678
JOHN ALROY
FIGURE 5. Effect of recycling the mean posterior probability for a population of species as a prior extinction probability. Lines and simulation parameters are as in Figure 2. A, Cumulative totals (compare with Fig. 2B). B, Interval-by-interval totals (compare with Fig. 2D).
large catalogue of museum specimens (as in Alroy 2015).
Conclusions The agnostic equation is highly distinctive for
two closely related reasons: it has an extremely lowfalse-positive rate (Figs. 3Cand 4C,D) and it rarely produces a near-one extinction probabil- ity unless sampling is fairly intensive, sampling trends downward or is flat, and the extinction rate is well above zero (Figs. 1, 3B,D, and 4A). Conversely, under such circumstances the new method produces near-zero probabilities at pretty much the same rate as CSD. We might then ask why anyone would favor
such a stubbornly conservative method. The reason is that although one always wishes to obtain an accurate estimate of the total number of extinctions, inferring extinction in any one case
FIGURE 6. Effect of recycling posteriors given near-zero extinction rates. There are 10,000 species, ps=0.5, and E=0.001. A, Results obtained using the standard method. B, Results obtained by recycling.
maybe
costly.Agoodanalogy is the life insurance industry. Inferring any one death is literally
costly and therefore to be avoided, but correctly figuring the total number of deaths is crucially important for the purpose of determining premiums. The new method accomplishes both goals. In a biological context, it is therefore probably most useful for assessing endangered species: strong conservation efforts are parti- cularlymandatedwhenever the status of a species is uncertain, making it imperative that a fair and not extreme number be put on the chance of extinction to
date.Conservativeness in the formof indecisiveness is important in any such context.
Acknowledgments I thank A. Solow for pointing me to the key
contribution of Höhle and Held (2006), which led me to Goodman (1952).
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