# Calculate quasi-extinction threshold.

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This workflow estimates by simulation the quasi-extinction probability time cumulative distribution function for a structured population in an independently and identically distributed (iid) stochastic environment. This workflow is based on the popbio package (stoch.quasi.ext - Calculate quasi-extinction threshold, Stubben, Milligan and Nantel, 2013) based on the The MATLAB code in Box 7.5 (Morris and Doak 2002). For more details of the analysis see: Calculating the probability of hitting a quesi-extinction threshold by time t, method: simulating extinction probabilities (Morris and Doak 2002, pag: 241-244 and Caswell 2001, pag: 443-444).

This models do not permit extinction, however we can study quasi-extinction (Caswell 2001). A population is quasi-extinct if it shrinks to a specific fraction of its current size (Ginsbur et al 1982 in Caswell 2001). The quasi-extinction threshold can be chosen in the belief that it would pose a significant threat of the real exaction (Caswell 2001).

METHOD: SIMULATING EXTINCTION PROBABILITIES Keep track of whether the total population density (or the density summed across a subset of the classes with which we are particularly concerned, such as the reproductive classes) has fallen below the quasiextinction threshold each year. The fraction of realizations that first hit the threshold during or before year t gives the cumulative probability of extinction (Morris and Doak 2002). This workflow performs such a calculation.

This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.

This workflow was created using and based on Package ‘popbio’ in R. (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011).

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Literature

Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.

Oostermeijer J.G.B., M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.

Morris, W. F., and D. F. Doak. 2002. Quantitative conservation biology: Theory and practice of population viability analysis. Sinauer, Sunderland, Massachusetts, USA. 480 pages

Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23

Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1