Precision of Population Viability Analysis - ResearchGate

Ellner et al. Precision of PVA 259simulations. White (2000) and Sæther et al. (2000) showhow to use simulations to obtain confidence intervals forcomplicated models. Alternatively, confidence intervalscan be obtained for some models by repeatedly resamplingreal data (Sokal & Rohlf 1981). Brook et al. (2000)do not estimate confidence intervals for their extinctionriskestimates, leaving the precision of their estimates unclear.The tests of Brook et al. (2000) are applied to an ensembleof species rather than to individual species. Such atest provides information about the bias in the risk estimates,but it provides little information about their precisionbecause the expected total number of extinctionsdepends only on the average risk over the ensemble. Weillustrate this distinction with two models ( Fig. 1) basedon Tables 2 and 3 in the supplementary material of Brooket al. (2000). The first model ( Fig. 1a & 1b) is the unstructureddensity-independent growth model n(t 1) n(t)exp(r (t )) (the model used for theoretical analyses byDennis et al. [1991] and Fieberg & Ellner [2000]), withr(t) a Gaussian(, 2 ) random variable with 0.044, 0.3. The value of is a rounded average over speciesof the values in Brook et al.’s Table 2, and the absolutevalue of (0.044) equals the average of || overspecies. The second model (Fig. 1c & 1d) is an age-structuredLeslie matrix model with logistic density dependencein neonate survival. The mean and coefficient ofvariation of each vital rate for this model were derivedby taking the average of the corresponding values foreach species in Brook et al.’s Table 3, and roundingFigure 1. Results from simulatedpopulation viability analyses(PVA) using parameters based onTables 2 and 3 in the supplementarymaterial of Brook et al.(2000). (a) Comparison of observedand predicted total numberof extinctions for a set of 21 species,as in Fig. 1 of Brook et al.(2000), based on the unstructuredmodel described in the text. Fivereplicates are plotted. For each ofthe 105 trials (21 species 5 replicates),we simulated a PVA as describedin the text. (b) Comparisonof actual and estimated extinctionrisks for each of the 105 trials usedin panel (a). Actual extinction riskswere calculated by running 25,000simulations of the model using thetrue parameter values and recordingthe fraction of runs crossing beloweach estimated threshold from(a). Dashed lines show the tenthand ninetieth percentiles of the distributionsof estimated extinctionrisks. (c) Comparison of observedand predicted total number of extinctions,as in panel (a), based onthe age-structured, density-dependentmodel described in the text. Allsimulations began with a populationin stable age distribution forthe mean matrix with a populationdensity of 500. (d) Comparison ofactual and estimated extinctionrisks, as in panel (b), for the 105trials with the age-structured, density-dependentmodel.Conservation BiologyVolume 16, No. 1, February 2002