A statistical approach to quasi-extinction forecasting

Elizabeth Eli Holmes, John Sabo, Steven Vincent Viscido, William Fredric Fagan

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

Forecasting population decline to a certain critical threshold (the quasi-extinction risk) is one of the central objectives of population viability analysis (PVA), and such predictions figure prominently in the decisions of major conservation organizations. In this paper, we argue that accurate forecasting of a population's quasi-extinction risk does not necessarily require knowledge of the underlying biological mechanisms. Because of the stochastic and multiplicative nature of population growth, the ensemble behaviour of population trajectories converges to common statistical forms across a wide variety of stochastic population processes. This paper provides a theoretical basis for this argument. We show that the quasi-extinction surfaces of a variety of complex stochastic population processes (including age-structured, density-dependent and spatially structured populations) can be modelled by a simple stochastic approximation: the stochastic exponential growth process overlaid with Gaussian errors. Using simulated and real data, we show that this model can be estimated with 20-30 years of data and can provide relatively unbiased quasi-extinction risk with confidence intervals considerably smaller than (0,1). This was found to be true even for simulated data derived from some of the noisiest population processes (density-dependent feedback, species interactions and strong age-structure cycling). A key advantage of statistical models is that their parameters and the uncertainty of those parameters can be estimated from time series data using standard statistical methods. In contrast for most species of conservation concern, biologically realistic models must often be specified rather than estimated because of the limited data available for all the various parameters. Biologically realistic models will always have a prominent place in PVA for evaluating specific management options which affect a single segment of a population, a single demographic rate, or different geographic areas. However, for forecasting quasi-extinction risk, statistical models that are based on the convergent statistical properties of population processes offer many advantages over biologically realistic models.

Original languageEnglish (US)
Pages (from-to)1182-1198
Number of pages17
JournalEcology Letters
Volume10
Issue number12
DOIs
StatePublished - Dec 2007

Fingerprint

extinction risk
extinction
population viability analysis
statistical models
population decline
age structure
confidence interval
population growth
viability
trajectory
time series
parameter uncertainty
prediction
trajectories
time series analysis
parameter
statistical analysis
demographic statistics

Keywords

  • Extinction analysis
  • Population models
  • Population viability analysis
  • Stochastic estimation
  • Stochastic models

ASJC Scopus subject areas

  • Ecology

Cite this

A statistical approach to quasi-extinction forecasting. / Holmes, Elizabeth Eli; Sabo, John; Viscido, Steven Vincent; Fagan, William Fredric.

In: Ecology Letters, Vol. 10, No. 12, 12.2007, p. 1182-1198.

Research output: Contribution to journalArticle

Holmes, Elizabeth Eli ; Sabo, John ; Viscido, Steven Vincent ; Fagan, William Fredric. / A statistical approach to quasi-extinction forecasting. In: Ecology Letters. 2007 ; Vol. 10, No. 12. pp. 1182-1198.
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