An example

Eric Menges has collected 20 years of data on marked individuals from 4 populations of Dicerandra frutescens, an endangered member of the mint family endemic to the Lake Wales ridge in Florida. That is probably more data than are available for any other rare plant, and more than for most animals. Using these data, Eric, Margaret Evans, and I [1] estimated vital rates using a sophisticated hierarchical Bayesian model and projected quasi-extinction probabilities³ within 75 years using the estimated rates under several different fire return scenarios (Figure 1). In addition to a ``best guess'', our projections include the range of uncertainty associated with the projections.

Figure 1: The distribution of quasi-extinction probabilities at different fire return intervals and different quasi-extinction probabilities. The boxes represent the interquartile range of the exinction probability, the whiskers extend 1.5 times beyond that, and the circles are ``outliers'' (from [1]).

The first thing to notice is that the populations are very likely to drop below 100 plants within 75 years, even though the simulations started with 10$^6$ seeds. The second thing to notice is that there is a lot of uncertainty about how likely extinction is over this period, even though we have more data to work with than we are likely to have for most endangered species. That poses a real problem.

To the extent that we're focusing on conservation of individual species, we're going to have to set priorities. To some extent those priorities will be affected by our assessment of how threatened a species is, i.e., how likely it is to become extinct.⁴But if even after collecting 20 years of data, we have as much uncertainty about the probability of extinction as we do with Dicerandra frutescens, how can we possibly set conservation priorities that depend on knowing those probabilities?