10. Using Matrix Models to Focus Research and Management Efforts
165
growth, and fecundity on population growth rates. There are a number of arguments against using models without variability in vital rates; however, in many
situations the deterministic elasticity calculations are qualitatively robust. Dixon
and associates (1997) examined the changes in elasticity through time in a
stochastic population model for the endangered plant Northern Monkshood
(Aconitum noveboracense). Four different matrices, calculated from 4 years of
sampling, were run in a stochastic simulation with varying levels of autocorrelation. The authors calculated proportional sensitivities for the average matrix of
each simulation. Although the transition probabilities and fertilities in each matrix
were different, there were no qualitative changes in the elasticities; the most
critical matrix parameters had the highest elasticities in every simulation. Further
examination by using hypothetical population models revealed that except in
cases in which life histories varied tremendously from one year to the next (e.g., a
switch from iteroparity to semelparity), qualitative measures of elasticity were
robust. However, uncertainty in parameter estimates can alter the relative “ranking” of elasticities, particularly when critical life history variables such as age at
maturity and adult annual survival are unknown. In general, only large differences
in elasticities should be regarded as useful indicators of the potential effects of
management on a population.
The objective of matrix population models as we have used them is neither to
produce a model for its own sake nor to make quantitative predictions of population growth rate or population size. Instead, we use matrix analysis as an heuristic
device to synthesize available biological information regarding species of concern
to conservation biologists. Elasticity analysis allows us to direct research efforts
toward parameters or life stages that have the greatest effect on our ability to
predict population responses. Sensitivity analysis and simulations altering vital
rates appropriate to particular management options allow us to screen among
arrays of management alternatives and to determine which are most (and least)
likely to enhance threatened populations.
Acknowledgments. This research reported in this paper was supported by the
following agencies: NOAA/NMFS (NA90AA-D-S6847); UNC Sea Grant (R/
MER-21, R/MRD-27); NOAA Coastal Ocean Program SABRE Project R/SAB-4
(NA16RG0492-01); Center for Marine Conservation; and National Science Foundation Graduate Fellowship. Many individuals collaborated on these efforts including Hal Caswell, who provided an extremely helpful review of an earlier
draft, and Libby Marschall, Tom Martin, John Quinlan, and Jeff Walters; we thank
them for their advice and counsel. Two anonymous reviewers also provided
valuable comments.
Literature Cited
Caswell H (1978) A general formula for the sensitivity of population growth rate to changes
in life history parameters. Theoretical Population Biology 14:215–230
165
growth, and fecundity on population growth rates. There are a number of arguments against using models without variability in vital rates; however, in many
situations the deterministic elasticity calculations are qualitatively robust. Dixon
and associates (1997) examined the changes in elasticity through time in a
stochastic population model for the endangered plant Northern Monkshood
(Aconitum noveboracense). Four different matrices, calculated from 4 years of
sampling, were run in a stochastic simulation with varying levels of autocorrelation. The authors calculated proportional sensitivities for the average matrix of
each simulation. Although the transition probabilities and fertilities in each matrix
were different, there were no qualitative changes in the elasticities; the most
critical matrix parameters had the highest elasticities in every simulation. Further
examination by using hypothetical population models revealed that except in
cases in which life histories varied tremendously from one year to the next (e.g., a
switch from iteroparity to semelparity), qualitative measures of elasticity were
robust. However, uncertainty in parameter estimates can alter the relative “ranking” of elasticities, particularly when critical life history variables such as age at
maturity and adult annual survival are unknown. In general, only large differences
in elasticities should be regarded as useful indicators of the potential effects of
management on a population.
The objective of matrix population models as we have used them is neither to
produce a model for its own sake nor to make quantitative predictions of population growth rate or population size. Instead, we use matrix analysis as an heuristic
device to synthesize available biological information regarding species of concern
to conservation biologists. Elasticity analysis allows us to direct research efforts
toward parameters or life stages that have the greatest effect on our ability to
predict population responses. Sensitivity analysis and simulations altering vital
rates appropriate to particular management options allow us to screen among
arrays of management alternatives and to determine which are most (and least)
likely to enhance threatened populations.
Acknowledgments. This research reported in this paper was supported by the
following agencies: NOAA/NMFS (NA90AA-D-S6847); UNC Sea Grant (R/
MER-21, R/MRD-27); NOAA Coastal Ocean Program SABRE Project R/SAB-4
(NA16RG0492-01); Center for Marine Conservation; and National Science Foundation Graduate Fellowship. Many individuals collaborated on these efforts including Hal Caswell, who provided an extremely helpful review of an earlier
draft, and Libby Marschall, Tom Martin, John Quinlan, and Jeff Walters; we thank
them for their advice and counsel. Two anonymous reviewers also provided
valuable comments.
Literature Cited
Caswell H (1978) A general formula for the sensitivity of population growth rate to changes
in life history parameters. Theoretical Population Biology 14:215–230