Stochastic matrix projection:: A comparison of the effect of element and matrix selection methods on quasi-extinction risk for Haplopappus radiatus (Asteraceae)

We compared two methods of stochastic matrix projection, element selection and matrix selection, to determine how they differed in their estimate of quasi-extinction risk for Haplopappus radiatus (Snake River goldenweed, Asteraceae), a local endemic along the Snake River in Oregon and Idaho. Demographic data were collected annually from 1991 to 1994 from four populations of H. radiatus. Matrix population models were used to analyze transition matrices deterministically, and element selection and matrix selection methods were employed for stochastic matrix projections. Quasi-extinction risk was significantly higher at all four sites when the matrix selection method was used. Both methods yielded the same ranking of populations by quasi-extinction risk. Element selection appears to smooth out extreme differences in survival and fecundity between years, resulting in fewer population trajectories dropping below the extinction threshold. Both methods should be examined when performing a population viability analysis to determine which yields the more conservative results.