148
10
Using Matrix Models to Focus
Research and Management Efforts
in Conservation
Selina S. Heppell, Deborah T. Crouse, and Larry B. Crowder
Introduction
More than 1,000 North American species are listed or will soon be listed as
endangered or threatened under the Endangered Species Act of 1973 (Glitzenstein
1993; U.S. Fish and Wildlife Service 1995). In addition, more than half the marine
fish stocks used by U.S. commercial fisheries are depleted or declining (Sissenwine and Rosenberg 1993), with similar declines occurring in many freshwater
fish species (Williams et al. 1989). The future of many of these species hinges on
effective management and recovery plans that must be implemented in this decade
(Sissenwine and Rosenberg 1993).
Unfortunately, our knowledge of a threatened species’ life history and the
potential conservation costs and benefits of various management alternatives is
often extremely limited. Further, the research budgets of most resource management agencies are insufficient, and in many cases decisions must be made quickly.
To enhance the effectiveness of conservation management under these constraints, it is important to evaluate the relative effectiveness of specific changes in
vital rates (e.g., juvenile survival versus fecundity) on population responses (e.g.,
population growth rate, size, or structure) and the importance of uncertainty in our
knowledge of each of these vital rates.
One set of tools for enhancing such decision making involves using deterministic matrix models to evaluate management alternatives as hypotheses. Rather than
making quantitative predictions of population size through time or probability of
extinction, deterministic model analyses focus on relative changes in population
responses as certain parameters in the model are changed. One population response examined commonly is the intrinsic rate of increase (r) of a population. In
a linear deterministic model, r (or ln [λ], where λ is the dominant eigenvector of a
matrix) predicts exponential increase or decline in a population occupying a
constant environment. Sensitivity analyses reveal how changes in stage-specific
vital rates (e.g. survival, growth, or fecundity) affect λ.
We can apply this method to determine (1) which stage-specific vital rates
contribute most to the asymptotic population growth rate; (2) how small perturbations of sensitive life history stages compare with similar perturbations of less
10
Using Matrix Models to Focus
Research and Management Efforts
in Conservation
Selina S. Heppell, Deborah T. Crouse, and Larry B. Crowder
Introduction
More than 1,000 North American species are listed or will soon be listed as
endangered or threatened under the Endangered Species Act of 1973 (Glitzenstein
1993; U.S. Fish and Wildlife Service 1995). In addition, more than half the marine
fish stocks used by U.S. commercial fisheries are depleted or declining (Sissenwine and Rosenberg 1993), with similar declines occurring in many freshwater
fish species (Williams et al. 1989). The future of many of these species hinges on
effective management and recovery plans that must be implemented in this decade
(Sissenwine and Rosenberg 1993).
Unfortunately, our knowledge of a threatened species’ life history and the
potential conservation costs and benefits of various management alternatives is
often extremely limited. Further, the research budgets of most resource management agencies are insufficient, and in many cases decisions must be made quickly.
To enhance the effectiveness of conservation management under these constraints, it is important to evaluate the relative effectiveness of specific changes in
vital rates (e.g., juvenile survival versus fecundity) on population responses (e.g.,
population growth rate, size, or structure) and the importance of uncertainty in our
knowledge of each of these vital rates.
One set of tools for enhancing such decision making involves using deterministic matrix models to evaluate management alternatives as hypotheses. Rather than
making quantitative predictions of population size through time or probability of
extinction, deterministic model analyses focus on relative changes in population
responses as certain parameters in the model are changed. One population response examined commonly is the intrinsic rate of increase (r) of a population. In
a linear deterministic model, r (or ln [λ], where λ is the dominant eigenvector of a
matrix) predicts exponential increase or decline in a population occupying a
constant environment. Sensitivity analyses reveal how changes in stage-specific
vital rates (e.g. survival, growth, or fecundity) affect λ.
We can apply this method to determine (1) which stage-specific vital rates
contribute most to the asymptotic population growth rate; (2) how small perturbations of sensitive life history stages compare with similar perturbations of less