the dynamics of animal population time series. Proceedings of the Royal Society B 278: 985–992.

Lande R, Engen S and Saether BE (2003) Stochastic Population Dynamics in Ecology and Conservation. Oxford, UK: Oxford University Press.

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.

Lewontin RC and Cohen D (1969) On population growth in a randomly varying environment. Proceedings of the National Academy of Sciences 62: 1056–1060.

Lindley ST (2003) Estimation of population growth and extinction parameters from noisy data. Ecological Applications 13: 806–813.

Manly BFJ (2005) Multivariate Statistical Methods: A Primer, 3rd edn. Boca Raton, FL: Chapman and Hall/CRC.

Mantua NJ and Hare SR (2002) The pacific decadal oscillation. Journal of Oceanography 58: 35–44.

McCullagh P and Nelder JA (1989) Generalized Linear Models, 2nd edn. Boca Raton, FL: Chapman & Hall/CRC.

Moran PAP (1953) The statistical analysis of the Canadian lynx cycle. 2. Synchronization and meteorology. Australian Journal of Zoology 1: 291–298.

Morris WF and Doak DF (2002) Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis. Sunderland, MA: Sinauer Associates.

Nisbet RM and Gurney W (1982) Modelling Fluctuating Populations. Caldwell, NJ: The Blackburn Press.

Øksendal B (2013) Stochastic Differential Equations: An Introduction with Applications. Heidelberg: Springer‐Verlag.

Orzack SH and Tuljapurkar S (2001) Reproductive effort in variable environments, or environmental variation is for the birds. Ecology 82: 2659–2665.

Philippi T and Seger J (1989) Hedging one's evolutionary bets, revisited. Trends in Ecology & Evolution 42: 41–44.

Pyper BJ and Peterman RM (1998) Comparison of methods to account for autocorrelation in correlation analyses of fish data (vol 55, pg 2127, 1998). Canadian Journal of Fisheries and Aquatic Sciences 55: 2710.

Schnute JT (1994) A general framework for developing sequential fisheries models. Canadian Journal of Fisheries and Aquatic Sciences 51: 1676–1688.

Sinko JW and Streifer W (1967) A new model for age‐size structure of a population. Ecology 48: 910–918.

Silvertown J (1984) Introduction to Plant Ecology. New York, NY: Longman.

Steele JH (1985) A comparison of terrestrial and marine ecological systems. Nature 313: 355–358.

Takada T and Hara T (1994) The relationship between the transition matrix model and the diffusion model. Journal of Mathematical Biology 32: 789–807.

Tuljapurkar S and Orzack SH (1980) Population‐dynamics in variable environments. 1. Long‐run growth‐rates and extinction. Theoretical Population Biology 18: 314–342.

Tuljapurkar SD (1982) Population dynamics in variable environments. II. Correlated environments, sensitivity analysis and dynamics. Theoretical Population Biology 21 (1): 114–140.

Tuljapurkar S, Horvitz CC and Pascarella JB (2003) The many growth rates and elasticities of populations in random environments. American Naturalist 162 (4): 489–502.

Tuljapurkar S and Haridas CV (2006) Temporal autocorrelation and stochastic population growth. Ecology Letters 9: 327–337.

Vasseur DA and Yodzis P (2004) The color of environmental noise. Ecology 85: 1146–1152.

Zhou C, Fujiwara M and Grant WE (2016) Finding regulation among seemingly unregulated populations: a practical framework for analyzing multivariate population time series for their interactions. Environmental and Ecological Statistics 23: 181–204.

Further Reading

Caswell H (2001) Matrix Population Models. Sunderland, MA: John Wiley & Sons, Ltd.

Nisbet RM and Gurney W (1982) Modelling Fluctuating Populations. Caldwell, NJ: The Blackburn Press.

Contact Editor close
Submit a note to the editor about this article by filling in the form below.

* Required Field

How to Cite close
Fujiwara, Masami, and Takada, Takenori(Jan 2017) Environmental Stochasticity. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0021220.pub2]