6
Andrew Solow and Thomas Helser
One way in which auxiliary information can be incorporated into the methods
described here is through a Bayesian approach (Solow 1993a). It may happen in
practice that conditional prior information about T E given that T E < T is available.
For example, critical habitat may be disturbed or lost as a result of a hurricane.
Alternatively, more effective fishing technology may be introduced. Information
of this kind can be converted into a conditional prior distribution for T E and used
in a Bayesian test of H 0 against H 1 .
In applying the methods described here, it is important to think carefully about
the meaning of extinction. For example, in the applications described in the
previous section, due to the limited nature of the observation program, conclusions are limited both spatially and seasonally. Moreover, in this example, extinction may be related to temporary environmental changes (e.g., related to ocean
circulation), and the species may return in the future.
There are several possible extensions of this work. For example, Solow (1996)
considered the problem of testing for a common extinction time for two or more
species that are known to be extinct. This would be of interest in determining
whether the extinctions had a common cause.
Acknowledgments. The helpful comments of two anonymous reviewers are gratefully acknowledged.
Literature Cited
Beg MA (1982) Optimal tests and estimators for truncated exponential families. Metrika
29:103–113
Clark SH (1979) Application of bottom trawl survey data to fish stock assessment. Fisheries 4:9–15
Cox DR, Lewis PAW (1978) The statistical analysis of series of events. Chapman and Hall,
London
David HA (1981) Order statistics. Wiley, New York
Diamond JM (1989) The present, past and future of human-caused extinctions. Philosophical Transactions of the Royal Society of London B 325:469– 477
Fisher RA (1929) Tests of significance in harmonic analysis. Proceedings of the Royal
Society Series A 125:54 –59
Lande R, Orzack SH (1988) Extinction dynamics of age-structured populations in a fluctuating environment. Proceedings of the National Academy of Sciences 85:7418–7421
Smith FDM, May RM, Pellew R, Johnson TH, Walter KR (1993) How much do we know
about the current extinction rate? Trends in Ecology and Evolution 8:375–378
Solow AR (1993a) Inferring extinction from sighting data. Ecology 74:962–964
Solow AR (1993b) Inferring extinction in a declining population. Journal of Mathematical
Biology 32:79–82
Solow AR (1996) A test for a common upper endpoint in fossil taxa. Paleobiology 22:406–
410
Taylor HM, Karlin S (1984) An introduction to stochastic modeling. Academic Press,
London
Andrew Solow and Thomas Helser
One way in which auxiliary information can be incorporated into the methods
described here is through a Bayesian approach (Solow 1993a). It may happen in
practice that conditional prior information about T E given that T E < T is available.
For example, critical habitat may be disturbed or lost as a result of a hurricane.
Alternatively, more effective fishing technology may be introduced. Information
of this kind can be converted into a conditional prior distribution for T E and used
in a Bayesian test of H 0 against H 1 .
In applying the methods described here, it is important to think carefully about
the meaning of extinction. For example, in the applications described in the
previous section, due to the limited nature of the observation program, conclusions are limited both spatially and seasonally. Moreover, in this example, extinction may be related to temporary environmental changes (e.g., related to ocean
circulation), and the species may return in the future.
There are several possible extensions of this work. For example, Solow (1996)
considered the problem of testing for a common extinction time for two or more
species that are known to be extinct. This would be of interest in determining
whether the extinctions had a common cause.
Acknowledgments. The helpful comments of two anonymous reviewers are gratefully acknowledged.
Literature Cited
Beg MA (1982) Optimal tests and estimators for truncated exponential families. Metrika
29:103–113
Clark SH (1979) Application of bottom trawl survey data to fish stock assessment. Fisheries 4:9–15
Cox DR, Lewis PAW (1978) The statistical analysis of series of events. Chapman and Hall,
London
David HA (1981) Order statistics. Wiley, New York
Diamond JM (1989) The present, past and future of human-caused extinctions. Philosophical Transactions of the Royal Society of London B 325:469– 477
Fisher RA (1929) Tests of significance in harmonic analysis. Proceedings of the Royal
Society Series A 125:54 –59
Lande R, Orzack SH (1988) Extinction dynamics of age-structured populations in a fluctuating environment. Proceedings of the National Academy of Sciences 85:7418–7421
Smith FDM, May RM, Pellew R, Johnson TH, Walter KR (1993) How much do we know
about the current extinction rate? Trends in Ecology and Evolution 8:375–378
Solow AR (1993a) Inferring extinction from sighting data. Ecology 74:962–964
Solow AR (1993b) Inferring extinction in a declining population. Journal of Mathematical
Biology 32:79–82
Solow AR (1996) A test for a common upper endpoint in fossil taxa. Paleobiology 22:406–
410
Taylor HM, Karlin S (1984) An introduction to stochastic modeling. Academic Press,
London