11. Variability and Measurement Error in Extinction Risk Analysis
185
limitations induced by measurement errors may prevent us from being able to
accurately estimate long-term risks. Because a large degree of uncertainty is
unavoidable over long-time periods and it severely limits the value of any longterm analysis, one possible solution is to develop probabilistically equivalent
criteria for shorter time periods. In particular, a criterion specifying a certain level
of risk over a certain time horizon could be considered equivalent to a more
stringent level of risk over a shorter time horizon. For instance, a 2% extinction
probability for 35 years might be used in place of a 10% probability for 100 years.
Although equivalent only under certain scaling assumptions (Ak¸ cakaya 1992),
this approach may allow one to use shorter time horizons for which measurement
error does not overwhelm our ability to forecast.
Ak¸ cakaya and Atwood (1997) described practical benefits of modeling based
on time horizons of a few decades (or 50 years) in a recent analysis of the
California gnatcatcher. Such benefits include use in sensitivity analyses, ranking
management options according to predicted effects on a target species’ viability
and prioritizing conservation measures. The validity of such an approach probably
depends on the particulars of the situation, because it may be possible for changes
in some demographic rates to alter the relative ordering of some scenarios by their
probabilities of extinction.
We believe that Mace and Lande (1991; Mace 1994) have initiated an important
discussion on quantifying the degree of threat in conservation biology. However,
the time scales at which these criteria are formulated may need to be reanalyzed
and possibly defined differently, depending on relative accumulation of the two
sources of uncertainty: variability and measurement error.
Acknowledgments. We thank David Anderson, Ken Burnham (National Biological Survey), Eric Forsman (U.S. Forest Service), James K. Agee (University of
Washington), Daniel E. Varland, David P. Kenney, and Robert Meier (Rayonier)
for sharing data and analyses with us, and H. Resit Ak¸ cakaya (Applied Biomathematics) for discussions and technical assistance. We also thank D. Anderson, K. Burnham, and E. Forsman for suggesting many improvements to the
manuscript. This work was supported by a grant from Rayonier in 1994.
Literature Cited
Agee JK (1994) An analysis of catastrophic forest disturbance on the Olympic Peninsula.
Unpublished report prepared for Rayonier, Inc., Olympia, WA
Ak¸ cakaya HR (1991) A method for simulating demographic stochasticity. Ecological Modelling 54:133–136
Ak¸ cakaya HR (1992) Population viability analysis and risk assessment. In: McCullough
DR, Barrett RH (eds) Wildlife 2001: populations. Elsevier Applied Science, London, pp
148–157
Ak¸ cakaya HR, Atwood JL (1997) A habitat-based metapopulation model of the California
Gnatcatcher. Conservation Biology 11:422– 434
Allee WC (1931) Animal aggregations: a study in general sociology. University of Chicago
Press, Chicago, IL
185
limitations induced by measurement errors may prevent us from being able to
accurately estimate long-term risks. Because a large degree of uncertainty is
unavoidable over long-time periods and it severely limits the value of any longterm analysis, one possible solution is to develop probabilistically equivalent
criteria for shorter time periods. In particular, a criterion specifying a certain level
of risk over a certain time horizon could be considered equivalent to a more
stringent level of risk over a shorter time horizon. For instance, a 2% extinction
probability for 35 years might be used in place of a 10% probability for 100 years.
Although equivalent only under certain scaling assumptions (Ak¸ cakaya 1992),
this approach may allow one to use shorter time horizons for which measurement
error does not overwhelm our ability to forecast.
Ak¸ cakaya and Atwood (1997) described practical benefits of modeling based
on time horizons of a few decades (or 50 years) in a recent analysis of the
California gnatcatcher. Such benefits include use in sensitivity analyses, ranking
management options according to predicted effects on a target species’ viability
and prioritizing conservation measures. The validity of such an approach probably
depends on the particulars of the situation, because it may be possible for changes
in some demographic rates to alter the relative ordering of some scenarios by their
probabilities of extinction.
We believe that Mace and Lande (1991; Mace 1994) have initiated an important
discussion on quantifying the degree of threat in conservation biology. However,
the time scales at which these criteria are formulated may need to be reanalyzed
and possibly defined differently, depending on relative accumulation of the two
sources of uncertainty: variability and measurement error.
Acknowledgments. We thank David Anderson, Ken Burnham (National Biological Survey), Eric Forsman (U.S. Forest Service), James K. Agee (University of
Washington), Daniel E. Varland, David P. Kenney, and Robert Meier (Rayonier)
for sharing data and analyses with us, and H. Resit Ak¸ cakaya (Applied Biomathematics) for discussions and technical assistance. We also thank D. Anderson, K. Burnham, and E. Forsman for suggesting many improvements to the
manuscript. This work was supported by a grant from Rayonier in 1994.
Literature Cited
Agee JK (1994) An analysis of catastrophic forest disturbance on the Olympic Peninsula.
Unpublished report prepared for Rayonier, Inc., Olympia, WA
Ak¸ cakaya HR (1991) A method for simulating demographic stochasticity. Ecological Modelling 54:133–136
Ak¸ cakaya HR (1992) Population viability analysis and risk assessment. In: McCullough
DR, Barrett RH (eds) Wildlife 2001: populations. Elsevier Applied Science, London, pp
148–157
Ak¸ cakaya HR, Atwood JL (1997) A habitat-based metapopulation model of the California
Gnatcatcher. Conservation Biology 11:422– 434
Allee WC (1931) Animal aggregations: a study in general sociology. University of Chicago
Press, Chicago, IL